Infectious disease kinetic model analysis method and electronic equipment

Abstract

The invention relates to the field of infectious disease prediction, and provides an infectious disease kinetic model analysis method and electronic equipment, the method considers factors such as vaccine, isolation, admission and treatment in the actual infectious disease transmission situation, constructs an SEIAQVHR model which better accords with the actual situation, and improves the prediction accuracy of the infectious disease. The endemic disease balance point and the disease-free balance point of the SEIAQVHR model are calculated and analyzed on the basis of the basic regeneration number of the SEIAQVHR model; in consideration of the influence of random interference, a random SEIAQVHR model is constructed on the basis of the SEIAQVHR model, and mathematical property analysis is performed on an equivalent model of the random SEIAQVHR model. By utilizing the method, the influence of the random factors on the transmission of the infectious diseases can be more clearly displayed based on the random SEIAQVHR model, and the mathematical property analysis on the random SEIAQVHR model is beneficial to formulating an effective prevention and control strategy of the infectious diseases.

Description

Technical Field

[0001] The present application relates to the technical field of infectious disease prediction, and in particular to an infectious disease dynamics model analysis method and electronic equipment. Background Art

[0002] Infectious disease dynamics is an important research field in public health and epidemiology, which aims to study the mechanism of disease transmission in the population. The relevant infectious disease dynamics models lack a comprehensive analysis of the uncertain factors that affect the spread of infectious diseases, resulting in unreasonable models and poor model fitting and prediction results. Summary of the invention

[0003] In view of the above, it is necessary to propose an infectious disease dynamics model analysis method and electronic equipment that can solve the problem of poor model fitting results and prediction results caused by the lack of comprehensive analysis of the uncertain factors affecting the spread of infectious diseases.

[0004] An embodiment of the present application provides an infectious disease dynamics model analysis method, the method comprising: constructing a SEIAQVHR model, determining the basic reproduction number of the SEIAQVHR model based on a reproduction matrix algorithm; determining the endemic disease equilibrium point of the SEIAQVHR model according to the basic reproduction number; determining the disease-free equilibrium point of the SEIAQVHR model, and performing a stability analysis on the disease-free equilibrium point based on the basic reproduction number; constructing a random SEIAQVHR model based on the SEIAQVHR model, and determining an equivalent model of the random SEIAQVHR model; performing a mathematical property analysis on the equivalent model, the result of the mathematical property analysis comprising that the equivalent model has a unique positive solution, the equivalent model satisfies the conditions for system extinction, and the equivalent model has a unique and ergodic stationary distribution; based on the result of the stability analysis and the result of the mathematical property analysis, determining the dynamic behavior of the infectious disease.

[0005] In one embodiment, the SEIAQVHR model includes a differential equation group consisting of a plurality of differential equations, in each of which the system state variable changes with time, and the differential equation group is expressed as:

[0006] dS / dt=Λ-{S[1-(φ+μ+o S )]}(β1E+β2I+β3A)-μS-o S S-cS,

[0007] dE / dt={s[1-(φ+μ+o S )]}(β1E+β2I+β3A)-o e E-ωE-cE,

[0008] dI / dt=ωpE-λI-γ1I-cI,

[0009] dA / dt=ω(1-p)E-κA-γ2A-cA,

[0010] dQ s / dt=o s Q s ,

[0011] dQ e / dt=o e Q e ,

[0012] dV / dt=μS-cV,

[0013] dH / dt=λI+κA-γ3H-cH,

[0014] dR / dt=γ1I+γ2A+γ3H-cR,

[0015] The multiple system state variables of the SEIAQVHR model include {S, E, I, A, Q s ,Q e ,V,H,R}, S represents susceptible population, E represents latent population, I represents obvious infection population, A represents asymptomatic infection population, Q s Indicates susceptible people isolated from the population, Q e represents the isolated population of patients in the incubation period, V represents the vaccinated population, H represents the hospitalized population, and R represents the removed population; t represents time;

[0016] The parameters of the SEIAQVHR model include {Λ, c, φ, μ, o s ,β1,β2,β3,o e ,ω,p,λ,κ,γ1,γ2,γ3}, Λ represents the population growth rate, c represents the population reduction rate; φ represents the effective mask wearing rate, μ represents the effective vaccination rate, o s represents the isolation rate of susceptible population, β1 represents the infection rate of latent population to susceptible population, β2 represents the infection rate of apparent infected population to susceptible population, β3 represents the infection rate of asymptomatic infected population to susceptible population, o e represents the isolation rate of the latent population, ω represents the rate at which the latent population is transformed into the explicitly infected population, p represents the probability that the latent population is transformed into the explicitly infected population, λ represents the hospitalization rate of the explicitly infected population, κ represents the hospitalization rate of the asymptomatic infected population, γ1 represents the removal rate of the explicitly infected population, γ2 represents the removal rate of the asymptomatic infected population, and γ3 represents the removal rate of the hospitalized population; each parameter is non-negative.

[0017] In one embodiment, the basic reproduction number of the SEIAQVHR model is expressed as:

[0018]

[0019] In one embodiment, the endemic equilibrium point of the SEIAQVHR model is represented by P * =(S * ,E * ,I * ,A * ,Q s * ,Q e - ,V * ,H * ,R * ),in:

[0020]

[0021] Wherein, R0 represents the basic reproduction number of the SEIAQVHR model.

[0022] In one embodiment, the disease-free equilibrium point of the SEIAQVHR model is expressed as The stability analysis of the disease-free equilibrium point based on the basic reproduction number includes: determining the Jacobian matrix of the SEIAQVHR model corresponding to the disease-free equilibrium point, and determining multiple characteristic roots of the equation group corresponding to the SEIAQVHR model according to the Jacobian matrix; determining negative characteristic roots among the multiple characteristic roots and characteristic roots to be verified other than the negative characteristic roots based on the non-negativity of parameters of the SEIAQVHR model; judging whether the characteristic root to be verified is a negative characteristic root based on the negative characteristic root and the basic reproduction number; and determining the stability of the disease-free equilibrium point according to the judgment result of the characteristic root to be verified.

[0023] In one embodiment, the method also includes: if the basic reproduction number is less than a preset value, determining that the characteristic root to be verified is a negative characteristic root, and determining that the disease-free equilibrium point is locally asymptotically stable; or, if the basic reproduction number is greater than the preset value, determining that the characteristic root to be verified is not a negative characteristic root, and determining that the disease-free equilibrium point is unstable.

[0024] In one embodiment, constructing a random SEIAQVHR model based on the SEIAQVHR model includes: introducing the Wiener process into the SEIAQVHR model, and the constructed random SEIAQVHR model is expressed as:

[0025] dS=[-{S[1-(φ+μ+o S )]}(β1E+β2I+β3A)-μS-o S S]dt+σ1(t)SdB1(t),

[0026] dE=[{S[1-(φ+μ+o S )]}(β1E+β2I+β3A)-o e E-ωE]dt+σ2EdB2(t),

[0027] dI=[ωpE-λI-γ1I]dt+σ3(t)IdB3(t),

[0028] dA=[ω(1-p)E-κA-γ2A]dt+σ4(t)AdB4(t),

[0029] dQ s =(o S S)dt+σ5(t)Q s dB5(t),

[0030] dQ e =(o e E)dt+σ6(t)Q e dB6(t),

[0031] dV=(μS)dt+σ7(t)VdB7(t),

[0032] dH=(λI+κA-γ3H)dt+σ8(T)HdB8(t),

[0033] dR=(γ1I+γ2A+γ3H)dt+σ9(t)RdB9(t),

[0034] Among them, B i (t)(i=1,2,3,4,5,6,7,8,9) represents B i (0)=0, and for any t≥0, σ i (t)(i=1,2,3,4,5,6,7,8,9) represents a continuous bounded function, Represents the strength of the Wiener process.

[0035] In one embodiment, the equivalent model of the stochastic SEIAQVHR model is expressed as:

[0036]

[0037] dI=[ωpE-(γ1+c)I]dt+σ3IdB3(t),

[0038] dA=[ω(1-p)E-(γ2+c)A]dt+σ4AdB4(t),

[0039] dQ=(oS-cQ)dt+σ5QdB5(t),

[0040] dR=(γ1I+γ2A-cR)dt+σ6RdB6(t);

[0041] The multiple system state variables of the equivalent model include {S, E, I, A, Q, R}, and the equivalent model compared with the random SEIAQVHR model performs the equivalent update including: (susceptible isolation population Q s + Isolation of latent patients Q e ) is equivalently updated to the quarantine population Q, the vaccinated population V is equivalently updated to 0, and the hospitalized population H is equivalently updated to 0;

[0042] The multiple parameters of the equivalent model include {N, Λ, c, φ, μ, o, β1, β2, β3, ω, p, γ1, γ2}, wherein N represents the total population, Λ represents the population growth rate, and c represents the population reduction rate; φ represents the effective mask wearing rate, μ represents the effective vaccination rate, o represents the isolation rate of the susceptible population S, β1 represents the infection rate of the latent population to the susceptible population, β2 represents the infection rate of the explicit infected population to the susceptible population, β3 represents the infection rate of the asymptomatic infected population to the susceptible population, ω represents the rate at which the latent population is converted into the explicit infected population, p represents the probability of the latent population being converted into the explicit infected population, γ1 represents the removal rate of the explicit infected population, and γ2 represents the removal rate of the asymptomatic infected population; wherein each parameter is non-negative.

[0043] In one embodiment, the method for determining that the equivalent model has a unique correct solution includes: setting the stopping time τ k , the stop time τ k Indicates that at least one of the system state variables {S, E, I, A, Q, R} of the equivalent model exceeds the preset interval for the first time time, where k0≥0 represents a preset integer as large as possible, and k≥k0, where k represents an integer; where: In which, set inf{empty set} = ∞; according to τ k Regarding the monotonically increasing property of k, we can determine And determine τ by contradiction ∞ =∞, including: setting τ ∞ ≠∞; construct Lyapunov function based on Formula determination function The differential equation According to the differential equation The expectation determines the setting τ ∞ ≠∞There is a contradiction, determine τ ∞ =∞; According to the stop time τ k The definition of τ ∞ =∞=inf{empty set}, indicating that the system state variables of the equivalent model always remain within a limited preset interval for an arbitrary long time, and it is determined that the equivalent model has a unique positive solution.

[0044] In one embodiment, the method for determining that the equivalent model satisfies the condition of system extinction includes: setting the function P(t)=ωE+(ω+c)(I(t)+A(t)), according to The differential equation dlnP(t) is determined by the formula; the differential equation dlnP(t) is integrated and averaged, and the strong law of large numbers is applied to the result of the integrated average to determine that the function P(t) satisfies According to the non-negativity of the parameters of the equivalent model and the function P(t) satisfies It is determined that the system state variables of the equivalent model gradually tend to zero over time, and it is determined that the equivalent model satisfies the conditions of system extinction.

[0045] In one embodiment, the method for determining whether the equivalent model has a unique and ergodic stationary distribution includes: determining a diffusion matrix of the equivalent model based on the intensity of the Wiener process in the equivalent model; constructing a Lyapunov function according to the diffusion matrix of the equivalent model. according to The formula determines the function The infinitesimal generator LV1 represents the function The expected rate of change of the solution along the equivalent model; according to the negative upper bound of the infinitesimal generator LV1, determine the function is a continuous function; according to the function With the initial function The difference between , construct the function V(S,Q,E,I,A,R); according to The formula determines the infinitesimal generator LV of the function V(S,Q,E,I,A,R); set Where η>0; the area corresponding to the equivalent model The method is divided into multiple sub-regions, and it is determined that the infinitesimal generator LV in each sub-region has a negative upper bound, and it is determined that the equivalent model has a unique and ergodic stationary distribution.

[0046] In one embodiment, determining the infectious disease transmission mechanism, predicting the infectious disease dynamic behavior and the infectious disease prevention and control strategy based on the results of the stability analysis and the results of the mathematical property analysis includes: performing numerical simulation on the results of the stability analysis and the results of the mathematical property analysis, and determining the infectious disease transmission mechanism and predicting the infectious disease dynamic behavior based on the results of the numerical simulation.

[0047] An embodiment of the present application provides an infectious disease dynamics model analysis device, the device comprising: a construction module, used to construct a SEIAQVHR model, and determine the basic reproduction number of the SEIAQVHR model based on a reproduction matrix algorithm; a determination module, used to determine the endemic equilibrium point of the SEIAQVHR model according to the basic reproduction number; an analysis module, used to determine the disease-free equilibrium point of the SEIAQVHR model, and perform stability analysis on the disease-free equilibrium point based on the basic reproduction number; the construction module is also used to construct a random SEIAQVHR model based on the SEIAQVHR model, and determine an equivalent model of the random SEIAQVHR model; the analysis module is also used to perform mathematical property analysis on the equivalent model, the result of the mathematical property analysis includes that the equivalent model has a unique positive solution, the equivalent model satisfies the conditions of system extinction, and the equivalent model has a unique and ergodic stationary distribution; the determination module is also used to determine the dynamic behavior of the infectious disease based on the result of the stability analysis and the result of the mathematical property analysis.

[0048] An embodiment of the present application provides an electronic device, which includes a processor and a memory, and the processor is used to implement the infectious disease dynamics model analysis method when executing a computer program stored in the memory.

[0049] An embodiment of the present application provides a computer-readable storage medium having a computer program stored thereon, and the computer program implements the infectious disease dynamics model analysis method when executed by a processor.

[0050] In summary, the infectious disease dynamics model analysis method described in this application can provide a method for constructing a SEIAQVHR infectious disease dynamics model based on saturated contact rate and containing random interference. This model takes into account random interference while also taking into account factors such as vaccines, isolation, and hospitalization in actual situations, providing a more reasonable infectious disease model for predicting the spread of infectious diseases. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 It is a structural diagram of an electronic device provided in one embodiment of the present application.

[0052] Figure 2It is a flow chart of an infectious disease dynamics model analysis method provided in one embodiment of the present application.

[0053] Figure 3 Schematic diagram of the SEIAQVHR model provided in one embodiment of the present application.

[0054] Figure 4 It is a schematic diagram of the effect of the numerical simulation of simulation 1 provided in an embodiment of the present application.

[0055] Figure 5 It is a schematic diagram of the effect of the numerical simulation of simulation 2 provided in an embodiment of the present application.

[0056] Figure 6 It is a schematic diagram of the effect of the numerical simulation of simulation three provided in one embodiment of the present application.

[0057] Figure 7 It is a schematic diagram of the effect of the numerical simulation of simulation four provided in one embodiment of the present application.

[0058] Figure 8 It is a schematic diagram of the effect of the numerical simulation of simulation five provided in one embodiment of the present application.

[0059] Fig. 9 It is a schematic diagram of the effect of the numerical simulation of simulation six provided in one embodiment of the present application.

[0060] Fig.10 It is a schematic diagram of the effect of the numerical simulation of simulation seven provided in one embodiment of the present application.

[0061] Fig.11 It is a flow chart of an infectious disease dynamics model analysis method provided by another embodiment of the present application.

[0062] Fig.12 A structural diagram of an infectious disease dynamics model analysis device provided in one embodiment of the present application. DETAILED DESCRIPTION

[0063] In order to more clearly understand the above-mentioned purposes, features and advantages of the present application, the present application is described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be noted that the embodiments of the present application and the features in the embodiments can be combined with each other without conflict.

[0064] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those commonly understood by those skilled in the art to which this application belongs. The terms used herein in the specification of this application are only for the purpose of describing the embodiments in one embodiment and are not intended to limit this application.

[0065] It should be noted that in this application, "at least one" means one or more, and "more than one" means two or more than two. "And / or" describes the association relationship of associated objects, indicating that three relationships may exist. For example, A and / or B can mean: A exists alone, A and B exist at the same time, and B exists alone, where A and B can be singular or plural. The terms "first", "second", "third", "fourth", etc. (if any) in the specification, claims and drawings of this application are used to distinguish similar objects, rather than to describe a specific order or sequence.

[0066] In the embodiments of the present application, words such as "exemplary" or "for example" are used to indicate examples, illustrations or descriptions. Any embodiment or design described as "exemplary" or "for example" in the embodiments of the present application should not be interpreted as being more preferred or more advantageous than other embodiments or designs. Specifically, the use of words such as "exemplary" or "for example" is intended to present related concepts in a concrete way. The following embodiments and features in the embodiments may be combined with each other without conflict.

[0067] Infectious disease dynamics is an important research field in public health and epidemiology, which aims to study the transmission mechanism of diseases in the population. The dynamic model is a method that divides the population into different compartments according to the occurrence and spread of infectious diseases, simulates and displays the disease development process with a set of differential equations, and solves the equations using methods such as the fourth-order Runge-Kutta method to predict the development trend of the disease, which can provide a strong reference for the formulation of infectious disease prevention and control strategies.

[0068] Research results show that in actual situations, the environment of population activities is not static. Climate change, population mobility, crowd activities, etc. are all uncertain factors that affect the spread of infectious diseases, and these factors have random characteristics. However, all parameters of conventional infectious disease dynamics models are unique within a certain period of time, so it is difficult to deal with these random factors using the current common infectious disease dynamics models. In response to this problem, some studies have used fixed parameters to change to variable coefficients when predicting infectious diseases for a long time, that is, using functions to represent certain changing parameters in order to avoid changes in parameters during long-term predictions, which leads to poor model fitting results and prediction results. However, variable coefficients can only be expressed by a certain predictable functional relationship, which cannot reflect the interference of various random factors on the entire system in actual situations.

[0069] To solve the above problems, an embodiment of the present application provides an infectious disease dynamics model analysis method, which can provide a method for constructing a SEIAQVHR infectious disease dynamics model based on saturated contact rate and containing random interference. The model takes into account random interference while also taking into account factors such as vaccines, isolation, and hospitalization in actual situations, providing a more reasonable infectious disease model for predicting the spread of infectious diseases.

[0070] Figure 1 The electronic device 10 can be a computer, a server, a mobile phone, a tablet computer, a notebook computer, or other electronic devices. The specific type of the electronic device is not limited in any way in the embodiment of the present application.

[0071] like Figure 1 As shown, the electronic device 10 may include a communication module 101, a memory 102, a processor 103, an input / output (I / O) interface 104 and a bus 105. The processor 103 is coupled to the communication module 101, the memory 102 and the I / O interface 104 through the bus 105.

[0072] The communication module 101 may include a wired communication module and / or a wireless communication module. The wired communication module may provide one or more wired communication solutions such as universal serial bus (USB), controller area network bus (CAN), etc. The wireless communication module may provide one or more wireless communication solutions such as wireless fidelity (Wi-Fi), bluetooth (BT), mobile communication network, frequency modulation (FM), near field communication technology (NFC), infrared technology (IR), etc.

[0073] The memory 102 may include one or more random access memories (RAM) and one or more non-volatile memories (NVM). The random access memory can be directly read and written by the processor 103, and can be used to store executable programs (such as machine instructions) of the operating system or other running programs, and can also be used to store user and application data. The random access memory may include static random-access memory (SRAM), dynamic random access memory (DRAM), synchronous dynamic random access memory (SDRAM), double data rate synchronous dynamic random access memory (DDR SDRAM), etc.

[0074] The non-volatile memory may also store executable programs and user and application data, etc., and may be loaded into the random access memory in advance for direct reading and writing by the processor 103. The non-volatile memory may include a disk storage device and a flash memory.

[0075] The memory 102 is used to store one or more computer programs. The one or more computer programs are configured to be executed by the processor 103. The one or more computer programs include multiple instructions, and when the multiple instructions are executed by the processor 103, the infectious disease dynamics model analysis method executed on the electronic device 10 can be implemented.

[0076] In other embodiments, the electronic device 10 further includes an external memory interface for connecting to an external memory to expand the storage capacity of the electronic device 10 .

[0077] The processor 103 may include one or more processing units, for example, the processor 103 may include an application processor (AP), a modem processor, a graphics processor (GPU), an image signal processor (ISP), a controller, a video codec, a digital signal processor (DSP), a baseband processor, and / or a neural-network processing unit (NPU), etc. Different processing units may be independent devices or integrated into one or more processors.

[0078] The processor 103 provides computing and control capabilities. For example, the processor 103 is used to execute a computer program stored in the memory 102 to implement the above-mentioned infectious disease dynamics model analysis method.

[0079] The I / O interface 104 is used to provide a channel for user input or output. For example, the I / O interface 104 can be used to connect various input and output devices, such as a mouse, keyboard, touch device, display screen, etc., so that the user can enter information or visualize information.

[0080] The bus 105 is at least used to provide a channel for mutual communication among the communication module 101 , the memory 102 , the processor 103 , and the I / O interface 104 in the electronic device 10 .

[0081] It is to be understood that the structure illustrated in the embodiment of the present application does not constitute a specific limitation on the electronic device 10. In other embodiments of the present application, the electronic device 10 may include more or fewer components than shown in the figure, or combine some components, or split some components, or arrange the components differently. The components shown in the figure may be implemented in hardware, software, or a combination of software and hardware.

[0082] Figure 2 1 is a flow chart of an infectious disease dynamics model analysis method provided by an embodiment of the present application. The infectious disease dynamics model analysis method is applied to electronic devices, such as Figure 1 The electronic device 10 in the flowchart specifically includes the following steps. According to different requirements, the order of the steps in the flowchart can be changed, and some steps can be omitted.

[0083] S21, constructing a SEIAQVHR model, and determining a basic reproduction number of the SEIAQVHR model based on a reproduction matrix algorithm.

[0084] In one embodiment, literature related to respiratory infectious diseases can be consulted to summarize the transmission characteristics of respiratory infectious diseases. For example, through data summary, it can be determined that the transmission characteristics of respiratory infectious diseases include: mainly transmitted through air, droplets, direct contact, etc., with fast transmission speed and wide range, the general population is susceptible, most respiratory infectious diseases have an incubation period, and patients and invisible infected persons are their main sources of infection.

[0085] In one embodiment, considering the characteristics of respiratory infectious diseases, a SEIAQVHR model that can be applied to most actual situations of respiratory infectious diseases is constructed. There are 9 compartments in the SEIAQVHR model: susceptible population (S), latent population (E), obvious infection population (I), asymptomatic infection population (A), susceptible isolation population (Q s ), quarantined population of patients in the incubation period (Q e ), vaccinated population (V), hospitalized population (H), and removed population (R); there are 16 parameters in total, including: population growth rate (Λ), population reduction rate (c), infection rate of latent population to susceptible population (β1), infection rate of apparent infected population to susceptible population (β2), infection rate of asymptomatic infected population to susceptible population (β3), effective vaccination rate (μ), effective mask wearing rate (φ), isolation rate of susceptible population (ο s ), isolation rate of latent population (ο e ), the rate at which the latent population is transformed into the explicitly infected population (ω), the probability that the latent population is transformed into the explicitly infected population (p), the hospitalization rate of the explicitly infected population (λ), the hospitalization rate of the asymptomatic infected population (κ), the migration rate of the explicitly infected population (γ1), the migration rate of the asymptomatic infected population (γ2), and the migration rate of the hospitalized population (γ3).

[0086] Specifically, the SEIAQVHR model includes the following features:

[0087] ① The model not only has a latent period, but also the latent population is contagious; assuming that the susceptible (S) becomes the latent population (E) after being infected, the latent population may become an overtly infected person (I) or a latently infected person (A) after an incubation period. The latent population, overtly infected persons and latently infected persons are all contagious, but the transmission probability (β) is different;

[0088] ② Susceptible people (S) and people in the incubation period (E) have a certain probability of becoming isolated people (Q); relevant parameters can be adjusted according to actual conditions. If no isolation measures are taken, the isolation parameters can be set to 0;

[0089] ③ Overtly infected persons (I) and latently infected persons (A) have a certain probability of becoming hospitalized persons (H); relevant parameters can be adjusted according to actual conditions. If there are no hospitalized persons for latently infected persons, the hospitalization rate can be set to 0;

[0090] ④ Susceptible people (S) have a certain probability of receiving relevant vaccines; the study found that common respiratory infectious diseases are generally susceptible to the general population, and only a few infectious diseases are susceptible to special ages (children or the elderly) and special populations (males or females); respiratory infectious diseases such as influenza have corresponding vaccines, so adding vaccination measures to susceptible populations and establishing chamber V can play a certain protective role for susceptible people;

[0091] ⑤ Because some infectious diseases are prevalent for a long time, consider the population mobility, natural population growth and mortality during this period.

[0092] For example Figure 3 , which is a schematic diagram of the SEIAQVHR model provided in the embodiment of the present application. Specifically, the SEIAQVHR model includes a differential equation group consisting of multiple differential equations, in which the system state variable in each differential equation changes with time, and the differential equation group is expressed as:

[0093] dS / dt=Λ-{S[1-(φ+μ+o s )]}(β1E+β2I+β3A)-μS-o s S-cS,

[0094] dE / dt={S[1-(φ+μ+o S )]}(β1E+β2I+β3A)-o e E-ωE-cE,

[0095] dI / dt=ωpE-λI-γ1I-cI,

[0096] dA / dt=ω(1-p)E-kA-γ2A-cA,

[0097] dQ s / dt=o S Q s ,

[0098] dQ e / dt=o e Q e ,

[0099] dV / dt=μS-cV,

[0100] dH / dt=λI+κA-γ3H-cH,

[0101] dR / dt=γ1I+γ2A+γ3H-cR,

[0102] The multiple system state variables of the SEIAQVHR model include {S, E, I, A, Q s ,Q e ,V,H,R}, S represents susceptible population, E represents latent population, I represents obvious infection population, A represents asymptomatic infection population, Q s Indicates susceptible people isolated from the population, Q e represents the isolated population of patients in the incubation period, V represents the vaccinated population, H represents the hospitalized population, and R represents the removed population; t represents time;

[0103] The parameters of the SEIAQVHR model include {Λ, c, φ, μ, o s ,β1,β2,β3,o e ,ω,p,λ,κ,γ1,γ2,γ3}, Λ represents the population growth rate, c represents the population reduction rate; φ represents the effective mask wearing rate, μ represents the effective vaccination rate, o s represents the isolation rate of susceptible population, β1 represents the infection rate of latent population to susceptible population, β2 represents the infection rate of apparent infected population to susceptible population, β3 represents the infection rate of asymptomatic infected population to susceptible population, o e represents the isolation rate of the latent population, ω represents the rate of latent population conversion to explicit infection population, p represents the probability of latent population conversion to explicit infection population, λ represents the hospitalization rate of explicit infection population, κ represents the hospitalization rate of asymptomatic infection population, γ1 represents the removal rate of explicit infection population, γ2 represents the removal rate of asymptomatic infection population, and γ3 represents the removal rate of hospitalized population; each parameter is non-negative. In an example, the value range of each parameter is (0,1).

[0104] In one embodiment, the Basic Reproduction Number (R0) (or expressed as R0) is an important indicator for measuring the transmission capacity of infectious diseases. It reflects the average number of other susceptible people transmitted by an infected person during his average illness period without external intervention, and can be used to measure the transmission capacity of infectious diseases. When R0>1, the infectious disease will continue to spread among the population. The larger the R0, the faster the spread and the higher the epidemic risk; when R0=1, the incidence rate will remain at a stable level and reach the "disease-free equilibrium point"; when R0<1, the infectious disease will gradually disappear and will not cause a large-scale epidemic.

[0105] When the basic regeneration number of the SEIAQVHR model is determined based on the regeneration matrix algorithm, the first influencing parameter of the basic regeneration number corresponding to the SEIAQVHR model can be determined; the SEIAQVHR model is simplified and updated according to the first influencing parameter to obtain the SEIA model corresponding to the first influencing parameter; and the basic regeneration number formula of the basic regeneration number is determined according to the second-generation regeneration matrix solution algorithm of the basic regeneration number of the SEIA model.

[0106] Specifically, combining the actual calculation process of the second-generation regeneration matrix method and the characteristics of the R0 expression, parameters or differential equations that are not related to R0 are omitted in the calculation process, and the parts of the model that do not affect the calculation of the basic regeneration number are simplified, thereby determining the first influencing parameter of the basic regeneration number corresponding to the SEIAQVHR model; and the SEIAQVHR model is simplified and updated according to the first influencing parameter.

[0107] For example, in the SEIAQVHR model, the S (susceptible), E (latent population), I (explicit infection), and A (latent infection) compartments in the model can be determined as the first influencing parameters, because the populations in other compartments do not participate in the spread of infectious diseases, thereby obtaining the SEIA model corresponding to the first influencing parameter. Moreover, the simplified SEIA model still represents the SEIAQVHR model. The purpose of simplification is only to facilitate the calculation of the basic reproduction number of the model. After simplification, the calculation program that originally required the writing of a 9th-order matrix is ​​simplified to a 3rd-order matrix calculation program, so that the calculation efficiency of R0 can be improved while accurately calculating R0 of the SEIAQVHR model.

[0108] In one embodiment, the SEIA model includes:

[0109] dS / dt=Λ-{S[1-(φ+μ+o S )]}(β1E+β2I+β3A)-μS-o S S-cS,

[0110] dE / dt={S[1-(φ+μ+o S )]}(β1E+β2I+β3A)-o e E-ωE-cE,

[0111] dI / dt=ωpE-λI-γ1I-cI,

[0112] dA / dt=ω(1-p)E-κA-γ2A-cA,

[0113] Among them, S represents the susceptible population, E represents the incubation period population, I represents the apparent infection population, A represents the asymptomatic infection population, t represents time; Λ represents the population growth rate, c represents the population reduction rate; φ represents the effective mask wearing rate, μ represents the effective vaccination rate, o s represents the isolation rate of susceptible population, β1 represents the infection rate of latent population to susceptible population, β2 represents the infection rate of apparent infected population to susceptible population, β3 represents the infection rate of asymptomatic infected population to susceptible population, o e represents the isolation rate of the latent population, ω represents the rate at which the latent population is transformed into the explicitly infected population, p represents the probability that the latent population is transformed into the explicitly infected population, λ represents the hospitalization rate of the explicitly infected population, κ represents the hospitalization rate of the asymptomatic infected population, γ1 represents the removal rate of the explicitly infected population, and γ2 represents the removal rate of the asymptomatic infected population.

[0114] In one embodiment, the second generation regeneration matrix solution algorithm of the basic regeneration number of the SEIA model includes:

[0115] Assume that the right side of the SEIA model equations is 0 and determine the disease-free equilibrium point P0 (S * ,0,0,0), where S * =Λ / μ+o S +c,

[0116] Let x=(E,I,A) T ,get:

[0117]

[0118] in,

[0119]

[0120] The calculation results are:

[0121]

[0122] Then confirm

[0123]

[0124] Determine FV based on the second generation regeneration matrix algorithm -1 The spectral radius is used as the basic reproduction number formula R0 of the SEIA model:

[0125]

[0126] In one embodiment, a basic reproduction number derivation platform can also be constructed based on the basic reproduction number formula, and the platform's input rules, reading and parsing rules for input data and data storage rules can be defined. Software programming and initial output rules can be defined based on the custom algorithm, thereby constructing a platform for automatically deriving the basic reproduction number of the infectious disease dynamics model.

[0127] S22, determining the endemic equilibrium point of the SEIAQVHR model according to the basic reproduction number.

[0128] In one embodiment, when an infectious disease continues to spread among the population and reaches a stable state, the disease will remain at a certain epidemic level, which is the endemic equilibrium point. * =(S * ,E * ,I * ,A * ,Q s * ,Q e * ,V * ,H * ,R * ) corresponds to the following set of equations (1)-(9):

[0129] (1)Λ-{S * [1-(φ+μ+o S )]}(β1E * +β2I * +β3A * )-μS * -o S S * -cS * =0,

[0130] (2){S * [1-(φ+μ+o S )]}(β1E * +β2I * +β3A * )-o e E * -ωE * -cE * =0,

[0131] (3)ωpE * -λI * -γ1I * -cI * =0,

[0132] (4)ω(1-p)E* -κA * -γ2A * -cA * =0,

[0133] (5) s S * -cQ s * =0,

[0134] (6) e E * -cQ e * =0,

[0135] (7)μS * -cV * =0,

[0136] (8)λI * +κA * -γ3H * -cH * =0,

[0137] (9)γ1I * +γ2A * +γ3H * -cR * =0.

[0138] In one embodiment, the endemic equilibrium point P is determined based on the above equations (1)-(9): * ,include:

[0139] According to equation (1) and equation (2), determine:

[0140] (1-1)Λ-(μ+o s +c)S-(o e +ω+c)E=0,

[0141] According to equation (3), determine: ωpE * -λI * -γ1I * -cI * =0,

[0142] (1-2) That is

[0143] According to (1-2) and equation (4), we can determine:

[0144] ω(1-p)E * -κA * -γ2A * -cA * =0,

[0145]

[0146] According to (1-2) and (1-1), we can determine:

[0147] (1-4) According to (1-4) and equation (5), we can determine:

[0148] (1-5) According to (1-2) and equation (6), we can determine:

[0149] (1-6)

[0150] According to (1-4) and equation (7), determine:

[0151] (1-7) According to (1-3) and equation (8), we can determine:

[0152] (1-8)

[0153] According to (1-3), (1-8) and equation (9), we can determine:

[0154] (1-9) According to (1-2), (1-3), (1-4) and equation (1), determine:

[0155]

[0156] In one embodiment, the endemic equilibrium point is denoted as P * =(S * ,E * ,I * ,A * ,Q s * ,Q e * ,V * ,H * ,R * ),in:

[0157]

[0158]

[0159] Wherein, R0 represents the basic reproduction number of the SEIAQVHR model.

[0160] In one embodiment, if the basic reproduction number is greater than the preset value (e.g., 1), according to the non-negativity of the parameters of the SEIAQVHR model and the I *The expression of I * The expression of is positive, and it is determined that the endemic equilibrium point exists.

[0161] In one example, I * From the expression, we can see that when R0>1, I * >0. And the endemic equilibrium point P * =(S * ,E * ,I * ,A * ,Q s * ,Q e * ,V * ,H * ,R * ) is consistent with I * Therefore, the SEIAQVHR model has a unique endemic equilibrium point P * =(S * ,E * ,I * ,A * ,Q s * ,Q e * ,V * ,H * ,R * ), the endemic equilibrium point was demonstrated.

[0162] In one embodiment, determining the existence of an endemic equilibrium point can help formulate effective prevention and control strategies, such as vaccination, isolation measures, etc., to reduce disease transmission and reduce epidemic levels. By analyzing the endemic equilibrium point, the long-term epidemic trend of the disease in the population can also be predicted, including the epidemic scale, duration, etc., so as to assist in the allocation of public health resources and the adjustment of prevention and control measures.

[0163] S23, determining a disease-free equilibrium point of the SEIAQVHR model, and performing stability analysis on the disease-free equilibrium point based on the basic reproduction number.

[0164] In one embodiment, in the absence of any infected person, the disease will not spread and the system reaches a disease-free equilibrium point. The disease-free equilibrium point of the SEIAQVHR model is expressed as

[0165] In one embodiment, the stability of the disease-free equilibrium point is a key indicator for evaluating the possibility of eliminating the disease. If the disease-free equilibrium point is determined to be globally asymptotically stable, then through effective prevention and control measures, the disease can be controlled at an extremely low level, and even eventually eliminated. Continuous monitoring of the stability of the disease-free equilibrium point is also an important means of evaluating the effectiveness of prevention and control. If the disease-free equilibrium point remains stable, it means that the disease has been effectively controlled; if the disease-free equilibrium point shows signs of fluctuation or instability, timely measures need to be taken to respond.

[0166] In one embodiment, the stability analysis of the disease-free equilibrium point is performed based on the basic reproduction number, including: determining the Jacobian matrix of the SEIAQVHR model corresponding to the disease-free equilibrium point, and determining multiple characteristic roots of the equation group corresponding to the SEIAQVHR model according to the Jacobian matrix; determining negative characteristic roots among the multiple characteristic roots and characteristic roots to be verified other than the negative characteristic roots based on the non-negativity of parameters of the SEIAQVHR model; judging whether the characteristic root to be verified is a negative characteristic root based on the negative characteristic root and the basic reproduction number; and determining the stability of the disease-free equilibrium point according to the judgment result of the characteristic root to be verified.

[0167] In one embodiment, if the basic reproduction number is less than a preset value (for example, 1), it is determined that the characteristic root to be verified is a negative characteristic root, and that the disease-free equilibrium point is locally asymptotically stable; or, if the basic reproduction number is greater than the preset value, it is determined that the characteristic root to be verified is not a negative characteristic root, and that the disease-free equilibrium point is unstable.

[0168] In one example, the disease-free equilibrium The corresponding Jacobian matrix is ​​expressed as:

[0169]

[0170] The equation group corresponding to the SEIAQVHR model has 9 characteristic roots: λ′1=λ′2=λ′3=λ′4=-C,λ′5=-(γ3+c),λ′6=-(κ+γ2+c),λ′7=-(μ+o s +c), λ′8=-(λ+γ1+C), Based on the non-negativity of the parameters of the SEIAQVHR model, λ′1=λ′2=λ′3=λ′4=-c, λ′5=-(γ3+C), λ′6=-(κ+γ2+C), λ′7=-(μ+O s +C), λ′8=-(λ+γ1+c), these characteristic roots are negative in any case, so they are all negative characteristic roots, only is the characteristic root to be verified.

[0171] In one example, according to the basic reproduction number If R0<1 (indicating that the infectious disease will gradually disappear and reach a disease-free state), then the formula for the basic reproduction number R0 can be determined as follows:

[0172] β1Λ[1-(φ+μ+o S )](λ+γ1+c)(κ+γ2+c)+β2Λωp[1-(φ+μ+o S )](κ+γ2+c)+β3Λω(1-p)[1-(φ+μ+o S )](λ+γ1+c)<(o e +ω+c)(μ+o S +c)(λ+γ1+c)(κ+γ2+c),

[0173] It can be further determined that:

[0174]

[0175] In one example, according to the characteristic roots λ′8 and λ′9, the formula aλ′ can be determined 2 +bλ′+C=λ′ 2 The solution of -(λ′8+λ′9)λ′+λ′8λ′9=0 is λ′8, λ′9, where a, b and C are all non-negative numbers. According to Vieta's theorem, it can be determined that λ′8+λ′9=-b>0, λ′8λ′9′=C≤0, that is:

[0176]

[0177] Therefore, when R0<1 and λ′8 is a negative characteristic root, the characteristic root λ′9 to be verified is also a negative characteristic root. Therefore, all characteristic roots of the system of equations corresponding to the SEIAQVHR model are negative characteristic roots. According to the first method of Lyapunov (or linear stability theory), it can be determined that the disease-free equilibrium point is locally asymptotically stable. If R0>1, it can be determined that λ′8λ′9≤0, and the characteristic root λ′9 to be verified is not a negative characteristic root. According to the first method of Lyapunov, it can be determined that the disease-free equilibrium point is unstable.

[0178] S24, constructing a random SEIAQVHR model based on the SEIAQVHR model, and determining an equivalent model of the random SEIAQVHR model.

[0179] In one embodiment, based on the established SEIAQVHR model, random factors can be considered, and the Wiener process can be introduced into the SEIAQVHR model to establish a random SEIAQVHR model. The constructed random SEIAQVHR model is expressed as:

[0180] dS=[-{S[1-(φ+μ+o S )]}(β1E+β2I+β3A)-μS-o S S]dt+σ1(t)SdB1(t),

[0181] dE=[{S[1-(φ+μ+o S )]}(β1E+β2I+β3A)-O e E-ωE]dt+σ2EdB2(t),

[0182] dI=[ωpE-λI-γ1I]dt+σ3(t)IdB3(t),

[0183] dA=[ω(1-p)E-κA-γ2A]dt+σ4(t)AdB4(t),

[0184] dQ s =(o S S)dt+σ5(t)Q s dB5(t),

[0185] dQ e =(o e E)dt+σ6(t)Q e dB6(t),

[0186] dV=(μS)dt+σ7(t)VdB7(t),

[0187] dH=(λI+κA-γ3H)dt+σ8(t)HdB8(t),

[0188] dR=(γ1I+γ2A+γ3H)dt+σ9(t)RdB9(t),

[0189] Among them, B i (t)(i=1,2,3,4,5,6,7,8,9) represents B i (0)=0, and for any t≥0, σ i (t)(i=1,2,3,4,5,6,7,8,9) represents a continuous bounded function, Represents the strength of the Wiener process.

[0190] In one embodiment, in order to facilitate the study of the properties of the model, an equivalent model of the random SEIAQVHR model can be established, which is expressed as:

[0191]

[0192] dI=[ωpE-(γ1+c)I]dt+σ3IdB3(t),

[0193] dA=[ω(1-p)E-(γ2+c)A]dt+σ4AdB4(t),

[0194] dQ=(oS-cQ)dt+σ5QdB5(t),

[0195] dR=(γ1I+γ2A-cR)dt+σ6RdB6(t);

[0196] The multiple system state variables of the equivalent model include {S, E, I, A, Q, R}, and the equivalent model compared with the random SEIAQVHR model performs the equivalent update including: (susceptible isolation population Q s + Isolation of latent patients Q e ) is equivalently updated to the isolated population Q, the vaccinated population V is equivalently updated to 0, and the hospitalized population H is equivalently updated to 0; the multiple parameters of the equivalent model include {N, Λ, c, φ, μ, o, β1, β2, β3, ω, p, γ1, γ2}, wherein N represents the total population, Λ represents the population growth rate, and C represents the population reduction rate; φ represents the effective mask wearing rate, μ represents the effective vaccination rate, o represents the isolation rate of the susceptible population S, β1 represents the infection rate of the incubation period population to the susceptible population, β2 represents the infection rate of the explicit infection population to the susceptible population, β3 represents the infection rate of the asymptomatic infection population to the susceptible population, ω represents the rate at which the latent population is transformed into the explicit infection population, p represents the probability that the latent population is transformed into the explicit infection population, γ1 represents the removal rate of the explicit infection population, and γ2 represents the removal rate of the asymptomatic infection population; wherein each parameter is non-negative.

[0197] In one embodiment, in the equivalent model It indicates the standard incidence rate with isolation measures, and (NQ) indicates the non-isolated population.

[0198] S25, performing mathematical property analysis on the equivalent model, the results of the mathematical property analysis include that the equivalent model has a unique positive solution, the equivalent model satisfies the conditions of system extinction, and the equivalent model has a unique and ergodic stationary distribution.

[0199] In one embodiment, the method for determining that the equivalent model has a unique correct solution includes: setting the stopping time τ k , the stop time τ k Indicates that at least one of the system state variables {S, E, I, A, q, R} of the equivalent model exceeds the preset interval for the first time time, where k0≥0 represents a preset integer as large as possible, and k≥k0, where k represents an integer; where: In which, set inf{empty set} = ∞; according to τ k Regarding the monotonically increasing property of k, we can determine And determine τ by contradiction ∞ =∞, including: setting τ ∞ ≠∞; construct Lyapunov function based on Formula determination function The differential equation According to the differential equation The expectation determines the setting τ ∞ ≠∞There is a contradiction, determine τ ∞ =∞; According to the stop time τ k The definition of τ ∞ =∞=inf{empty set}, indicating that the system state variables of the equivalent model always remain within a limited preset interval for an arbitrary long time, and it is determined that the equivalent model has a unique positive solution.

[0200] In one example, suppose there exists k, let k0≥0 be large enough so that the initial values ​​of the system state variables of the equivalent model all fall within the interval Assume that the integer k ≥ k0 and define the stopping time:

[0201]

[0202] In which, we set inf{empty set} = ∞, the empty set is a set that does not contain any elements. e ), no value of any system state variable exceeds the interval Then τ k is defined as infinite, indicating that the system state of the equivalent model always remains within the specified interval within a given time. Obviously, τ k is monotonically increasing with respect to k. Assume Then τ ∞ ≤τ e as(almost surely)if τ ∞ =∞, then τ e =∞. So to prove the only correct answer, we only need to prove that τ ∞ =∞. Because τ ∞ =∞ means that there is an infinite interval only at the infinite time node. Conversely, any finite time node corresponds to a finite interval, which means that the system state variables of the equivalent model will always remain within any finite interval, thus proving that the equivalent model has a unique positive solution.

[0203] In one example, τ can be determined by proof by contradiction.∞ =∞. Set τ ∞ ≠∞, indicating that there is a finite time T>0 and probability Make This means that before time T, the system state variables are greater than The probability of will exceed some finite interval. For example, there exists an integer k1 ≥ k0 such that k≥k1, that is, k exceeds the interval Lyapunov function can be constructed Define the C2 function V:

[0204] based on Formula, which can determine the function The differential equation

[0205]

[0206] in,

[0207]

[0208] M0 represents a positive constant. So:

[0209]

[0210] The above formula From 0 to τ at both ends k ∧T integral, and then take its expectation, we have

[0211]

[0212] In one example, since we assume that τ ∞ The probability of ≤T is greater than We can determine a sufficiently large k1 so that when k ≥ k1, Can be used The properties of the function and The upper bound of derives a contradiction: that is, when k→∞, The expectation will tend to infinity, but this is different from The initial value of is inconsistent with the finiteness of T.

[0213] Assume Ω k ={τ k ≤T},k≤k1, by k≥k1, we can get For any ω∈Ω k , there exists i(1≤i≤n) such that S i (τ k ,ω),Ei (τ k ,ω),I i (τ k ,ω),A i (τ k ,ω),Q i (τ k ,ω),R i (τ k ,ω) at least one of them is equal to k or so

[0214]

[0215] Further

[0216]

[0217] Represents Ω k The characteristic function of (ω) when k→∞:

[0218]

[0219] Obviously, there is a contradiction in the above formula, so there is no T>0 and Make So the setting τ ∞ ≠∞There is a contradiction, determine τ ∞ =∞.

[0220] In one embodiment, the method for determining that the equivalent model satisfies the condition of system extinction includes: setting the function P(t)=ωE+(ω+c)(I(t)+A(t)), according to The differential equation dlnP(t) is determined by the formula; the differential equation dlnP(t) is integrated and averaged, and the strong law of large numbers is applied to the result of the integrated average to determine that the function P(t) satisfies According to the non-negativity of the parameters of the equivalent model and the function P(t) satisfies It is determined that the system state variables of the equivalent model gradually tend to zero over time, and it is determined that the equivalent model satisfies the conditions of system extinction.

[0221] In one example, let P(t) = ωE + (ω + c)(I(t) + A(t)), by The formula gives the differential equation dlnP(t):

[0222]

[0223] Integrating both sides of the above inequality from 0 to t and dividing by t gives:

[0224]

[0225] Thus we get This upper bound contains a constant term (related to the parameters of the model) and three random integral terms. According to the strong law of large numbers, when t→∞, the random integral term will almost certainly converge to 0: as. Therefore, we can ignore the random terms in the above upper bound and only focus on the constant terms. Then when t→∞, we have:

[0226]

[0227] Right now

[0228] It means that the constant term is less than 0 when t→∞, will almost certainly be less than 0; since P(t) is the weighted sum of the system state variables (E, I, A), we have

[0229]

[0230] This means that in the long term, the incubation population E, the apparent infection population I, and the asymptomatic infection population A in the equivalent model will almost certainly disappear;

[0231] It can be further determined that:

[0232]

[0233] Therefore, the system state variables of the equivalent model will almost inevitably tend to 0, that is, the system extinction condition will be satisfied.

[0234] In one embodiment, the method for determining whether the equivalent model has a unique and ergodic stationary distribution includes: determining a diffusion matrix of the equivalent model based on the intensity of the Wiener process in the equivalent model; constructing a Lyapunov function according to the diffusion matrix of the equivalent model. according to The formula determines the function The infinitesimal generator LV1 represents the function The expected rate of change of the solution along the equivalent model; according to the negative upper bound of the infinitesimal generator LV1, determine the function is a continuous function; according to the function With the initial function The difference between , construct the function V(S,Q,E,I,A,R); according to The formula determines the infinitesimal generator LV of the function V(S,Q,E,I,A,R); set Where η>0; the area corresponding to the equivalent model The method is divided into multiple sub-regions, and it is determined that the infinitesimal generator LV in each sub-region has a negative upper bound, and it is determined that the equivalent model has a unique and ergodic stationary distribution.

[0235] In one example, the diffusion matrix of the equivalent model is expressed as:

[0236]

[0237] have

[0238] (xi1,xi2,xi3,xi4,xi5,xi6)∈R 6 .

[0239] And k>1 is an integer as large as possible, construct the Lyapunov function Define C2-function as follows:

[0240]

[0241] It can capture the difference between the system state variables and their natural logarithms, which helps analyze the persistence and stability of the system;

[0242] according to The formula gets the infinitesimal generator LV1:

[0243]

[0244] in

[0245] Therefore, the infinitesimal generator LV1 has a negative upper bound, there is a constant Γ>0, and,

[0246]

[0247] It can be determined is continuous and

[0248]

[0249] according to With the initial function The difference in C 2 -Function V:

[0250]

[0251] according to The formula can be used to obtain the infinitesimal generator LV of V(S,Q,E,I,A,R):

[0252]

[0253] The expression of LV includes the derivative terms of the system state variables and the noise terms;

[0254] definition Where η>0, when it exists a sufficiently small number, the following inequality condition holds:

[0255]

[0256]

[0257] in,

[0258]

[0259] In order to prove that On, LV≤-1, you can The LV was divided into 12 regions and analyzed in each region. Divided into 12 sub-areas:

[0260]

[0261] In D1, S<η, according to the expression of LV and the given inequality conditions, it can be determined that:

[0262]

[0263] because Therefore, on D1, LV≤-1 holds. We can analyze the other 11 sub-regions similarly and prove that on each sub-region, LV is less than or equal to -1. Therefore, for all LV≤-1, that is, LV is in the region D of the equivalent model system η If the value is less than -1 continuously, the system state will tend to area D. η The boundary of D η The stable state is reached within 10000. η is a compact set, so the system state will traverse all possible states in this compact set, that is, the equivalent model has a unique and ergodic stationary distribution.

[0264] S26, determining the dynamic behavior of the infectious disease based on the results of the stability analysis and the results of the mathematical property analysis.

[0265] In one embodiment, the determination of the infectious disease transmission mechanism, prediction of the infectious disease dynamic behavior and infectious disease prevention and control strategy based on the results of the stability analysis and the results of the mathematical property analysis includes: numerical simulation of the results of the stability analysis and the results of the mathematical property analysis, and determination of the infectious disease dynamic behavior according to the results of the numerical simulation. Numerical simulation can not only provide numerical results of the infectious disease dynamic behavior, but also intuitively display the changing trend of the infectious disease dynamic behavior through charts and other forms, such as the increase or decrease in the number of infected people, the transformation of susceptible people to other states, etc.

[0266] In one example, Matlab software can be selected to perform numerical simulation on the SEIAQVHR model. Three groups of different parameters and initial values ​​are selected to perform three simulations (including simulation one, simulation two and simulation three) to study the stability of the disease-free equilibrium point of the SEIAQVHR model.

[0267] The values ​​used in simulation 1 include: N=1000, S=999, E=0, I=,1, A=0, Q=Qs+Qe, V=0, H=0, R=0, β1=0.0006, β2=0.0005, β3=0.0008, μ=0.0002, o s =0.0003,o e =0.0002, ω=0.017, p=0.4, λ=0.006, κ=0.03, γ1=0.02, γ2=0.01, γ3=0.03, Λ=0.003, c=0.003. The effect of numerical simulation is as follows Figure 4 shown.

[0268] The values ​​used in simulation 2 include: N = 100000, S = 99999, E = 0, I =, 1, A = 0, Q = Qs + Qe, V = 0, H = 0, R = 0, β1 = 0.000009, β2 = 0.000004, β3 = 0.000007, μ = 0.002, o s =0.006,o e =0.008, ω=0.017, p=0.4, λ=0.08, κ=0.06, γ1=0.05, γ2=0.05, γ3=0.04, Λ=0.004, c=0.004. The results of numerical simulation are as follows Figure 5 shown.

[0269] The values ​​used in simulation three include: N = 1000000, S = 999999, E = 0, I =, 1, A = 0, Q = Qs + Qe, V = 0, H = 0, R = 0, β1 = 0.000007, β2 = 0.000003, β3 = 0.000005, μ = 0.02, o s =0.005,o e =0.006, ω=0.017, p=0.8, λ=0.7, κ=0.2, γ1=0.7, γ2=0.3, γ3=0.8, Λ=0.002, c=0.002. The results of numerical simulation are as follows Figure 6 shown.

[0270] The results of the above numerical simulations 1 to 3 show that the number of apparent infected persons (I) and asymptomatic infected persons (A) and hospitalized persons (H) in the SEIAQVHR model will increase to a peak value and then decrease to zero over time, and the susceptible population (S) will eventually be transformed into evacuees (R) and quarantined persons (Q s )、(Q e ) and the vaccinated population (V), which is the same as the stability of the disease-free equilibrium point inferred from the above-mentioned embodiments of this case. The stability of the disease-free equilibrium point is a key indicator for evaluating the possibility of eliminating the disease. If the disease-free equilibrium point is determined to be globally asymptotically stable, then through effective prevention and control measures, the disease can be controlled to an extremely low level, and even ultimately the disease can be eliminated. Continuous monitoring of the stability of the disease-free equilibrium point is also an important means of evaluating the effectiveness of prevention and control. If the disease-free equilibrium point remains stable, it means that the disease has been effectively controlled; if the disease-free equilibrium point shows signs of fluctuation or instability, timely measures must be taken to respond.

[0271] In one example, Matlab software can be selected to perform numerical simulation on the equivalent model. Three groups of different parameters and initial values ​​are selected to perform three simulations (including simulation four, simulation five and simulation six) to study the system extinction of the equivalent model.

[0272] The values ​​used in simulation 4 include: N = 1000, S = 999, E = 0, I = , 1, A = 0, Q = 0, R = 0, β1 = 0.0006, β2 = 0.0005, β3 = 0.0008, μ = 0.0002, o=0.0003, ω=0.017, p=0.4, γ1=0.02, γ2=0.01, Λ=0.003, c=0.003, σ1=0.0025, σ2=0.025, σ3=0.035, σ4=0.025, σ5=0.025, σ6=0.0025. The effect of numerical simulation is as follows: Figure 7 shown.

[0273] The values ​​used in simulation 5 include: N = 100000, S = 99999, E = 0, I = , 1, A = 0, Q = 0, R = 0, β1 = 0.000009, β2 = 0.000004, β3 = 0.000007, μ = 0.002, o=0.006, ω=0.017, p=0.4, γ1=0.05, γ2=0.05, Λ=0.004, c=0.004, σ1=0.0025, σ2=0.025, σ3=0.035, σ4=0.025, σ5=0.025, σ6=0.0025. The effect of numerical simulation is as follows: Figure 8 shown.

[0274] The values ​​used in simulation VI include: N = 1000000, S = 999999, E = 0, I = ,1, A = 0, Q = 0, R = 0, β1 = 0.000007, β2 = 0.000003, β3 = 0.000005, μ = 0.02, o=0.0005, ω=0.017, p=0.8, γ1=0.07, γ2=0.03, Λ=0.002, c=0.002, σ1=0.0025, σ2=0.025, σ3=0.035, σ4=0.025, σ5=0.025, σ6=0.0025. The effect of numerical simulation is as follows: Fig. 9 shown.

[0275] The results of the above numerical simulations four to six show that when the basic reproduction number is less than 1, the infectious disease will quickly become extinct. The disappearance of the infectious disease can be seen in the effect diagram of the numerical simulation results of the random infectious disease dynamics model. The number of obvious infections, asymptomatic infections and latent infections will eventually drop to 0.

[0276] In order to further analyze the impact of the intensity of random interference on disease transmission, the intensity of random interference can be changed to determine the impact of random interference on the dynamic behavior of infectious diseases. In one example, based on the parameter values ​​of simulation six, simulation seven changes the intensity of all random interferences in simulation six to 0.3, that is, σ1 = σ2 = σ3 = σ4 = σ5 = σ6 = 0.3, and draws a time series diagram of the dominant infected population. The effect of numerical simulation is shown in Figure 2. Fig.10 As shown in the figure, it means that the increase in the intensity of random interference will accelerate the extinction of the disease in the population, that is, random interference is beneficial to the control of the disease. It is possible to consider introducing more random elements into the prevention and control strategy, such as random testing, random isolation, etc., to formulate a more effective infectious disease prevention and control strategy.

[0277] The infectious disease dynamics model analysis method provided in this application takes into account factors such as vaccines, isolation, and hospitalization in actual infectious disease transmission situations, and constructs a SEIAQVHR model that is more in line with actual conditions. The endemic disease equilibrium point and disease-free equilibrium point of the SEIAQVHR model are calculated and analyzed based on the basic reproduction number of the SEIAQVHR model. Taking into account the impact of random interference, a random SEIAQVHR model is constructed on the basis of the SEIAQVHR model, and the mathematical properties of the equivalent model of the random SEIAQVHR model are analyzed. Using the above method, the random SEIAQVHR model can more clearly demonstrate the impact of random factors on the spread of infectious diseases. Mathematical property analysis of the random SEIAQVHR model helps to formulate effective infectious disease prevention and control strategies.

[0278] refer to Fig.11 As shown, it is a flow chart of an infectious disease dynamics model analysis method provided by another embodiment of the present application. The method comprises: consulting relevant literature on infectious disease dynamics models and constructing a SEIAQVHR model. Performing mathematical property analysis on the SEIAQVHR model, for example, determining whether the SEIAQVHR model has an endemic equilibrium point, and performing stability analysis on the disease-free equilibrium point of the SEIAQVHR model. A random SEIAQVHR model is established based on the SEIAQVHR model, and various properties of the model are proved. For example, a mathematical property analysis is performed on an equivalent model of the random SEIAQVHR model, and the results of the mathematical property analysis include that the equivalent model has a unique positive solution, that the equivalent model satisfies the conditions for system extinction, and that the equivalent model has a unique and ergodic stationary distribution. Numerical simulation of the random SEIAQVHR model is performed based on the equivalent model.

[0279] Fig.12 It is a structural diagram of an infectious disease dynamics model analysis device provided in one embodiment of the present application.

[0280] In some embodiments, the infectious disease dynamics model analysis device 60 may include a plurality of functional modules composed of computer program segments. The computer programs of the various program segments in the infectious disease dynamics model analysis device 60 may be stored in a memory of an electronic device and executed by at least one processor to perform (see Figure 2 Description) Functions for analyzing infectious disease dynamics models.

[0281] In this embodiment, the infectious disease dynamics model analysis device 60 can be divided into multiple functional modules according to the functions it performs. The functional modules may include: a construction module 601, a determination module 602, and an analysis module 603. The module referred to in this application refers to a series of computer program segments that can be executed by at least one processor and can complete fixed functions, which are stored in a memory. In this embodiment, the functional implementation method of each module in the infectious disease dynamics model analysis device 60 can refer to the above definition of the infectious disease dynamics model analysis method, and will not be repeated here.

[0282] The construction module 601 is used to construct the SEIAQVHR model and determine the basic reproduction number of the SEIAQVHR model based on the reproduction matrix algorithm.

[0283] The determination module 602 is used to determine the endemic equilibrium point of the SEIAQVHR model according to the basic reproduction number.

[0284] The analysis module 603 is used to determine the disease-free equilibrium point of the SEIAQVHR model and perform stability analysis on the disease-free equilibrium point based on the basic reproduction number.

[0285] The construction module 601 is further used to construct a random SEIAQVHR model based on the SEIAQVHR model, and determine an equivalent model of the random SEIAQVHR model.

[0286] The analysis module 603 is also used to perform mathematical property analysis on the equivalent model. The results of the mathematical property analysis include that the equivalent model has a unique positive solution, the equivalent model satisfies the conditions of system extinction, and the equivalent model has a unique and ergodic stationary distribution.

[0287] The determination module 602 is further used to determine the dynamic behavior of the infectious disease based on the results of the stability analysis and the results of the mathematical property analysis.

[0288] An embodiment of the present application further provides a computer-readable storage medium, on which a computer program is stored. The computer program includes program instructions. The method implemented when the program instructions are executed can refer to the methods in the above-mentioned embodiments of the present application.

[0289] The computer-readable storage medium may be an internal memory of the electronic device described in the above embodiment, such as a hard disk or memory of the electronic device. The computer-readable storage medium may also be an external storage device of the electronic device, such as a plug-in hard disk, a smart memory card (Smart Media Card, SMC), a secure digital (Secure Digital, SD) card, a flash card (Flash Card), etc. equipped on the electronic device.

[0290] In some embodiments, the computer-readable storage medium may include a program storage area and a data storage area, wherein the program storage area may store an operating system, an application required for at least one function, etc.; the data storage area may store data created according to the use of the electronic device, etc.

[0291] In the above embodiments, the description of each embodiment has its own emphasis. For parts that are not described or recorded in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0292] Those of ordinary skill in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of this application.

[0293] In the embodiments provided in the present application, it should be understood that the disclosed devices / terminal equipment and methods can be implemented in other ways. For example, the device / terminal equipment embodiments described above are only schematic. For example, the division of the modules or units is only a logical function division. There may be other division methods in actual implementation, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of devices or units, which can be electrical, mechanical or other forms.

[0294] The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0295] The embodiments described above are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, a person skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. Such modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present application, and should all be included in the protection scope of the present application.

Claims

1. A method for analyzing infectious disease dynamics models, characterized in that: The method comprises: Constructing a SEIAQVHR model, and determining a basic reproduction number of the SEIAQVHR model based on a reproduction matrix algorithm; Determining the endemic equilibrium point of the SEIAQVHR model according to the basic reproduction number; Determining a disease-free equilibrium point of the SEIAQVHR model, and performing stability analysis on the disease-free equilibrium point based on the basic reproduction number; Constructing a random SEIAQVHR model based on the SEIAQVHR model, and determining an equivalent model of the random SEIAQVHR model; Performing mathematical property analysis on the equivalent model, the results of the mathematical property analysis include that the equivalent model has a unique positive solution, the equivalent model satisfies the conditions of system extinction, and the equivalent model has a unique and ergodic stationary distribution; Based on the results of the stability analysis and the results of the mathematical property analysis, the dynamic behavior of the infectious disease is determined.

2. The infectious disease dynamics model analysis method according to claim 1, characterized in that: The SEIAQVHR model includes a differential equation group consisting of multiple differential equations, in which the system state variable changes with time. The differential equation group is expressed as: dS / dt=Λ-{S[1-(φ+μ+o S )]}(β1E+β2I+β3A)-μS-o S S-cS, dE / dt={S[1-(φ+μ+o S )]}(β1E+β2I+β3A)-o e E-ωE-cE, dI / dt=ωpE-λI-γ1I-cI, dA / dt=ω(1-p)E-κA-γ2A-cA, dQ s / dt=o S S-cQ s , dQ e / dt=o e E-cQ e , dV / dt=μS-cV, dH / dt=λI+κA-γ3H-cH, dR / dt=γ1I+γ2A+γ3H-cR, The multiple system state variables of the SEIAQVHR model include {S, E, I, A, Q s , Q e , V, H, R}, S represents susceptible population, E represents latent population, I represents obvious infection population, A represents asymptomatic infection population, Q s Indicates susceptible people isolated from the crowd, Q e represents the isolated population of patients in the incubation period, V represents the vaccinated population, H represents the hospitalized population, and R represents the removed population; t represents time; The parameters of the SEIAQVHR model include {Λ, c, φ, μ, o s ,β1,β2,β3,o e , ω, p, λ, κ, γ1, γ2, γ3}, Λ represents the population growth rate, c represents the population reduction rate; φ represents the effective mask wearing rate, μ represents the effective vaccination rate, o s represents the isolation rate of susceptible population, β1 represents the infection rate of latent population to susceptible population, β2 represents the infection rate of apparent infected population to susceptible population, β3 represents the infection rate of asymptomatic infected population to susceptible population, o e represents the isolation rate of the latent population, ω represents the rate at which the latent population is transformed into the explicitly infected population, p represents the probability that the latent population is transformed into the explicitly infected population, λ represents the hospitalization rate of the explicitly infected population, κ represents the hospitalization rate of the asymptomatic infected population, γ1 represents the removal rate of the explicitly infected population, γ2 represents the removal rate of the asymptomatic infected population, and γ3 represents the removal rate of the hospitalized population; each parameter is non-negative.

3. The infectious disease dynamics model analysis method according to claim 2, characterized in that: The basic reproduction number of the SEIAQVHR model is expressed as:

4. The infectious disease dynamics model analysis method according to claim 2, characterized in that: The endemic equilibrium point of the SEIAQVHR model is denoted as P * =(S * , E * , I * , A * , Q s * , Q e * , V * , H * , R * ),in: Wherein, R0 represents the basic reproduction number of the SEIAQVHR model.

5. The infectious disease dynamics model analysis method according to claim 1, characterized in that: The disease-free equilibrium point of the SEIAQVHR model is expressed as The stability analysis of the disease-free equilibrium point based on the basic reproduction number includes: Determine the Jacobian matrix of the SEIAQVHR model corresponding to the disease-free equilibrium point, and determine a plurality of characteristic roots of the equation group corresponding to the SEIAQVHR model according to the Jacobian matrix; Determine negative characteristic roots among the plurality of characteristic roots and characteristic roots to be verified other than the negative characteristic roots based on the non-negativity of the parameters of the SEIAQVHR model; Based on the negative characteristic root and the basic reproduction number, determining whether the characteristic root to be verified is a negative characteristic root; and The stability of the disease-free equilibrium point is determined according to the judgment result of the characteristic root to be verified.

6. The infectious disease dynamics model analysis method according to claim 5, characterized in that: The method further comprises: If the basic reproduction number is less than a preset value, the characteristic root to be verified is determined to be a negative characteristic root, and the disease-free equilibrium point is determined to be locally asymptotically stable; or, If the basic reproduction number is greater than the preset value, it is determined that the characteristic root to be verified is not a negative characteristic root, and it is determined that the disease-free equilibrium point is unstable.

7. The infectious disease dynamics model analysis method according to claim 2, characterized in that: The constructing of a random SEIAQVHR model based on the SEIAQVHR model includes: introducing the Wiener process into the SEIAQVHR model, and the constructed random SEIAQVHR model is expressed as: dS=[-{S[1-(φ+μ+o S )]}(β1E+β2I+β3A)-μS-o S S]dt+σ1(t)SdB1(t), dE=[{S[1-(φ+μ+o S )]}(β1E+β2I+β3A)-o e E-ωE]dt+σ2EdB2(t), dI=[ωpE-λI-γ1I]dt+σ3(t)IdB3(t), dA=[ω(1-p)E-κA-γ2A]dt+σ4(t)AdB4(t), dQ s =(o S S)dt+σ5(t)Q s dB5(t), dQ e =(o e E)dt+σ6(t)Q e dB6(t), dV=(μS)dt+σ7(t)VdB7(t), dH=(λI+κA-γ3H)dt+σ8(t)HdB8(t), dR=(γ1I+γ2A+γ3H)dt+σ9(t)RdB9(t), Among them, B i (t)(i=1,2,3,4,5,6,7,8,9) represents B i (0)=0, and for any t≥0, σ i (t)(i=1,2,3,4,5,6,7,8,9) represents a continuous bounded function, Represents the strength of the Wiener process.

8. The infectious disease dynamics model analysis method according to claim 7, characterized in that: The equivalent model of the stochastic SEIAQVHR model is expressed as: dI=[ωpE-(γ1+c)I]dt+σ3IdB3(t), dA=[ω(1-p)E-(γ2+c)A]dt+σ4AdB4(t), dQ=(oS-cQ)dt+σ5QdB5(t), dR=(γ1I+γ2A-cR)dt+σ6RdB6(t); Among them, the multiple system state variables of the equivalent model include {S, E, I, A, Q, R}, and the equivalent model compared with the random SEIAQVHR model performs the equivalent update including: (susceptible isolation population Q s + Isolation of latent patients Q e ) is equivalently updated to the quarantine population Q, the vaccinated population V is equivalently updated to 0, and the hospitalized population H is equivalently updated to 0; The multiple parameters of the equivalent model include {N, Λ, c, φ, μ, o, β1, β2, β3, ω, p, γ1, γ2}, wherein N represents the total population, Λ represents the population growth rate, and c represents the population reduction rate; φ represents the effective mask wearing rate, μ represents the effective vaccination rate, o represents the isolation rate of the susceptible population S, β1 represents the infection rate of the latent population to the susceptible population, β2 represents the infection rate of the explicit infected population to the susceptible population, β3 represents the infection rate of the asymptomatic infected population to the susceptible population, ω represents the rate at which the latent population is converted into the explicit infected population, p represents the probability of the latent population being converted into the explicit infected population, γ1 represents the removal rate of the explicit infected population, and γ2 represents the removal rate of the asymptomatic infected population; wherein each parameter is non-negative.

9. The infectious disease dynamics model analysis method according to claim 8, characterized in that: Methods for determining that the equivalent model has a unique correct solution include: Set the stop time τ k , the stop time τ k Indicates that at least one of the system state variables {S, E, I, A, Q, R} of the equivalent model exceeds the preset interval for the first time time, where k0≥0 represents a preset integer as large as possible, k≥k0, k represents an integer; where: τ k = inf{t∈[0,τ e ): or In which, inf{empty set} is set to ∞; According to τ k Regarding the monotonically increasing property of k, we can determine And determine τ by contradiction ∞ =∞, including: setting τ ∞ ≠∞; construct Lyapunov function (S, E, I, A, Q, R), based on Formula determination function Differential equations of (S, E, I, A, Q, R) According to the differential equation The expectation determines the setting τ ∞ ≠∞There is a contradiction, determine τ ∞ =∞; According to the stop time τ k The definition of τ ∞ =∞=inf{empty set}, indicating that the system state variables of the equivalent model always remain within a limited preset interval for an arbitrary long time, and it is determined that the equivalent model has a unique positive solution.

10. The infectious disease dynamics model analysis method according to claim 8, characterized in that: The method for determining that the equivalent model satisfies the conditions for system extinction includes: Assume function P(t) = ωE + (ω + c)(I(t) + A(t)), according to Formula determines the differential equation dlnP(t); The differential equation dlnP(t) is integrated and averaged, and the strong law of large numbers is applied to the result of the integrated average to determine whether the function P(t) satisfies According to the non-negativity of the parameters of the equivalent model and the function P(t) satisfies It is determined that the system state variables of the equivalent model gradually tend to zero over time, and it is determined that the equivalent model satisfies the conditions of system extinction.

11. The infectious disease dynamics model analysis method according to claim 8, characterized in that: Methods for determining that the equivalent model has a unique and ergodic stationary distribution include: determining a diffusion matrix of the equivalent model based on the intensity of the Wiener process in the equivalent model; According to the diffusion matrix of the equivalent model, the Lyapunov function is constructed according to The formula determines the function The infinitesimal generator LV1 represents the function the expected rate of change of the solution along the equivalent model; According to the negative upper bound of the infinitesimal generator LV1, the function is a continuous function; According to the function With the initial function The difference between , construct the function V(S, Q, E, I, A, R); according to The formula determines the infinitesimal generator LV of the function V(S, Q, E, I, A, R); set up Where η>0; The area corresponding to the equivalent model The method is divided into multiple sub-regions, and it is determined that the infinitesimal generator LV in each sub-region has a negative upper bound, and it is determined that the equivalent model has a unique and ergodic stationary distribution.

12. The infectious disease dynamics model analysis method according to claim 1, characterized in that: The determination of infectious disease transmission mechanisms, prediction of infectious disease dynamic behaviors and infectious disease prevention and control strategies based on the results of the stability analysis and the results of the mathematical property analysis include: The results of the stability analysis and the results of the mathematical property analysis are numerically simulated, and the infectious disease transmission mechanism is determined and the dynamic behavior of the infectious disease is predicted based on the results of the numerical simulation.

13. An electronic device, characterized in that: The electronic device includes a processor and a memory, and the processor is used to implement the infectious disease dynamics model analysis method as described in any one of claims 1 to 12 when executing the computer program stored in the memory.

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