Method and device for estimating basic reproduction number of infectious disease, medium and equipment

Abstract

The disclosure provides an estimation method and device for a basic reproduction number of an infectious disease, a computer readable storage medium and an electronic device, relating to the technical field of medical data processing. The method comprises: determining the patient generation time of the infectious disease according to the incubation period of the infectious disease and the time from the onset of the infectious disease to the diagnosis, wherein the patient generation time is the time between the time point when the susceptible person is infected and enters the incubation period and the time point when the person becomes a remover; determining the first parameter of the differential equation set corresponding to the infectious disease model according to the patient generation time; determining the starting statistical time point, and obtaining the actual cumulative value of the infected person corresponding to the starting statistical time point to the current time point; and based on the differential equation set, the basic reproduction number of the infectious disease is inversely calculated according to the first parameter, the actual cumulative value of the infected person and the starting statistical time point. The technical scheme can determine the basic reproduction number with high accuracy in a timely manner in the early stage of the epidemic.

Description

[0001] Case Analysis

[0002] This patent application is a divisional application of patent application No. 202011254137.1, filed on November 11, 2020, entitled "Method, Apparatus, Medium and Device for Estimating the Basic Reproduction Number of Infectious Diseases". Technical Field

[0003] This disclosure relates to the field of medical data processing technology, and more specifically, to a method for estimating the basic reproduction number of an infectious disease, an apparatus for estimating the basic reproduction number of an infectious disease, and a computer-readable storage medium and electronic device for implementing the above method. Background Technology

[0004] During the normalization period of infectious disease outbreaks, it is necessary to effectively predict and estimate the transmissibility of infectious diseases.

[0005] Existing technologies use SIR or SEIR models to fit the existing number of patients. The basic reproduction number R0 at the beginning of the epidemic can be obtained through the relevant parameters of the fitted model.

[0006] However, due to the limited amount of data in the early stages of an infectious disease outbreak, this fitting method is prone to significant errors. Furthermore, even after the outbreak has progressed for a period (more than 10 days), while the amount of data is sufficiently large, the obtained R0 does not provide timely reference for policy decisions.

[0007] It should be noted that the information disclosed in the background section above is only used to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0008] The purpose of this disclosure is to provide a method, apparatus, computer-readable storage medium, and electronic device for estimating the basic reproduction number of an infectious disease, which can determine the basic reproduction number with high accuracy in the early stages of an epidemic, thereby helping to accurately assess the prevalence of the infectious disease and adjust reasonable prevention and control policies in a timely manner.

[0009] Other features and advantages of this disclosure will become apparent from the following detailed description, or may be learned in part from practice of this disclosure.

[0010] According to a first aspect of the present disclosure, a method for estimating the basic reproduction number of an infectious disease is provided, the method comprising:

[0011] Based on the incubation period of the infectious disease and the time from onset to diagnosis of the infectious disease, the patient generation time for the infectious disease is determined, wherein the patient generation time is the time between the time when a susceptible person is infected and enters the incubation period and the time when they become a removed person.

[0012] The first parameter of the differential equation system corresponding to the infectious disease model is determined based on the patient generation time.

[0013] Determine the starting statistical time point and obtain the cumulative value of actual infected persons from the starting statistical time point to the current time point;

[0014] Based on the system of differential equations, the basic reproduction number of the infectious disease is calculated in reverse according to the first parameter, the cumulative value of actual infected persons, and the starting statistical time point.

[0015] In one embodiment of this disclosure, based on the foregoing scheme, determining the patient generation time for the infectious disease according to the incubation period and the time from onset to diagnosis includes:

[0016] The first distribution is obtained by fitting the incubation period of the infectious disease to the distribution function;

[0017] The second distribution is obtained by fitting the duration from onset to diagnosis of the infectious disease to the distribution function;

[0018] The patient generation time is determined based on the parameter values ​​of the first distribution and the parameter values ​​of the second distribution.

[0019] In one embodiment of this disclosure, based on the foregoing scheme, both the first distribution and the second distribution are normal distributions; wherein, determining the patient generation duration based on the parameter values ​​of the first distribution and the parameter values ​​of the second distribution includes:

[0020] Obtain the first mean and first standard deviation of the first distribution to obtain the parameter values ​​of the first distribution, and obtain the second mean and second standard deviation of the second distribution to obtain the parameter values ​​of the second distribution; determine a first confidence level for the incubation period of the infectious disease, and determine a second confidence level for the duration from onset to diagnosis of the infectious disease; determine a confidence interval for the duration of patient generation based on the first mean, the first standard deviation and the first confidence interval, and the second mean, the second standard deviation and the second confidence interval.

[0021] In one embodiment of this disclosure, based on the foregoing scheme, the first parameter is the average probability that an infected person becomes a remover within a unit of time, wherein,

[0022] The first parameter of the differential equation system corresponding to the infectious disease model is determined based on the patient generation time, including:

[0023] The reciprocal of the patient generation time is determined as the first parameter.

[0024] In one embodiment of this disclosure, determining the starting statistical time point based on the foregoing scheme includes:

[0025] Obtain the earliest exposure time point of the infectious disease;

[0026] The starting statistical time point is obtained by extrapolating backward from the earliest exposure time point based on the incubation period of the infectious disease.

[0027] In one embodiment of this disclosure, based on the foregoing scheme and the system of differential equations, the basic reproduction number of the infectious disease is calculated backward from the first parameter, the cumulative value of actual infected persons, and the starting statistical time point, including:

[0028] Obtain the value range of the basic regeneration number and the iteration step size;

[0029] Based on the value range and the iteration step size, N basic reproduction number test values ​​are obtained;

[0030] The i-th test value of the differential equation system with respect to the second parameter is determined based on the i-th basic reproduction number test value, where i is a positive integer less than or equal to N;

[0031] Substituting the i-th test value of the second parameter, the first parameter, and the starting statistical time point into the system of differential equations, we obtain the cumulative value of the i-th infected person.

[0032] Obtain the cumulative value of the j-th tested infected person that has the smallest difference from the cumulative value of the actual infected persons, and take the j-th basic reproduction number test value corresponding to the cumulative value of the j-th tested infected person as the basic reproduction number of the infectious disease, where j is a positive integer less than or equal to N.

[0033] In one embodiment of this disclosure, based on the foregoing scheme, the infection model is a SIR model, SIR model or SEIR model with the deletion and removal portion removed.

[0034] In one embodiment of this disclosure, based on the foregoing scheme, the first distribution is a normal distribution, a Poisson distribution, or a gamma distribution; and the second distribution is a normal distribution, a Poisson distribution, or a gamma distribution.

[0035] According to a second aspect of the present disclosure, an estimation apparatus is provided, comprising: the first determining module, the second determining module, the acquisition module, and the estimation module described above.

[0036] The first determining module is configured to: determine the patient generation time of the infectious disease based on the incubation period of the infectious disease and the time from onset to diagnosis of the infectious disease, wherein the patient generation time is the time between the time when a susceptible person is infected and enters the incubation period and the time when the person becomes a removed person.

[0037] The aforementioned second determining module is configured to: determine the first parameter of the differential equation system corresponding to the infectious disease model based on the patient generation time;

[0038] The aforementioned acquisition module is configured to: determine the starting statistical time point, and acquire the cumulative value of actual infected persons from the starting statistical time point to the current time point;

[0039] The aforementioned estimation module is configured to: based on the system of differential equations, reverse-calculate the basic reproduction number of the infectious disease according to the first parameter, the cumulative value of actual infected persons, and the starting statistical time point.

[0040] According to a third aspect of the present disclosure, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the method for estimating the basic reproduction number of an infectious disease as described in the first aspect of the above embodiments.

[0041] According to a fourth aspect of the present disclosure, an electronic device is provided, comprising: one or more processors; and a storage device for storing one or more programs, which, when executed by the one or more processors, cause the one or more processors to implement the method for estimating the basic reproduction number of an infectious disease as described in the first aspect of the above embodiments.

[0042] The technical solutions provided in this disclosure may have the following beneficial effects:

[0043] Some embodiments of this disclosure provide a technical solution for estimating the basic reproduction number of an infectious disease based on a system of differential equations from an infectious disease model. On one hand, the duration of patient generation for the infectious disease is determined to obtain the first parameter of the aforementioned system of differential equations, thus ensuring that the unknowns in the current system of differential equations only include the basic reproduction number. On the other hand, the statistical start time point of the infectious disease is determined to obtain the cumulative value of actual infections from the start time point to the current time point. Further, the basic reproduction number of the infectious disease is calculated backward based on the system of differential equations containing only the basic reproduction number and the aforementioned cumulative value of actual infections. This technical solution allows for the determination of a relatively reasonable and accurate basic reproduction number in the early stages of an epidemic, thereby helping to accurately assess the prevalence of the infectious disease and adjust appropriate prevention and control policies in a timely manner. Simultaneously, this technical solution uses the cumulative value of infections from the aforementioned start time point to the current time point, rather than using daily infection values ​​fitted on a daily basis. This better avoids the impact of large fluctuations in the fitting during periods of low daily confirmed cases, further improving the accuracy of the basic reproduction number estimation.

[0044] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and are not intended to limit this disclosure. Attached Figure Description

[0045] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this disclosure and, together with the description, serve to explain the principles of this disclosure. It is obvious that the drawings described below are merely some embodiments of this disclosure, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort. In the drawings:

[0046] Figure 1 This diagram illustrates a system architecture schematic for a method and apparatus for estimating the basic reproduction number of an infectious disease in an exemplary embodiment of this disclosure.

[0047] Figure 2 A flowchart illustrating a method for estimating the basic reproduction number of an infectious disease according to an embodiment of the present disclosure is shown.

[0048] Figure 3 A flowchart illustrating a method for estimating the basic reproduction number of an infectious disease according to another embodiment of the present disclosure is shown.

[0049] Figure 4 A flowchart illustrating a method for estimating the basic reproduction number of an infectious disease according to yet another embodiment of the present disclosure is shown.

[0050] Figure 5 A schematic diagram of the structure of an apparatus for estimating the basic reproduction number of an infectious disease according to an embodiment of the present disclosure is shown.

[0051] Figure 6 This diagram illustrates the structure of a computer-readable storage medium in an exemplary embodiment of this disclosure.

[0052] Figure 7 A schematic diagram of the structure of an electronic device in an exemplary embodiment of this disclosure is shown. Detailed Implementation

[0053] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that this disclosure will be more thorough and complete, and will fully convey the concept of the exemplary embodiments to those skilled in the art.

[0054] Furthermore, the described features, structures, or characteristics can be combined in any suitable manner in one or more embodiments. Numerous specific details are provided in the following description to give a thorough understanding of embodiments of this disclosure. However, those skilled in the art will recognize that the technical solutions of this disclosure can be practiced without one or more of the specific details, or other methods, components, apparatuses, steps, etc., can be employed. In other instances, well-known methods, apparatuses, implementations, or operations are not shown or described in detail to avoid obscuring various aspects of this disclosure.

[0055] The block diagrams shown in the accompanying drawings are merely functional entities and do not necessarily correspond to physically independent entities. That is, these functional entities can be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor devices and / or microcontroller devices.

[0056] The flowcharts shown in the accompanying drawings are merely illustrative and do not necessarily include all content and operations / steps, nor do they necessarily have to be performed in the described order. For example, some operations / steps can be broken down, while others can be combined or partially combined; therefore, the actual execution order may change depending on the specific circumstances.

[0057] This example implementation first provides a system architecture for estimating the basic reproduction number of infectious diseases, which can be applied to various data processing scenarios. (Reference) Figure 1 As shown, the system architecture 100 may include terminal devices 101, 102, and 103, a network 104, and a server 105. The network 104 serves as the medium for providing communication links between the terminal devices 101, 102, and 103 and the server 105. The network 104 may include various connection types, such as wired or wireless communication links, or fiber optic cables, etc.

[0058] Users can use terminal devices 101, 102, and 103 to interact with server 105 via network 104 to receive or send request commands, etc. Various communication client applications can be installed on terminal devices 101, 102, and 103, such as image processing applications, shopping applications, web browser applications, search applications, instant messaging tools, email clients, social media platform software, etc.

[0059] Terminal devices 101, 102, and 103 can be various electronic devices with displays and web browsing capabilities, including but not limited to smartphones, tablets, laptops, and desktop computers.

[0060] Server 105 can determine the patient generation time for the infectious disease based on the incubation period and the time from onset to diagnosis (for example only). Server 105 can also determine the first parameter of the differential equation system corresponding to the infectious disease model based on the patient generation time (for example only), determine the starting statistical time point, and obtain the cumulative value of actual infected persons from the starting statistical time point to the current time point (for example only). Finally, based on the differential equation system, server 105 reverse-engineers the basic reproduction number of the infectious disease according to the first parameter, the cumulative value of actual infected persons, and the starting statistical time point.

[0061] In the early stages of an infectious disease outbreak, or in small-scale outbreaks under normalized epidemic conditions, everyone is susceptible, making the estimation of the "basic reproduction number" necessary. The basic reproduction number (R0) represents the average number of people a single infected person can infect during their illness, without intervention in an environment where everyone is susceptible. Therefore, in the early stages of an epidemic, the basic reproduction number is generally used to measure the actual transmissibility of the virus. Specifically, disease control can involve controlling the size of the basic reproduction number.

[0062] Furthermore, in order to estimate the basic reproduction number of infectious disease outbreaks and improve the accuracy of the estimation to a certain extent, this technical solution provides a method and apparatus for estimating the basic reproduction number of infectious diseases, a computer-readable storage medium, and an electronic device. The method for estimating the basic reproduction number of infectious diseases is explained below:

[0063] Figure 2 A flowchart illustrating a method for estimating the basic reproduction number of an infectious disease according to embodiments of the present disclosure is shown. (Reference) Figure 2 The method for estimating the basic reproduction number of an infectious disease provided in this embodiment includes:

[0064] Step S210: Determine the patient generation time for the infectious disease based on the incubation period of the infectious disease and the time from onset to diagnosis of the infectious disease;

[0065] Step S220: Determine the first parameter of the differential equation system corresponding to the infectious disease model based on the patient generation time.

[0066] Step S230: Determine the starting statistical time point, and obtain the cumulative number of actual infected persons from the starting statistical time point to the current time point; and,

[0067] Step S240: Based on the system of differential equations, the basic reproduction number of the infectious disease is calculated in reverse according to the first parameter, the cumulative value of actual infected persons, and the starting statistical time point.

[0068] Some embodiments of this disclosure provide technical solutions for estimating the basic reproduction number of an infectious disease based on a system of differential equations from an infectious disease model. The infectious disease model can be a traditional SIR model or a SEIR model, or a SIR model with the remover component removed. Since the early stages of an infectious disease outbreak involve almost no cured patients, this stage focuses more on estimating the transmission process. During the transmission stage, to more closely reflect the actual scenario of the early transmission stage and to improve the accuracy of the effective reproduction number estimation, the remover component can be temporarily disregarded. Therefore, using a SIR model with the remover component removed is more conducive to obtaining a more accurate basic reproduction number. This technical solution will use a SIR model with the remover component removed as an example to illustrate the estimation scheme for the basic reproduction number of an infectious disease.

[0069] In an exemplary embodiment, Figure 3 A flowchart illustrating a method for estimating the basic reproduction number of an infectious disease according to another embodiment of this disclosure is shown. The following is in conjunction with... Figure 3 right Figure 2 The specific implementation methods of each step in the illustrated embodiment are explained below:

[0070] refer to Figure 3 In S1, the construction of the infectious disease model is performed.

[0071] In this embodiment, a basic SIR model is first constructed:

[0072] The SIR model divides the total population into three categories: susceptibles (S represents the susceptible population), denoted as s(t), representing the number of people who are not infected at time t but are potentially susceptible to the disease; infected individuals (I represents the infectious population), denoted as i(t), representing the number of people who have been infected and are infectious at time t; and recovered individuals (R represents the recovered population who no longer have an impact on the spread of the epidemic due to recovery and immunity, effective isolation, death from the disease, etc.), denoted as r(t), representing the number of people who have been removed from the infected population at time t.

[0073] As the epidemic situation changes, the rate of change of the three population groups over time t (days) can be represented by the following system of differential equations (i.e., the system of differential equations described in step S220):

[0074]

[0075]

[0076]

[0077] refer to Figure 3 In S2, the initialization of the values ​​of S, I, and R is performed:

[0078] Where S(t), I(t), and R(t) represent the number of people in the three states at time t, respectively.

[0079] Assuming the total population is N, then N = S(t) + I(t) + R(t). It should be noted that the actual value of N does not affect the estimation of the basic reproduction number R0; here, N can be 1,000,000. In this embodiment, based on the conventional definition of the source of epidemic transmission, the initial values ​​are S(t) = N-1, R(t) = 0, and I(t) = 1.

[0080] Continue to refer to Figure 3 In S3, the mapping of the second parameter β and the estimation of the first parameter γ are performed:

[0081] 1) β (i.e., the second parameter mentioned above) is the average probability that a susceptible person S will be infected and enter the incubation period after contact between an infected person I and a susceptible person S, according to the definition:

[0082] β=R0*γ

[0083] 2) γ (i.e., the first parameter mentioned above) is the average probability of an infected person I transforming into a remover R within a unit of time, denoted as 1 / T. Wherein, T represents the time between the time when a susceptible person S is infected and enters the incubation period and the time when they transform into a remover R, which is denoted as "patient generation time" in this technical solution.

[0084] As a specific implementation of step S210, the above-mentioned patient generation time can be expressed as T = incubation period T1 + time from onset to diagnosis T2.

[0085] In an exemplary embodiment, a specific implementation of determining the patient generation time of an infectious disease includes: fitting the incubation period of the infectious disease to a distribution function to obtain a first distribution; fitting the time from onset to diagnosis of the infectious disease to a distribution function to obtain a second distribution; and determining the patient generation time based on the parameter values ​​of the first distribution and the parameter values ​​of the second distribution.

[0086] Taking COVID-19 as an example, the values ​​of the incubation period T1 and the time from onset to diagnosis T2 can be determined by obtaining the incubation period data published by various provinces and cities.

[0087] The incubation period T1 can be distributed using a normal distribution, a Poisson distribution, or a gamma distribution; similarly, the time from onset to diagnosis T2 can also be distributed using a normal distribution, a Poisson distribution, or a gamma distribution. This technical solution obtains the first distribution by fitting the incubation period T1 of an infectious disease using a normal distribution function, and obtains the second distribution by fitting the time from onset to diagnosis T2 of an infectious disease using a normal distribution function.

[0088] Furthermore, by obtaining the mean μ1 and standard deviation σ1 of the first normal distribution, and the mean μ2 and standard deviation σ2 of the second normal distribution, and calculating the confidence interval corresponding to a 95% confidence level, the confidence interval for the patient's generation time T can be expressed as:

[0089] [μ1+μ2-1.96(σ1+σ2),μ1+μ2+1.96(σ1+σ2)].

[0090] As a specific implementation of step S220, γ = 1 / T, thereby determining the value of the first parameter γ of the differential equation system.

[0091] It should be noted that the incubation period mentioned above is from the time when the pathogenic irritant enters the body or takes effect on the body until the body reacts or begins to show symptoms.

[0092] In summary, for the above set of equations, given the initial values ​​S(t) = N-1, R(t) = 0, I(t) = 1, the first parameter γ = 1 / T, and the second parameter β = R0 * γ, and given that the patient generation time can be determined by fitting actual values, it can be seen that only the parameter R0 (the infection rate per contact) is the parameter to be estimated.

[0093] Continue to refer to Figure 3 In S4, the following steps are performed: determining the initial statistical time point t0, and calculating the value of infected individuals I(t) within the time period from the initial statistical time point t0 to the current time t.

[0094] In an exemplary embodiment, the starting statistical time point t0 is determined through step S230. Specifically, the starting statistical time point is obtained by acquiring the earliest exposure time point of the infectious disease and extrapolating it backward based on the incubation period of the infectious disease.

[0095] For example, based on the investigation of existing cases of COVID-19, the earliest exposure time can be determined according to the patient's past exposure locations and corresponding exposure times, i.e., the earliest exposure time point T0 of the infectious disease. Given that the source of infection is already infectious at the earliest exposure time point T0, it is necessary to trace back in conjunction with the incubation period T1. Considering that infectiousness generally develops after the middle of the incubation period, it is assumed that at T0, the first source of infection is already in the 60% (exemplary) stage of the incubation period, equivalent to having passed T1*60% of the time. Therefore, the infection time t0 of the first case is T1*0.6 days before T0 (for example, if T0 is January 11th, T1 = 5 days, then the infection time of the first case is 5*0.6 = 3 days before January 11th, i.e., January 8th).

[0096] t0 = T0 - T1 * s%

[0097] Wherein, the positive number s is a value determined according to actual needs, and in the above embodiment, the value is 60.

[0098] In this embodiment, the infection time of the first case is reasonably estimated by extrapolating the incubation period based on the earliest case discovery time in the news, which helps to improve the rationality and accuracy of the estimation of the basic reproduction number.

[0099] Furthermore, based on the above set of differential equations, the cumulative value of actual infected persons I(t) from the initial statistical time point t0 to the current time point t can be determined.

[0100] It should be noted that I(t) represents the total number of confirmed cases from the initial statistical time point t0 to the current time. The early R0 of the epidemic is estimated by using a cumulative value (rather than a daily fitted value). This method has less fluctuation than the traditional method of fitting the SIR curve based on daily data. Especially when the number of new cases fluctuates greatly in the early stage of the epidemic, this technique can better avoid the impact of large fluctuations in the fitting when the number of confirmed cases is low each day, thereby improving the accuracy of the basic reproduction number estimation of this infectious disease.

[0101] Continue to refer to Figure 3In step S5, the estimation of the basic reproduction number R0 is performed. Specifically, this technical solution uses the test value of the basic reproduction number corresponding to the minimum difference between the statistical value and the actual value of I(t) as the estimated basic reproduction number, wherein the statistical value of I(t) is related to the test value of the basic reproduction number substituted into the system of differential equations.

[0102] One specific implementation of step S240 is as follows: Figure 4 A flowchart illustrating a method for estimating the basic reproduction number of an infectious disease according to another embodiment of this disclosure is shown. (Reference) Figure 4 The method includes:

[0103] Step S410: Obtain the value range and iteration step size of the basic reproduction number (e.g., value range 0-10, iteration step size = 0.01 each time); Step S420: Obtain N basic reproduction number test values ​​based on the value range and the iteration step size.

[0104] For example, the basic reproduction number R0 of this infectious disease takes values ​​in the range [X1, X...]. N The test values ​​of the N basic reproduction numbers, determined based on the iteration step size, are: X1, X2, ..., X i ,……,X N , where i is a positive integer less than or equal to N.

[0105] Continue to refer to Figure 4 In step S430, the i-th test value of the differential equation system with respect to the second parameter is determined based on the i-th basic regeneration number test value.

[0106] For example, the basic reproduction number R0 takes the value X. i At that time, according to β=R0*γ, the i-th test value β of the second parameter of the differential equation system is... i =X i *γ.

[0107] Further, in step S440, the i-th test value β of the second parameter is... i Substituting the first parameter γ and the initial statistical time point t0 into the differential equation Then the cumulative value I(t)' of the i-th infected test subject can be obtained. And, in step S450, the cumulative value of the j-th infected test subject with the smallest difference from the actual cumulative value of infected subjects is obtained, and the j-th basic reproduction number test value X corresponding to the j-th cumulative value of the j-th infected test subject is set. j The basic reproduction number of the infectious disease is defined as j, where j is a positive integer less than or equal to N.

[0108] Taking COVID-19 as an example, the daily number of new cases in various regions was obtained, and the cumulative number of actual infections was determined. This was then used in the SIR model, which describes the rate of change of the infectious population over time. The cumulative number of infected individuals is calculated, which is the cumulative number of infected individuals tested, I(t)'.

[0109] By adjusting the value of R0 to X1, X2, ..., X i ,……, or X N This ensures that the cumulative number of infected individuals tested, I(t)', is close to the actual cumulative number of patients. In this process, we only refer to the following differential equation in the SIR model:

[0110]

[0111] In the early stages of an outbreak, when the epidemic is spreading uncontrolled, this invention focuses more on estimating the transmission process. During this stage, cured patients should not be considered, so the part involving the removal of patients R in the above formula can be removed to obtain a more accurate estimate of I(t):

[0112]

[0113] For example, in the evaluation phase of I(t), the first parameter γ can be a value estimated according to the above embodiment, that is, the γ value determined according to γ ​​= 1 / T when the mean of the patient's generation duration T is 95% confidence interval = μ1 + μ2. Further, by iterating through the test values ​​of R0 within its range, and combining with the ordinary differential equation (ODE), the following system of equations is solved to calculate the corresponding value of I(t):

[0114]

[0115]

[0116] When the obtained value of I(t) (the cumulative number of infected individuals tested, I(t)') is found to be equal to or very close to the actual cumulative number of cases, the corresponding R0 is output as the early R0 of this epidemic. At this point, R0 is estimated based on T = μ1 + μ2. To obtain the value of the 95% confidence interval, it can be inferred using β = R0 × (μ1 + μ2). When β is fixed, the 95% confidence interval corresponding to R0 is:

[0117] [R0×(μ1+μ2) / [μ1+μ2+1.96×(σ1+σ2)], R0×(μ1+μ2) / [μ1+μ2-1.96×(σ1+σ2)]].

[0118] The final output is the basic reproduction number R0 value with a 95% confidence interval.

[0119] This technical solution estimates the transmissibility of infectious diseases, allowing for a relatively accurate assessment of the epidemic's prevalence in the early stages of an outbreak. The specific timing of intervention for diseases with high transmissibility (e.g., COVID-19) will significantly impact the final total number of cases. Therefore, this invention enables early assessment of infectious disease risks and timely warnings. Furthermore, this technical solution provides a quantitative basis for deciding the intensity of intervention measures. When the transmissibility of an existing infectious disease outbreak is within a controllable range, overly strict policies can be avoided, or the intensity of strict policies can be adjusted promptly after implementation to minimize losses to people's livelihoods.

[0120] Those skilled in the art will understand that all or part of the steps of the above embodiments are implemented as a computer program executed by a processor (including CPU and GPU). When the computer program is executed by the CPU, it performs the functions defined by the methods provided in this disclosure. The program can be stored in a computer-readable storage medium, such as a read-only memory, a magnetic disk, or an optical disk.

[0121] Furthermore, it should be noted that the above figures are merely illustrative representations of the processes included in the methods according to exemplary embodiments of this disclosure, and are not intended to be limiting. It is readily understood that the processes shown in the above figures do not indicate or limit the temporal order of these processes. Additionally, it is readily understood that these processes may be executed synchronously or asynchronously, for example, in multiple modules.

[0122] The following describes an embodiment of the apparatus disclosed herein, which can be used to perform the basic reproduction number estimation method for infectious diseases described above.

[0123] Figure 5 A schematic diagram of a device for estimating the basic reproduction number of an infectious disease according to an embodiment of the present disclosure is shown, with reference to... Figure 5 The basic reproduction number estimation device 500 for infectious diseases provided in this embodiment includes: the first determining module 501, the second determining module 502, the acquisition module 503 and the estimation module 504 mentioned above.

[0124] The first determining module 501 is configured to: determine the patient generation time of the infectious disease based on the incubation period of the infectious disease and the time from onset to diagnosis of the infectious disease, wherein the patient generation time is the time between the time when a susceptible person is infected and enters the incubation period and the time when the person becomes a removed person.

[0125] The second determining module 502 mentioned above is configured to: determine the first parameter of the differential equation system corresponding to the infectious disease model based on the patient generation time;

[0126] The aforementioned acquisition module 503 is configured to: determine the starting statistical time point, and acquire the cumulative value of actual infected persons from the starting statistical time point to the current time point;

[0127] The aforementioned estimation module 504 is configured to: based on the system of differential equations, reverse-calculate the basic reproduction number of the infectious disease according to the first parameter, the cumulative value of actual infected persons, and the starting statistical time point.

[0128] In an exemplary embodiment, based on the foregoing scheme, the first determining module 501 is specifically configured as follows:

[0129] A first distribution is obtained by fitting the incubation period of the infectious disease to a distribution function; a second distribution is obtained by fitting the time from onset to diagnosis of the infectious disease to a distribution function; and the patient generation time is determined based on the parameter values ​​of the first distribution and the parameter values ​​of the second distribution.

[0130] In one embodiment of this disclosure, based on the foregoing scheme, both the first distribution and the second distribution are normal distributions; wherein, the first determining module 501 is specifically configured to:

[0131] Obtain the first mean and first standard deviation of the first distribution to obtain the parameter values ​​of the first distribution, and obtain the second mean and second standard deviation of the second distribution to obtain the parameter values ​​of the second distribution; determine a first confidence level for the incubation period of the infectious disease, and determine a second confidence level for the duration from onset to diagnosis of the infectious disease; determine a confidence interval for the duration of patient generation based on the first mean, the first standard deviation and the first confidence interval, and the second mean, the second standard deviation and the second confidence interval.

[0132] In an exemplary embodiment, based on the foregoing scheme, the first parameter is the average probability that an infected person becomes a remover within a unit of time, wherein the second determining module 502 is specifically configured as follows:

[0133] The reciprocal of the patient generation time is determined as the first parameter.

[0134] In an exemplary embodiment, based on the foregoing scheme, the acquisition module 503 is specifically configured as follows:

[0135] Obtain the earliest exposure time of the infectious disease; and, based on the incubation period of the infectious disease, calculate backward from the earliest exposure time to obtain the starting statistical time point.

[0136] In an exemplary embodiment, based on the foregoing scheme, the estimation module 504 is specifically configured as follows:

[0137] Obtain the value range and iteration step size of the basic reproduction number; obtain N basic reproduction number test values ​​based on the value range and iteration step size; determine the i-th test value of the differential equation system with respect to the second parameter based on the i-th basic reproduction number test value, where i is a positive integer less than or equal to N; substitute the i-th test value with respect to the second parameter, the first parameter, and the starting statistical time point into the differential equation system to obtain the i-th cumulative value of the infected person in the test; and obtain the j-th cumulative value of the infected person in the test with the smallest difference from the actual cumulative value of the infected person in the test, and take the j-th basic reproduction number test value corresponding to the j-th cumulative value of the infected person in the test as the basic reproduction number of the infectious disease, where j is a positive integer less than or equal to N.

[0138] In an exemplary embodiment, based on the foregoing scheme, the infection model is an SIR model, an SIR model, or an SEIR model with the remover portion removed.

[0139] In an exemplary embodiment, based on the foregoing scheme, the first distribution is a normal distribution, a Poisson distribution, or a gamma distribution; and the second distribution is a normal distribution, a Poisson distribution, or a gamma distribution.

[0140] Since the functional modules of the basic reproduction number estimation device for infectious diseases in the exemplary embodiments of this disclosure correspond to the steps of the example embodiments of the basic reproduction number estimation method for infectious diseases described above, for details not disclosed in the embodiments of the basic reproduction number estimation device for infectious diseases in this disclosure, please refer to the embodiments of the basic reproduction number estimation method for infectious diseases described above in this disclosure.

[0141] From the above description of the embodiments, those skilled in the art will readily understand that the exemplary embodiments described herein can be implemented by software or by combining software with necessary hardware. Therefore, the technical solutions according to the embodiments of this disclosure can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (such as a CD-ROM, USB flash drive, external hard drive, etc.) or on a network, including several instructions to cause a computing device (such as a personal computer, server, mobile terminal, or network device, etc.) to execute the methods according to the embodiments of this disclosure.

[0142] In exemplary embodiments of this disclosure, a computer-readable storage medium capable of implementing the above-described methods is also provided. This medium stores a program product capable of implementing the methods described in this specification. In some possible embodiments, various aspects of this disclosure may also be implemented as a program product including program code, which, when run on a terminal device, causes the terminal device to perform the steps described in the "Exemplary Methods" section of this specification according to various exemplary embodiments of this disclosure.

[0143] refer to Figure 6 As shown, a program product 600 for implementing the above-described method according to an embodiment of the present disclosure is described. This product may employ a portable compact disc read-only memory (CD-ROM) and include program code, and may run on a terminal device, such as a personal computer. However, the program product of the present disclosure is not limited thereto. In this document, the readable storage medium may be any tangible medium containing or storing a program that may be used by or in conjunction with an instruction execution system, apparatus, or device.

[0144] The above-described program product may employ any combination of one or more readable media. A readable medium may be a readable signal medium or a readable storage medium. A readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of readable storage media (a non-exhaustive list) include: electrical connections having one or more wires, portable disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof.

[0145] Computer-readable signal media may include data signals propagated in baseband or as part of a carrier wave, carrying readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A readable signal medium may also be any readable medium other than a readable storage medium, capable of sending, propagating, or transmitting programs for use by or in conjunction with an instruction execution system, apparatus, or device.

[0146] The program code contained on the readable medium may be transmitted using any suitable medium, including but not limited to wireless, wired, optical fiber, RF, etc., or any suitable combination thereof.

[0147] Program code for performing the operations of this disclosure can be written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Java and C++, and conventional procedural programming languages ​​such as C or similar languages. The program code can execute entirely on the user's computing device, partially on the user's computing device, as a standalone software package, partially on the user's computing device and partially on a remote computing device, or entirely on a remote computing device or server. In cases involving remote computing devices, the remote computing device can be connected to the user's computing device via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computing device (e.g., via the Internet using an Internet service provider).

[0148] Furthermore, in an exemplary embodiment of this disclosure, an electronic device capable of implementing the above-described method is also provided.

[0149] Those skilled in the art will understand that various aspects of this disclosure can be implemented as a system, method, or program product. Therefore, various aspects of this disclosure can be specifically implemented in the following forms: a completely hardware implementation, a completely software implementation (including firmware, microcode, etc.), or a combination of hardware and software aspects, collectively referred to herein as a "circuit," "module," or "system."

[0150] The following reference Figure 7 To describe an electronic device 700 according to such an embodiment of the present disclosure. Figure 7 The electronic device 700 shown is merely an example and should not impose any limitation on the functionality and scope of use of the embodiments disclosed herein.

[0151] like Figure 7 As shown, the electronic device 700 is manifested in the form of a general-purpose computing device. The components of the electronic device 700 may include, but are not limited to: at least one processing unit 710, at least one storage unit 720, and a bus 730 connecting different system components (including storage unit 720 and processing unit 710).

[0152] The aforementioned storage unit stores program code, which can be executed by the aforementioned processing unit 710, causing the processing unit 710 to perform the steps described in the "Exemplary Methods" section of this specification according to various exemplary embodiments of this disclosure. For example, the aforementioned processing unit 710 can perform, as follows: Figure 2The steps are as follows: Step S210, determining the patient generation time of the infectious disease based on the incubation period and the time from onset to diagnosis, wherein the patient generation time is the time between the time when a susceptible person is infected and enters the incubation period and the time when they become a removed person; Step S220, determining the first parameter of the differential equation system corresponding to the infectious disease model based on the patient generation time; Step S230, determining the starting statistical time point and obtaining the cumulative value of actual infected persons from the starting statistical time point to the current time point; and Step S240, calculating the basic reproduction number of the infectious disease in reverse based on the differential equation system, the first parameter, the cumulative value of actual infected persons, and the starting statistical time point.

[0153] For example, the processing unit 710 described above can also perform the following: Figure 3 or Figure 4 The method for estimating the basic reproduction number of the infectious disease shown.

[0154] Storage unit 720 may include a readable medium in the form of a volatile storage unit, such as random access memory (RAM) 7201 and / or cache memory 7202, and may further include a read-only memory (ROM) 7203.

[0155] The storage unit 720 may also include a program / utility 7204 having a set (at least one) program module 7205, such program module 7205 including but not limited to: an operating system, one or more application programs, other program modules and program data, each or some combination of these examples may include an implementation of a network environment.

[0156] Bus 730 can represent one or more of several types of bus structures, including a memory cell bus or memory cell controller, a peripheral bus, a graphics acceleration port, a processing unit, or a local bus using any of the various bus structures.

[0157] The electronic device 700 can also communicate with one or more external devices 800 (e.g., keyboard, pointing device, Bluetooth device, etc.), and with one or more devices that enable a user to interact with the electronic device 700, and / or with any device that enables the electronic device 700 to communicate with one or more other computing devices (e.g., router, modem, etc.). This communication can be performed via an input / output (I / O) interface 750. Furthermore, the I / O interface 750 is connected to a display unit 740 to transmit content to be displayed to the display unit 740 for user viewing.

[0158] Furthermore, the electronic device 700 can also communicate with one or more networks (e.g., local area networks (LANs), wide area networks (WANs), and / or public networks, such as the Internet) via network adapter 760. As shown in the figure, network adapter 760 communicates with other modules of the electronic device 700 via bus 730. It should be understood that, although not shown in the figure, other hardware and / or software modules can be used in conjunction with the electronic device 700, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage systems.

[0159] From the above description of the embodiments, those skilled in the art will readily understand that the exemplary embodiments described herein can be implemented by software or by combining software with necessary hardware. Therefore, the technical solutions according to the embodiments of this disclosure can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (such as a CD-ROM, USB flash drive, external hard drive, etc.) or on a network, including several instructions to cause a computing device (such as a personal computer, server, terminal device, or network device, etc.) to execute the methods according to the embodiments of this disclosure.

[0160] Furthermore, the above figures are merely illustrative of the processes included in the method according to exemplary embodiments of this disclosure and are not intended to be limiting. It is readily understood that the processes shown in the above figures do not indicate or limit the temporal order of these processes. Additionally, it is readily understood that these processes may be executed synchronously or asynchronously, for example, in multiple modules.

[0161] Other embodiments of this disclosure will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not disclosed herein. The specification and embodiments are to be considered exemplary only, and the true scope and spirit of this disclosure are indicated by the claims.

Claims

1. A method for estimating the basic reproduction number of an infectious disease, characterized in that, include: Based on the incubation period of the infectious disease and the time from onset to diagnosis of the infectious disease, the patient generation time for the infectious disease is determined, wherein the patient generation time is the time between the time when a susceptible person is infected and enters the incubation period and the time when they become a removed person. The first parameter of the differential equation system corresponding to the infectious disease model is determined based on the patient generation time. Determine the starting statistical time point and obtain the cumulative value of actual infected persons from the starting statistical time point to the current time point; Obtain the value range of the basic reproduction number and the iteration step size; wherein the value range is 0-10, and the iteration step size is 0.01 each time; Based on the value range and the iteration step size, N basic reproduction number test values ​​are obtained; based on the i-th basic reproduction number test value, the i-th test value of the differential equation system with respect to the second parameter is determined, where i is a positive integer less than or equal to N; Substituting the i-th test value of the second parameter, the first parameter, and the starting statistical time point into the system of differential equations, we obtain the cumulative value of the i-th infected person. Obtain the cumulative value of the j-th tested infected person that has the smallest difference from the cumulative value of the actual infected persons, and take the j-th basic reproduction number test value corresponding to the cumulative value of the j-th tested infected person as the basic reproduction number of the infectious disease, where j is a positive integer less than or equal to N.

2. The estimation method according to claim 1, characterized in that, Based on the incubation period of the infectious disease and the time from onset to diagnosis, the patient generation time for the infectious disease is determined, including: The first distribution is obtained by fitting the incubation period of the infectious disease to the distribution function; The second distribution is obtained by fitting the duration from onset to diagnosis of the infectious disease to the distribution function; The patient generation time is determined based on the parameter values ​​of the first distribution and the parameter values ​​of the second distribution.

3. The estimation method according to claim 2, characterized in that, Both the first distribution and the second distribution are normal distributions; wherein, Determining the patient generation duration based on the parameter values ​​of the first distribution and the second distribution includes: Obtain the first mean and first standard deviation of the first distribution to obtain the parameter values ​​of the first distribution; and obtain the second mean and second standard deviation of the second distribution to obtain the parameter values ​​of the second distribution. Determine a first confidence level for the incubation period of the infectious disease, and a second confidence level for the time from onset of symptoms to diagnosis of the infectious disease; The confidence interval for the patient generation duration is determined based on the first mean, the first standard deviation, and the first confidence level, as well as the second mean, the second standard deviation, and the second confidence level.

4. The estimation method according to claim 1, characterized in that, The first parameter is the average probability that an infected person becomes a remover within a unit of time, where, The first parameter of the differential equation system corresponding to the infectious disease model is determined based on the patient generation time, including: The reciprocal of the patient generation time is determined as the first parameter.

5. The estimation method according to claim 1, characterized in that, Determine the starting statistical time point, including: Obtain the earliest exposure time point of the infectious disease; The starting statistical time point is obtained by extrapolating backward from the earliest exposure time point based on the incubation period of the infectious disease.

6. The estimation method according to any one of claims 1 to 5, characterized in that, The infectious disease model is a SIR model, SIR model, or SEIR model with the deletion / removal part removed.

7. A device for estimating the basic reproduction number of an infectious disease, characterized in that, include: The first determining module is configured to: determine the patient generation time of the infectious disease based on the incubation period of the infectious disease and the time from onset to diagnosis of the infectious disease, wherein the patient generation time is the time between the time when a susceptible person is infected and enters the incubation period and the time when the person becomes a removed person; The second determining module is configured to: determine the first parameter of the differential equation system corresponding to the infectious disease model based on the patient generation time; The first acquisition module is configured to: determine the starting statistical time point, and acquire the cumulative value of actual infected persons from the starting statistical time point to the current time point; The second acquisition module is configured to: acquire the value range of the basic regeneration number and the iteration step size; wherein the value range is 0-10, and the iteration step size is 0.01 each time; The test value acquisition module is configured to obtain N basic reproduction number test values ​​based on the value range and the iteration step size. The third determining module is configured to: determine the i-th test value of the differential equation system with respect to the second parameter based on the i-th basic reproduction number test value, where i is a positive integer less than or equal to N; The substitution module is configured to: substitute the i-th test value of the second parameter, the first parameter, and the starting statistical time point into the system of differential equations to obtain the cumulative value of the i-th infected person; The fourth determining module is configured to: obtain the cumulative value of the j-th test infected person with the smallest difference from the cumulative value of the actual infected persons, and take the j-th basic reproduction number test value corresponding to the cumulative value of the j-th test infected person as the basic reproduction number of the infectious disease, where j is a positive integer less than or equal to N.

8. A computer-readable storage medium, characterized in that, It stores a computer program that, when executed by a processor, implements a method for estimating the basic reproduction number of an infectious disease as described in any one of claims 1 to 6.

9. An electronic device, characterized in that, include: One or more processors; A storage device for storing one or more programs, which, when executed by one or more processors, cause the one or more processors to implement the method for estimating the basic reproduction number of an infectious disease as described in any one of claims 1 to 6.

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