Dynamic equilibrium analysis method under new crown growth and application

Abstract

The invention discloses a dynamic balance analysis method under new crown growth and application. The dynamic equilibrium analysis method under new crown growth comprises the following steps: S1, establishing an SEIRS model equation, and calculating each state value in an SEIRS model based on a disease-free equilibrium point (DFE) and an endemic equilibrium point (EE); s2, calculating a basic regeneration number R0 by using a next-generation matrix method; s3, by analyzing the stability of the disease-free balance point and the local balance point, calculating a Jacobian matrix and solving a characteristic value of the Jacobian matrix; s4, based on the calculation, simulating dynamic equilibrium processes under different immune decline rates and infection rates by using a numerical simulation technology; by adjusting parameters, the prevalence trend of the new crown growing in the crowd in the future and the occurrence time of a reinfection peak are predicted. According to the method, a feasible scheme can be provided for predicting the long-term dynamic balance condition of the new crown, and a reliable scientific basis is provided for deployment of medical resources and formulation of public health policies.

Description

Technical Field

[0001] The present invention relates to the field of big data analysis application technology, and more specifically, to a dynamic balance analysis method and application under long-term COVID-19. Background Art

[0002] Long COVID refers to the persistent symptoms or sequelae experienced by some patients infected with the novel coronavirus (COVID-19) after the acute phase of infection. These symptoms may involve multiple systems and include, but are not limited to, fatigue, dyspnea, cognitive impairment, muscle pain, insomnia, and palpitations. The pathogenesis of long COVID is not yet fully understood, but studies suggest that factors such as the persistence of the virus, immune system dysfunction, inflammatory responses, and damage to the nervous system may work together to cause long-term symptoms.

[0003] Due to the complexity of long-term COVID-19 and the inevitable decline in individual immunity, predicting the long-term dynamic balance of long-term COVID-19 is crucial for the allocation of medical resources and the formulation of public health policies. On the one hand, the large number of long-term COVID-19 patients and the diversity of their symptoms place continuous pressure on the medical system, requiring the rational allocation of medical resources to meet the rehabilitation needs of patients. On the other hand, accurate predictions and assessments can help public health departments formulate targeted policies in advance, such as strengthening the construction of rehabilitation treatment facilities, providing psychological support services, and conducting long-term follow-up. Summary of the Invention

[0004] The purpose of the present invention is to provide a dynamic balance analysis method and application under long-term COVID-19. The dynamic balance analysis method under long-term COVID-19 can provide a feasible solution for predicting the long-term dynamic balance of long-term COVID-19, and provide a reliable scientific basis for the allocation of medical resources and the formulation of public health policies.

[0005] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0006] In the first aspect, a dynamic equilibrium analysis method under COVID-19 comprises the following steps:

[0007] S1. Establish the SEIRS model equation and calculate the state values in the SEIRS model based on the disease-free equilibrium (DFE) and endemic equilibrium (EE);

[0008] S2. Calculate the basic reproduction number R0 using the next generation matrix method;

[0009] S3. Analyze the stability of the disease-free equilibrium point and the local equilibrium point, calculate the Jacobian matrix and solve its eigenvalues;

[0010] S4. Based on the above calculations, numerical simulation technology is used to simulate the dynamic equilibrium process of the system under different immune decline rates and infection rates; by adjusting parameters, the future epidemic trend of long-term new crown in the population and the time of the peak of reinfection are predicted.

[0011] Furthermore, the SEIRS model described in the present invention uses the following differential equations to describe the population changes in each state:

[0012]

[0013] in,

[0014] S represents the number of susceptible people, E represents the number of exposed people, I represents the number of infected people, R represents the number of recovered people, and N = S + E + I + R represents the total population;

[0015] β represents the infection rate, and the susceptible person S may be infected by contacting the infected person I;

[0016] σ is the incubation rate, which indicates the rate at which the exposed person E enters the infectious state;

[0017] γ represents the recovery rate of infected people;

[0018] p is the rate at which recovered individuals' immunity declines and they re-enter a susceptible state.

[0019] Furthermore, the disease-free equilibrium point of the present invention represents the equilibrium state reached by the system when there are no infected persons. When the number of infected persons and exposed persons is zero, the equilibrium state of the system is: (S * ,E * ,I * ,R * )=(N,0,0,0).

[0020] Furthermore, in step S1 of the present invention, the local equilibrium point represents the population equilibrium state when the disease persists in the society. By setting the derivatives of all states to zero, the state values in the SEIRS model are calculated:

[0021]

[0022] Optionally, before establishing the SEIRS model, initialize the conditions, set the total population, and assume that a portion of the population is initially infected and the rest are susceptible.

[0023] Furthermore, in step S2 of the present invention, the basic reproduction number R0 represents the average number of secondary cases infected by an infected person in a completely susceptible population. According to the SEIRS model, R0 can be expressed as:

[0024]

[0025] When R0>1, the infection will spread; when R0<1, the infection will gradually subside.

[0026] In step S3 of the present invention, the stability of the disease-free equilibrium and the endemic equilibrium is analyzed, the Jacobian matrix is calculated, and its eigenvalues are solved. If the real parts of all eigenvalues are negative, it indicates that the equilibrium is stable, that is, the system is tending towards this equilibrium state; if there are positive eigenvalues, the equilibrium is unstable, and the system will deviate from this equilibrium state.

[0027] In step S4 of the present invention, the dynamic equilibrium process of the system under different immune decline rates and infection rates is simulated by using numerical simulation technology, and the steps are as follows:

[0028] 1) Set the parameters and initial conditions of the SEIRS model;

[0029] 2) Use numerical integration methods to numerically solve the SEIRS differential equation; set the time step Δt and simulation duration;

[0030] 3) Parameter sensitivity analysis: adjust the values of δ and β respectively to study the impact of different parameters on the dynamic balance of the system;

[0031] 4) Draw time series curves: For each parameter combination, plot the curves of S(t), E(t), I(t), and R(t) over time to visually show how the system moves from the initial state to a dynamic equilibrium state, and how the equilibrium state changes when the parameters are changed;

[0032] 5) Predicting the peak of reinfection: By comparing different simulation results, predict the time of occurrence of the peak of reinfection.

[0033] In a second aspect, the present invention further provides an electronic device.

[0034] The electronic device includes at least one memory and at least one processor; the at least one memory is coupled to the at least one processor, the at least one memory is used to store a computer program, and the at least one processor is used to call the computer program, and the computer program includes instructions. When the instructions are executed by the at least one processor, the electronic device executes the dynamic balance analysis method under long-term COVID-19 as described in the first aspect.

[0035] In a third aspect, the present invention provides a computer storage medium.

[0036] The computer storage medium includes computer instructions. When the computer instructions are run on an electronic device, the electronic device executes the dynamic balance analysis method under the long coronavirus as described in the first aspect.

[0037] Compared with the prior art, the present invention has the following beneficial effects:

[0038] The present invention can provide a feasible solution for predicting the long-term dynamic balance of COVID-19, and provide a reliable scientific basis for the allocation of medical resources and the formulation of public health policies. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 This is a processing flow chart of the dynamic equilibrium analysis method under the long coronavirus described in the embodiment.

[0040] Figure 2 2 is a structural block diagram of the electronic device described in the embodiment. DETAILED DESCRIPTION

[0041] The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0042] The following describes a dynamic balance analysis method under long COVID-19 according to an embodiment of the present invention.

[0043] Specifically, such as Figure 1 As shown, the dynamic balance analysis method under the long new crown includes the following steps:

[0044] S1. Initialization

[0045] The entire target population is divided into four states: susceptible (S), exposed (E), infected (I) and recovered (R);

[0046] Under initial conditions, the total population is set, and it is assumed that a part of the population is initially infected and the rest are susceptible.

[0047] S2. Establish SEIRS model equation

[0048] The population changes in each state are described using the following differential equations:

[0049]

[0050] Among them, S represents the number of susceptible people, E represents the number of exposed people, I represents the number of infected people, R represents the number of recovered people, and N = S + E + I + R represents the total population;

[0051] β represents the infection rate, and the susceptible person S may be infected by contacting the infected person I;

[0052] σ is the incubation rate, which indicates the rate at which the exposed person E enters the infectious state;

[0053] γ represents the recovery rate of infected people;

[0054] p is the rate at which recovered individuals' immunity declines and they re-enter a susceptible state.

[0055] S3. Disease-immunity balance analysis

[0056] Calculate the disease-free equilibrium (DFE) and endemic equilibrium (EE);

[0057] The disease-free equilibrium point represents the equilibrium state reached by the system when there are no infected people. When the number of infected and exposed people is set to zero, the equilibrium state of the system is: (S * ,E * ,I * ,R * )=(N,0,0,0).

[0058] The local equilibrium point represents the population equilibrium state when the disease persists in the society. By setting the derivatives of all states to zero, the values of each state in the SEIRS model are calculated to obtain:

[0059]

[0060] S4. Calculation of basic reproduction number

[0061] Using the next generation matrix method, the basic reproduction number R0 is calculated. The specific steps are as follows:

[0062] S41. Classification of infected and non-infected states:

[0063] For the SEIRS model, the infection status usually includes two variables: exposed individuals E and infected individuals I. In the early stages of the disease, it is assumed that all individuals are susceptible, that is, S ≈ N (total population), and both E and I are small.

[0064] S42. Construct a new infection rate matrix and the transfer matrix

[0065] New infection item: For E, the new infection rate is There are no new infections for I, so F I =0.

[0066] Transfer term: Let σ be the incubation rate (the rate at which exposed people become infected), γ be the recovery rate of infected people, and δ be the rate at which the immunity of recovered people declines. Then the transfer term is V E =σE,V I =-σE+γI.

[0067] S43. Construct the Jacobian matrix:

[0068] At the disease-free equilibrium (DFE) (i.e. S=N, E=0, I=0), And V take partial derivatives of E and I respectively, and we get

[0069] S44. Calculate the next generation matrix K:

[0070] Calculate V -1 Later you can get

[0071] therefore,

[0072] S45. Find the spectral radius:

[0073] The basic reproduction number R0 is the maximum eigenvalue of K. For the above matrix, its eigenvalue is λ2=0.

[0074] Therefore, the basic reproduction number is R0 represents the average number of secondary cases infected by an infected person in a completely susceptible population. When R0>1, the infection will spread; when R0<1, the infection will gradually subside.

[0075] For example, if β = 0.3 (unit day -1 ) and γ=0.1(unit day -1 ), then R0 = 3, which means that in a fully infected population, one infected person will cause 3 new infected people on average, and the infection will spread.

[0076] S5. Stability Analysis

[0077] By analyzing the stability of disease-free equilibrium and endemic equilibrium, the Jacobian matrix is calculated and its eigenvalues are solved.

[0078] Stability analysis is mainly performed by calculating the Jacobian matrix of the system at the equilibrium point and then solving the eigenvalues of the matrix. The specific steps are as follows:

[0079] S51. Determine the balance point:

[0080] Disease-free equilibrium point (DFE): When E=I=0, the system equilibrium state is S=N, E=0, I=0, R=0.

[0081] Local equilibrium (EE): By setting the derivatives of all states to zero, that is, Solve to obtain the equilibrium value of each state (the specific solution process depends on the model parameters).

[0082] S52. Construct the system Jacobian matrix:

[0083] For the SEIRS model, let the model equation be Then the Jacobian matrix J is a 4×4 matrix composed of partial derivatives of (S, E, I, R). At the disease-free equilibrium point (N, 0, 0, 0), some of its elements are:

[0084]

[0085] S53. Find the eigenvalue:

[0086] The eigenvalues are obtained by solving the characteristic equation det(J - λI) = 0. If the real part of all eigenvalues is negative, the equilibrium point is stable, meaning the system is approaching that equilibrium state. If the real part of any eigenvalue is greater than zero, the equilibrium point is unstable, and the system will deviate from that equilibrium state.

[0087] For example, suppose that at the DFE, by solving the characteristic equation of the above matrix, the eigenvalue is obtained as λ1 = β - γ (closely related to R0). When β < γ, λ1 < 0, and the system is stable; when β > γ, λ1 > 0, and the system is unstable, which means that the infection will spread.

[0088] S6. Dynamic simulation and prediction

[0089] Based on the above calculations, numerical simulation technology is used to simulate the dynamic equilibrium process under different immune decline rates and infection rates; and by adjusting the parameters, the future epidemic trend of long-term new crown in the population and the time of the peak of reinfection can be predicted.

[0090] By using numerical simulation technology to simulate the dynamic equilibrium process of the system under different immune decay rates (p) and infection rates (β), the specific steps are as follows:

[0091] S61. Parameter settings and initial conditions:

[0092] Set the SEIRS model parameters, such as:

[0093] Infection rate β = 0.3

[0094] Latency rate σ=0.2

[0095] Recovery rate γ = 0.1

[0096] Immune decline rate p = 0.05

[0097] And set the initial conditions, such as the total population N = 10 6 , the initial infected person I(0) = 100, the rest are susceptible S(0) = 10 6 -100, E(0)=0, R(0)=0.

[0098] S62. Numerical integration method:

[0099] Use numerical integration methods (e.g., the fourth-order Runge-Kutta method) to numerically solve the SEIRS differential equation. Set the time step Δt and the simulation duration (e.g., 365 days).

[0100] S63. Parameter sensitivity analysis:

[0101] In order to study the influence of different parameters on the dynamic balance of the system, the values of p and β are adjusted respectively.

[0102] For example, keeping other parameters unchanged, set p to 0.03, 0.05, and 0.07 respectively, and observe how changes in the rate at which recovered patients become susceptible again affect the equilibrium value of the number of long-term COVID-19 patients.

[0103] At the same time, adjust β from 0.25 to 0.35 to observe the changes in the infection spread rate and equilibrium state.

[0104] S64. Draw a time series curve:

[0105] For each set of parameter combinations, curves of S(t), E(t), I(t) and R(t) changing with time are plotted to intuitively show how the system tends from the initial state to a dynamic equilibrium state, and how the equilibrium state changes when the parameters change.

[0106] S65. Predicting the peak of reinfection:

[0107] By comparing different simulation results, we can determine under what parameter conditions the peak of infected person I(t) is most obvious and when the peak occurs, thereby predicting the time of reinfection peak.

[0108] For example, assuming parameters β = 0.3, σ = 0.2, γ = 0.1, and δ = 0.05, a 365-day Runge-Kutta simulation shows that the number of infected individuals, I(t), peaks on day 120 and then gradually stabilizes. However, when the immune decay rate, δ, is increased to 0.07, the simulation results show that the peak number of infected individuals increases, the equilibrium level shifts upward, and the peak of reinfection occurs earlier, at day 100. These numerical simulation results provide a scientific basis for medical departments to adjust intervention measures.

[0109] This embodiment also provides an electronic device. The following describes an electronic device that can perform the above-mentioned dynamic balance analysis method under long-term COVID-19.

[0110] Figure 2A structural block diagram of an electronic device 100 for implementing a dynamic balance analysis method under long coronavirus is shown, and the electronic device 100 includes: at least one memory 101 and at least one processor 102; the at least one memory 101 is coupled to the at least one processor 102, the at least one memory 101 is used to store a computer program, and the at least one processor 102 is used to call the computer program, and the computer program includes instructions. When the instructions are executed by the at least one processor, the electronic device executes the above-mentioned dynamic balance analysis method under long coronavirus.

[0111] The device provided in this embodiment and the dynamic balance analysis method under long-term new crown provided in this application belong to the same concept. The specific implementation process is detailed in the full text of the specification and will not be repeated here.

[0112] This embodiment also provides a computer storage medium. The following describes a computer storage medium containing the above-mentioned dynamic equilibrium analysis method under long-term new crown.

[0113] A computer storage medium includes computer instructions, which, when executed on an electronic device, enable the electronic device to execute the above-mentioned dynamic balance analysis method under long-term COVID-19.

[0114] Obviously, the above embodiments of the present invention are merely examples for the purpose of clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Those skilled in the art will appreciate that other variations or modifications can be made based on the above description. It is not necessary and impossible to enumerate all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the claims of the present invention.

Claims

1. A dynamic balance analysis method under COVID-19, characterized in that: The following steps are involved: S1. Establish the SEIRS model equation and calculate the various state values in the SEIRS model based on the disease-free equilibrium point and the endemic equilibrium point; S2. Calculate the basic reproduction number R0 using the next generation matrix method; S3. Analyze the stability of the disease-free equilibrium point and the local equilibrium point, calculate the Jacobian matrix and solve its eigenvalues; S4. Use numerical simulation technology to simulate the dynamic equilibrium process of the system under different immune decline rates and infection rates; By adjusting parameters, we can predict the future prevalence trend of long-term COVID-19 in the population and the time of the peak of reinfection.

2. The dynamic balance analysis method under the condition of long COVID-19 according to claim 1, characterized in that: The SEIRS model uses the following differential equation to describe the population changes in each state: Among them, S represents the number of susceptible people, E represents the number of exposed people, I represents the number of infected people, R represents the number of recovered people, and N = S + E + I + R represents the total population; β represents the infection rate, and the susceptible person S may be infected by contacting the infected person I; σ is the incubation rate, which indicates the rate at which the exposed person E enters the infectious state; γ represents the recovery rate of infected people; p is the rate at which recovered individuals' immunity declines and they re-enter a susceptible state.

3. The dynamic balance analysis method under the condition of long crown according to claim 2 is characterized in that: The disease-free equilibrium point represents the equilibrium state reached by the system when there are no infected people. When the number of infected and exposed people is zero, the equilibrium state of the system is: (S * ,E * ,I * ,R * )=(N,0,0,0).

4. The dynamic balance analysis method under the condition of long COVID-19 according to claim 2, characterized in that: In step S1, the local equilibrium point represents the population equilibrium state when the disease persists in the society. By setting the derivatives of all states to zero, the state values in the SEIRS model are calculated:

5. The dynamic balance analysis method under the condition of long crown according to claim 2 is characterized in that: Before establishing the SEIRS model, the conditions are initialized, the total population is set, and it is assumed that a part of the population is initially infected and the rest are susceptible.

6. The dynamic balance analysis method under the condition of long crown according to claim 2 is characterized in that: In step S2, the basic reproduction number R0 represents the average number of secondary cases infected by an infected person in a completely susceptible population. According to the SEIRS model parameters, R0 can be expressed as:

7. The dynamic equilibrium analysis method under the condition of long COVID-19 according to claim 1 or 2, characterized in that: In step S4, the dynamic equilibrium process of the system under different immune decay rates and infection rates is simulated by using numerical simulation technology. The steps are as follows: 1) Set the parameters and initial conditions of the SEIRS model; 2) Use numerical integration methods to numerically solve the SEIRS differential equation; set the time step Δt and simulation duration; 3) Parameter sensitivity analysis: adjust the values of δ and β respectively to study the impact of different parameters on the dynamic balance of the system; 4) Draw time series curves: For each parameter combination, plot the curves of S(t), E(t), I(t), and R(t) over time to visually show how the system moves from the initial state to a dynamic equilibrium state, and how the equilibrium state changes when the parameters are changed; 5) Predicting the peak of reinfection: By comparing different simulation results, predict the time of occurrence of the peak of reinfection.

8. An electronic device, characterized in that: It includes at least one memory and at least one processor; the at least one memory is coupled to the at least one processor, the at least one memory is used to store a computer program, the at least one processor is used to call the computer program, and the computer program includes instructions. When the instructions are executed by the at least one processor, the electronic device executes the dynamic balance analysis method under long-term COVID-19 as described in any one of claims 1 to 7.

9. A computer storage medium, characterized in that It includes computer instructions, which, when executed on an electronic device, enable the electronic device to execute the dynamic balance analysis method under long COVID-19 as described in any one of claims 1 to 7.

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