An early dynamics reconstruction method of infectious diseases based on metapopulation model

Abstract

The application provides an early-stage dynamic reconstruction method of infectious diseases based on a population model, and belongs to the technical field of infectious disease modeling and risk assessment. Compared with the traditional population model which only focuses on a single dimension such as space or age, the application simultaneously considers age grouping, city migration and multiple disease states, significantly improves the model resolution and is more consistent with the actual transmission scenario, such as the cross-age and cross-city transmission characteristics of COVID-19. The application introduces asymptomatic infected persons and pre-symptom period states, quantifies their relative infectivity and more accurately depicts the early-stage transmission dynamics than the traditional model. The application uses a differential evolution adaptive metropolis algorithm (DREAM algorithm) to replace the traditional Markov chain Monte Carlo method (MCMC), improves the parameter convergence speed through multi-chain parallel search and adaptive parameter adjustment, and is particularly suitable for rapid fitting under the condition of sparse early-stage data.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of infectious disease modeling and risk assessment, and particularly relates to an infectious disease early dynamics reconstruction method based on a set population model. BACKGROUND

[0002] The infectious disease transmission dynamics model is a mechanism-based model, a mathematical tool for abstracting the spatiotemporal transmission process of infectious diseases, and a scientific bridge connecting the microscopic pathogen replication process to the macroscopic social phenomenon. It provides a reasoning and calculation method for studying how these factors interact with each other, and can be used for practical applications such as infectious disease transmission prediction, hazard effect assessment, intervention optimization, counterfactual reasoning, etc.

[0003] The compartment model is the main carrier of infectious disease dynamics research since the 20th century. Compartment models are simple to construct and easy to analyze, such as the well-known SIR and SEIR models. These models can be rigorously mathematically analyzed through initial value problems, equilibrium problems, and oscillation problems of differential equations, and can explain the complex system behaviors such as exponential growth, oscillation, and disappearance of cases in infectious disease transmission. They are favored by theoretical epidemiologists. In addition to theoretical analysis, compartment models, combined with actual geographical, population, social behavior, and case monitoring data, have great practical application value in actual epidemic dynamics reconstruction, parameter estimation, scenario simulation, etc., and are still the most widely used infectious disease dynamics model today.

[0004] The set population model is a trade-off between realistic representation and computational efficiency of infectious disease models. In the set population model, the total population N is divided into M different populations, Each population i maintains a specific compartment model S i (t),I i (t),R i (t), the inflow and outflow of the population in each compartment are determined by the state of other compartments within and between populations and the inter-population population mixing contact pattern. For example, an age-group-based set population model is constructed based on survey data of contact between different age groups; a spatial set population model is constructed by combining multiple cities into a population, with contact risks between cities established through population flow patterns. In the set population model, susceptible individuals in population i are at risk of infection from both the population and other populations:

[0005]

[0006] Where p represents the probability of an effective contact resulting in an infection event; C ij(t) represents the number of times a susceptible individual from population i comes into contact with all people in population j per unit time. It is called the mixed contact pattern, which represents the non-uniform mixing between different populations. It is usually synthesized by population migration matrix, age heterogeneous contact matrix, etc.

[0007] Ensemble population models offer a good balance between realistic representation and computational efficiency, especially useful in early-stage disease dynamics driven primarily by large-scale population movement. Spatial ensemble population models can also simulate some interventions such as traffic restrictions and social distancing, making them the most widely used type of ensemble population model. In constructing spatial ensemble populations, population allocation can be based on administrative divisions or user-defined spatial regions. Different spatial populations can move at any time through migration patterns, leading to individuals in different disease states within one population entering other populations, making effective contact, and causing cross-regional transmission. Therefore, state transitions between different population cells may depend on population and disease parameters of other relevant states within the same region, as well as the contact structure with populations in other regions. The principle of the spatial ensemble population algorithm is as follows: Figure 1 As shown. Figure 1 This represents a spatial ensemble population (SEIR) model consisting of three cities, A, B, and C. At the initial time T of each simulation time step, people in various disease states migrate between cities according to certain patterns. New immigrants mix evenly with the local, non-migrating population to form a temporary population, leading to the importation, export, and local transmission of the epidemic. To maintain a relatively stable population size for each spatial population, after realizing disease transmission and updating population states at the current time step, the population migrates back to its initial position, entering time T+1, and the above calculation process is repeated.

[0008] The existing technologies described above have the following drawbacks:

[0009] Insufficient model granularity: Traditional ensemble population models usually only consider the heterogeneity of age or space in the process of infectious disease transmission, failing to fully integrate age and spatial heterogeneity, resulting in a large deviation in the reconstruction of the dynamics of cross-regional transmission of infectious diseases.

[0010] Simplified treatment process: Traditional spatial ensemble population models do not adequately consider the differences in infectivity such as asymptomatic infected persons and the prodromal period of symptoms, resulting in limited accuracy in reconstructing transmission dynamics.

[0011] Data integration limitations: Traditional spatial ensemble population models lack multi-source data, such as dynamic coupling of population mobility matrices, age heterogeneous contact matrices, and epidemiological parameters, which limits their ability to represent reality.

[0012] Low parameter estimation efficiency: The traditional Markov Chain Monte Carlo (MCMC) method has a slow convergence speed, which makes it difficult to adapt to the fast parameter fitting requirements in the early stages of emerging infectious diseases where data is scarce. Summary of the Invention

[0013] In view of this, this invention integrates the age and spatial heterogeneity of infectious disease transmission, comprehensively considers different disease stages and complex treatment processes, and proposes an early dynamic reconstruction method for emerging infectious diseases based on an ensemble population model to improve the accuracy of infectious disease dynamic reconstruction. At the same time, it improves the parameter estimation algorithm to achieve efficient estimation of key epidemiological parameters under limited data conditions.

[0014] A method for reconstructing the early dynamics of infectious diseases based on an ensemble population model includes: constructing a dynamic model based on the transmission process of emerging infectious diseases, considering age and spatial population movement factors.

[0015]

[0016] Where, λ a This represents the probability that a susceptible individual of age a will be infected per unit of time. This represents the number of susceptible individuals in age group a within city c; This represents the number of susceptible individuals in age group a within city c; This represents the number of symptomatic infected individuals in city c, aged a, who are infectious but have not yet shown symptoms. This represents the number of asymptomatic carriers of age group a in city c; This represents the number of mild and moderate cases in the infectious period in age group a within city c; This represents the number of severe and critically ill cases in age group a within city c who are in the infectious period but have not yet progressed to hospitalization. This represents the number of cases in city c where age group a requires routine hospitalization; This represents the number of cases in city c whose age group a requires ICU care; This represents the number of severe and critically ill cases in isolation within city c, specifically those in age group a. This represents the number of mild to moderate cases in isolation in city c, where age a is the age group. This represents the cumulative number of people in age group a who have recovered in city c. This represents the cumulative number of deaths in age group C within city C. Let A and B represent the number of people in city C whose age group a and age group j may move to other cities, respectively. This represents the total number of people in city c who may move to other cities. and Correspondingly, this represents the number of susceptible individuals in age group a in city i; and Correspondingly, it represents the total number of people in city i who may move to other cities; and Correspondingly, this represents the number of symptomatic infected individuals of age group a in city i who have become infectious but have not yet shown symptoms; and Correspondingly, this represents the number of asymptomatic carriers of age group a in city i; and Correspondingly, this represents the number of ordinary and mild cases of age group a in city i that are in the infectious period; and Correspondingly, this represents the number of severe and critical cases of age group a in city i who are in the infectious period but have not yet progressed to hospitalization; and Correspondingly, this represents the cumulative number of people in age group a in city i who have recovered. This represents the summation of variables over all ages; This represents the summation of variables over all cities; This represents the rate of change over time in the number of susceptible individuals of age group a in city c. This represents the rate of change over time in the number of people in age group a in city c who are infected but have not yet become infectious. This represents the rate of change over time in the number of symptomatic infected individuals of age group a in city c who have become infectious but have not yet shown symptoms. This represents the rate of change over time in the number of asymptomatic carriers of age group a in city c. This represents the rate of change over time in the number of severe and critically ill cases of age group a in city c who are in the infectious period but have not yet progressed to hospitalization. This represents the rate of change over time in the number of ordinary and mild cases of age group a in the infectious period within city c; This represents the rate of change over time in the number of severe and critically ill cases in isolation within age group a in city c; This represents the rate of change over time in the number of mild to moderate cases in isolation within age group a in city c. This represents the rate of change over time in the number of cases in city c where age group a requires routine hospitalization; This represents the rate of change over time in the number of cases in city c with age group a requiring ICU care; This represents the rate of change over time in the cumulative number of people in age group a within city c who have recovered from COVID-19. This represents the rate of change over time in the cumulative number of deaths from illness in age group a within city c.

[0017] M c,i and M i,c Represents the number of people flowing from city c to city i at time t and the number of people flowing from city i to city c, respectively; ρ represents the relative infectivity of asymptomatic carriers; α represents the correction coefficient for inter-city population flow; σ -1 q represents the average duration of the non-infectious incubation period; q represents the proportion of symptomatic infected individuals. This indicates the average length of the prodromal period of symptoms; The θ represents the average infectious period of asymptomatic carriers. a This indicates the probability that an individual in age group a with an overt infection will develop severe or critical illness. This indicates the average infectious period for mild to moderate cases; This indicates the average recovery time for cases under routine isolation. Indicates the average infectious period for severe and critically ill cases; μ -1 This indicates the average time from isolation to hospital admission for severe and critically ill cases; f a τ represents the percentage of critically ill patients among severe cases in age group a; H,k,a τ represents the recovery rate of patients in age group a who require general hospitalization, regardless of whether they receive routine medical intervention k; U,k,a This represents the recovery rate of ICU-required cases in age group a, regardless of whether they received ICU medical intervention k; ν H,k,a This represents the mortality rate of patients in age group a who require general hospitalization, regardless of whether they receive routine medical intervention k; ν U,k,a This represents the mortality rate of cases requiring ICU treatment in age group a, regardless of whether they receive ICU medical intervention k.

[0018] Ideally, age group a should be divided into two or three age groups.

[0019] Preferably, when age group a is divided into two age groups, it is divided into children and adults; when it is divided into three age groups, it is defined as age group A, age group B and age group C, where age group A: 0-14 years old, age group B: 15-64 years old and age group C: 65 years old and above.

[0020] Ideally, the probability of a susceptible individual in age group a being infected per unit of time is:

[0021]

[0022] Where p represents the probability that a single close contact between a susceptible person and an infected person leads to transmission; η a This indicates the relative susceptibility of the susceptible population in age group a compared to adults; variable Respectively with variables One-to-one correspondence, indicating the corresponding variable value for age group j. This represents the number of times a susceptible individual in city c, whose age group is a, comes into contact with all individuals in age group j within a given time period.

[0023] Ideally, in a city c, an infected person of age j would infect an average number of people of age a during their infectious period:

[0024]

[0025] Where, θ j This represents the probability that an individual in age group j with an overt infection will develop severe or critical illness. This represents the number of times a susceptible individual in city c, whose age group j, comes into contact with all individuals in age group a within a unit of time.

[0026] Ideally, in age-dissimilar populations, the basic reproduction number of city c is [missing information]. It is the generation matrix K c The maximum value of the real part of all eigenvalues.

[0027] Preferably, the generation matrix is:

[0028]

[0029] remember but The operator ρ(·) represents the maximum value of the real part of the eigenvalues ​​of a matrix; K c The elements in the text are represented as follows: Let represent the average number of people of age group a infected person in city c who are infected during their infectious period, where j = A, B, C; and a = A, B, C.

[0030] Preferably, the parameter values ​​in the dynamic model are as follows:

[0031] M c,i Synthesized using Tencent migration observation data;

[0032] Artificial synthesis employed;

[0033] The value of P is estimated by MCMC;

[0034] η a :η A =0.5; η B =1.0; η C =1.3; ρ is estimated using MCMC;

[0035] α is estimated using MCMC.

[0036] σ -1 Take 2.9 days;

[0037] q is set to 0.8;

[0038] Take 2.3 days;

[0039] Take 5.2 days;

[0040] For θ a :;θ A =0.013; θ B =0.044; θ C =0.186;

[0041] Take 2.9 days; and

[0042] Take 2.9 days; and

[0043] For f a :f A =0.05; f B =0.084; f C =0.452

[0044] For τ H,k,a When k=1, τ H,1,A =0.09; τ H,1,B =0.089; τ H,1,C =0.068;

[0045] When k = 0, τ H,0,A =0.036; τ H,0,B =0.036; τ H,0,C =0.036;

[0046] For τ U,k,a When k=1, τ U,1,A =0.045; τ U,1,B =0.045; τ U,1,C =0.045; when k=0, τ U,0,A =0.009; τ U,0,B =0.009; τ U,0,C =0.009;

[0047] For ν H,k,a When k=1, ν H,1,A =0.001; ν H,1,B =0.002; ν H,1,C =0.0023; when k=0, v H,0,A =0.055; v H,0,B =0.055; vH,0,c =0.055; ν H,0,A =0.055; ν H,0,B =0.055; ν H,0,C =0.055;

[0048] For ν U,k,a When k=1, ν U,1,A =0.045; ν U,1,B =0.045; ν U,1,C =0.045; ν U,0,A =0.082; ν U,0,B =0.082; ν U,0,C =0.082.

[0049] The present invention has the following beneficial effects:

[0050] Compared to traditional ensemble population models that focus on only a single dimension (such as space or age), this invention simultaneously incorporates age grouping, migration to prefecture-level cities, and multiple disease states, significantly improving model resolution and better reflecting actual transmission scenarios (such as the cross-age and cross-city transmission characteristics of COVID-19). It introduces states such as asymptomatic infections and prodromal symptoms to quantify their relative infectivity, more accurately characterizing early transmission dynamics than traditional models. Furthermore, it replaces the traditional Markov Chain Monte Carlo (MCMC) method with the Differential Evolution Adaptive Metropolis (DREAM) algorithm, improving parameter convergence speed through multi-chain parallel search and adaptive parameter adjustment, making it particularly suitable for rapid fitting under early data sparsity conditions. Attached Figure Description

[0051] Figure 1 The calculation principle of the spatial set population model;

[0052] Figure 2 This is a schematic diagram of the disease progression process according to the present invention. Detailed Implementation

[0053] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0054] This invention simulates the transmission process of an emerging infectious disease as follows: After infection, a susceptible individual S enters a non-infectious incubation period L, during which they are not infectious. A portion of infected individuals are asymptomatic carriers I. A It is infectious, and the others are symptomatic carriers (I). P Asymptomatic case I A It recovers spontaneously without medical intervention and has full immunity. (I) Symptomatic infection.P It is infectious before the onset of clinical symptoms, during the prodromal period. After the prodromal period, some cases will develop into severe and critical illness I. S These cases require active clinical medical intervention and occupy medical bed resources; the remaining cases are mild to moderate (Category I). C Medical intervention may be carried out depending on the availability of medical resources, but is assumed to be unnecessary. Mild to moderate cases I C During their recovery process, they may be detected through monitoring and testing, and therefore may be isolated or self-isolate. QC Afterwards, they recovered (R). Severe and critical cases (I) S First, they were isolated at the hospital. QC Subsequently, some cases required ICU management. IC The remaining cases were admitted to general ward I. H After receiving medical intervention, some of them will die (D), while the rest will recover (R). The risk of death differs between those receiving active and no medical intervention; both the risk of severe illness and death after infection are age-related. Based on the above description, the compartmental structure of the infectious disease dynamics model can be divided as follows: Figure 2 As shown in the figure, each circle represents a cell where people in different epidemiological states reside. The order of the arrows reveals the sequence of disease transmission between different cells, and the symbol above the arrow indicates the probability (or proportion) of transmission between the corresponding cells.

[0055] Since age and spatial factors play important roles in the spread of infectious diseases, an ensemble population model is established using age and spatial heterogeneity as two factors. In the model, the superscript *c* represents a city, where *c* ∈ {1, 2, ..., 358} (a total of 358 prefecture-level cities); the subscript *a* represents an age group, where *a* ∈ {A, B, C}, A: 0-14 years old, B: 15-64 years old, and C: 65+ years old; C represents the age heterogeneous contact matrix within cities, and M represents the population flow matrix between cities. Let X represent the population in city c, belonging to age group a, and currently in state X. The dynamic model after incorporating age and spatial population mobility factors is as follows:

[0056]

[0057] The interpretations of the state variables in the model are shown in Table 1:

[0058] Table 1: Description of Model Compartments (Variables)

[0059]

[0060] It should be noted that in the model, and Correspondingly, this represents the number of susceptible individuals in age group a in city i; and Correspondingly, it represents the total number of people in city i who may move to other cities; and Correspondingly, this represents the number of symptomatic infected individuals of age group a in city i who have become infectious but have not yet shown symptoms; and Correspondingly, this represents the number of asymptomatic carriers of age group a in city i; and Correspondingly, this represents the number of ordinary and mild cases of age group a in city i that are in the infectious period; and Correspondingly, this represents the number of severe and critical cases of age group a in city i who are in the infectious period but have not yet progressed to hospitalization; and Correspondingly, this represents the cumulative number of people in age group a in city i who have recovered. This represents the summation of variables over all ages; This represents the summation of variables over all cities; the change in population over time is represented by the reciprocal of the number of people in different cells, and this relationship is used to model the disease transmission process, specifically:

[0061] This represents the rate of change over time in the number of susceptible individuals of age group a in city c.

[0062] This represents the rate of change over time in the number of people in age group a in city c who are infected but have not yet become infectious.

[0063] This represents the rate of change over time in the number of symptomatic infected individuals of age group a in city c who have become infectious but have not yet shown symptoms.

[0064] This represents the rate of change over time in the number of asymptomatic carriers of age group a in city c.

[0065] This represents the rate of change over time in the number of severe and critically ill cases of age group a in city c who are in the infectious period but have not yet progressed to hospitalization.

[0066] This represents the rate of change over time in the number of ordinary and mild cases of age group a in the infectious period within city c;

[0067] This represents the rate of change over time in the number of severe and critically ill cases in isolation within age group a in city c;

[0068] This represents the rate of change over time in the number of mild to moderate cases in isolation within age group a in city c.

[0069] This represents the rate of change over time in the number of cases in city c where age group a requires routine hospitalization;

[0070] This represents the rate of change over time in the number of cases in city c with age group a requiring ICU care;

[0071] This represents the rate of change over time in the cumulative number of people in age group a within city c who have recovered from COVID-19.

[0072] This represents the rate of change over time in the cumulative number of deaths from illness in age group a within city c.

[0073] The physical meanings of the parameters in the model are shown in Table 2:

[0074] Table 2: Parameter Description in the Model

[0075]

[0076] Individual risk of contracting disease λ a (t) and individual age-related susceptibility η a The bioinfectivity of the disease (p), the age-related mixed contact pattern (C), and the number of infected individuals in the current population who are capable of normal activity (activity status refers to any free state other than isolation, hospitalization, death, etc.) are all relevant factors. Based on the definitions of each parameter, the probability of a susceptible individual of age a being infected per unit time at time t is:

[0077]

[0078] Among them, variables Respectively with variables One-to-one correspondence, indicating the corresponding variable value for age group j. This invention utilizes an artificially synthesized social contact matrix, which combines data on population structure (e.g., the proportion of people in each age group), family size, labor force, and school enrollment in various countries, to calculate the number of contacts between people of different ages in places such as home, school, and workplace through a statistical model. (Prem K, Cook AR, Jit M. Projecting social contact matrices in 152 countries using contact surveys and demographic data[J]. PLoS Computational Biology, 2017, 13(9):e1005697.).

[0079] definition Let this be the number of people of age a that an infected individual of age j will infect during their infectious period in a population of city c under a state of complete susceptibility. According to the definition of the phased basic reproduction number (van den Driessche P, Watmough J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission[J]. Mathematical biosciences, 2002, 180:29-48.), in Let j be the number of reproductions in the prodromal phase of symptoms. Let j be the reproduction number when j is in an asymptomatic infectious state. Let j be the reproduction number of individuals in the normal symptomatic infectious state. Let be the reproduction number of person j in a severely symptomatic infectious state. Based on the model structure and the definition of the basic reproduction number, in this model, the average number of people of age a infected person of age j in a city c who infects others during their infectious cycle is:

[0080]

[0081] In age-heterogeneous populations, the basic reproduction number of city c It is the generation matrix K cThe maximum value of the real part of all eigenvalues ​​in the next generation matrix (Diekmann O, Heesterbeek JA, Metz JA. On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations[J]. Journal of mathematical biology, 1990, 28(4), 365–382.), the generation matrix defined in this model is:

[0082]

[0083] Let represent the average number of people of age a infected person of age j in city c who are infected during their infectious period, where j = A, B, C; and a = A, B, C. (Note:) but The operator ρ(·) represents the maximum value of the real part of the matrix eigenvalues, thus establishing an algebraic relationship between the basic reproduction number and the contact transmission rate. In simple model structures, this relationship can be obtained by solving for the largest eigenvalue of the matrix to obtain an analytical expression. However, in more complex model structures, it can only be calculated numerically using computational tools in simulations. The basic reproduction number itself is an abstract epidemiological concept, and how it is calculated depends entirely on the model assumptions and structure. Therefore, even for the same disease transmission, different modelers may arrive at different basic reproduction numbers, both mathematically and numerically, which can easily lead to debate. For example, in the early stages of COVID-19, many scholars at home and abroad proposed their own estimates of the reproduction number, and the differences between them were significant. Essentially, both model structure and basic reproduction number are an art and technique of averaging various heterogeneous phenomena that are widespread in real systems. They are always just a means of approximating reality. However, since ensemble population models are more granular than single population models, and with data support, it has been proven that using ensemble population models in influenza prediction can significantly improve the accuracy of predictions compared to single population models (Pei S, Kandula S, Yang W, et al. Forecasting the spatial transmission of influenza in the United States[C]. Proceedings of the National Academy of Sciences of the United States of America, 2018, 115(11):2752-2757.). Based on various assumptions, ensemble population models are currently the most important mathematical tool for studying the cross-regional spread of infectious diseases.

[0084] Most of the parameters in the model are derived from the results of biological, epidemiological and clinical studies of the pathogen, population behavior monitoring data and baseline environmental simulation data (as shown in Table 3). The remaining important parameters require statistical inference using the Markov chain Monte Carlo (MCMC) method based on observed case data. All parameters to be estimated adopt an information-free prior distribution.

[0085] Table 3: Parameter Value Description

[0086]

[0087] The data source for parameter fitting is the WHO situation report. Five Markov chains are randomly selected based on the algorithm, and the GR statistic is used. The model was monitored for convergence, with all estimated parameters exhibiting an autocorrelation value less than 0.8. Each Markov chain underwent 4000 iterations, with the first 2000 iterations discarded and the remaining iterations mixed to form the posterior distribution. The model was implemented using C++ and R languages, and 100 sets of parameters were randomly selected from the posterior distribution to reconstruct the early transmission dynamics of COVID-19.

[0088] In this embodiment, the current model uses 358 prefecture-level cities in China as nodes in the regional division method, which can be expanded to provincial-level administrative regions or global national nodes to reconstruct a larger-scale propagation network.

[0089] Age grouping method: The existing 3 age groups (0-14 years, 15-64 years, 65+ years) can be adjusted to 2 groups (children / adults), 5 groups (segmented every 20 years), or more than 10 groups (segmented every 5 years) to adapt to the age risk characteristics of different diseases.

[0090] For parameter estimation methods, in addition to the Differential Evolution Adaptive Metropolis (DREAM) algorithm, Bayesian filtering algorithms such as Ensemble Kalman filter (EnKF) or Particle Markov Chain Monte Carlo (pMCMC) can be used to estimate parameters to adapt to different computational resource requirements.

[0091] For pathogen types, the model framework is applicable to other respiratory infectious diseases (such as influenza and SARS), and only requires adjustment of epidemiological parameters (such as incubation period and infectivity rate) to adapt it.

[0092] For different data sources, migration data can be estimated using air traffic data or public transportation traffic data, while social contact matrices can be estimated using survey data or behavioral monitoring data.

[0093] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for reconstructing early dynamics of infectious diseases based on a metapopulation model, characterized in that, Comprise: Based on the transmission process of new infectious diseases, considering the age factor and the spatial population flow factor, a dynamic model is constructed: ； wherein, S (a, t) denotes the probability of infection of a susceptible person of age a in city c at time t, S (a, t) denotes the number of susceptible persons of age a in city c at time t; I (a, t) denotes the number of infected persons of age a in city I (a, t) denotes the number of infected persons of age a in city I (a, t) denotes the number of infected persons of age a in city I (a, t) denotes the number of infected persons of age a in city c at time t who have developed infectivity but have not yet developed symptoms; I (a, t) denotes the number of infected persons of age a in city c at time t who have developed infectivity but have not yet developed symptoms; I (a, t) denotes the number of infected persons of age a in city c at time t who have developed infectivity but have not yet developed symptoms; I (a, t) denotes the number of infected persons of age a in city c at time t who have developed infectivity but have not yet developed symptoms; I (a, t) denotes the number of infected persons of age a in city c at time t who have developed infectivity but have not yet developed symptoms; I (a, t) denotes the number of infected persons of age a in city c at time t who have developed infectivity but have not yet developed symptoms; I (a, t) denotes the number of infected persons of age a in city c at time t who have developed infectivity but have not yet developed symptoms; I (a, t) denotes the number of infected persons of age a in city c at time t who have developed infectivity but have not yet developed symptoms; I (a, t) denotes the number of infected persons of age a in city c at time t who have developed infectivity but have not yet developed symptoms; I (a, t) denotes the number of infected persons of age a in city c at time t who have developed infectivity but have not yet developed symptoms; I (a, t) denotes the number of infected persons of age a in city c at time t who have developed infectivity but have not yet developed symptoms; I (a, t) denotes the number of infected persons of age a in city c at time t who have developed infectivity but have not yet developed symptoms; I (a, t) denotes the number of infected persons of age a in city c at time t who have developed infectivity but have not yet developed symptoms; I (a, t) denotes the number of infected persons of age a in city c at time t who have developed infectivity but have not yet developed symptoms; I (a, t) denotes the number of infected persons of age a in city c at time t who have developed infectivity but have not yet developed symptoms; I (a, t) denotes the number of infected persons of age a in city c at time t who have developed infectivity but have not yet developed symptoms; I (a, t) denotes the number of infected persons of age a in city c at time t who have developed infectivity but have not yet developed symptoms; I (a, t) denotes the number of infected persons of age a in city c at time t who have developed infectivity but have not yet developed symptoms; I (a, t) denotes the number of infected persons of age a in city c at time t who have developed infectivity but have not yet developed symptoms; I (a, t) denotes the number of infected persons of age a in city c at time t who have developed infectivity but have not yet developed symptoms; I (a, t) denotes the number of infected persons of age a in city c at time t who have developed infectivity but have not yet developed symptoms; I (a, t) denotes the number of infected persons of age a in city c at time t who have developed infectivity but have not yet developed symptoms; I (a, t) denotes the number of infected persons of age a in city c at time t who have developed infectivity but have not yet developed symptoms; I (a, t) denotes the number of infected persons of age a in city c at time t who have developed infectivity but have not yet developed symptoms; I (a, t) denotes the number of infected persons of age a in city c at time t who have developed infectivity but have not yet developed symptoms; I (a, t) denotes the number of infected persons of age a in city c at time t who have developed infectivity but have not yet developed symptoms; I (a, t) denotes the number of infected persons of age a in city c at time t who have developed infectivity but have not yet developed symptoms; I (a, t) denotes the number of infected persons of age a in city c at time t who have developed infectivity but have not yet developed symptoms; I (a, t) denotes the number of infected persons of age a in city c at time t who have developed infectivity but have not yet developed symptoms; Corresponds to the number of severe and critical cases in the infectious stage, but not yet developed to hospitalization, in city i, for age group a; With Corresponds to the number of recovered people in city i, for age group a; Indicates the summation of variables for all ages; Indicates the summation of variables for all cities; Indicates the rate of change of the number of susceptible people in city c, for age group a, over time; Indicates the rate of change of the number of infected people in city c, for age group a, over time; Indicates the rate of change of the number of symptomatic infected people in city c, for age group a, over time; Indicates the rate of change of the number of asymptomatic infected people in city c, for age group a, over time; Indicates the rate of change of the number of severe and critical cases in the infectious stage, but not yet developed to hospitalization, in city c, for age group a, over time; Indicates the rate of change of the number of ordinary and mild cases in the infectious stage in city c, for age group a, over time; Indicates the rate of change of the number of isolated severe and critical cases in city c, for age group a, over time; Indicates the rate of change of the number of isolated mild cases in city c, for age group a, over time; Indicates the rate of change of the number of cases requiring routine hospitalization in city c, for age group a, over time; Indicates the rate of change of the number of cases requiring ICU management in city c, for age group a, over time; Indicates the rate of change of the number of recovered people in city c, for age group a, over time; Indicates the rate of change of the number of cumulative deaths in city c, for age group a, over time; and respectively represent the number of people flowing from city c to city and city to city c; represent the relative infectivity of asymptomatic infectors; represent the correction coefficient of the amount of population flow between cities; represent the average length of non-infectious incubation period; q represents the proportion of symptomatic infections; This indicates the average length of the prodromal period of symptoms; This indicates the average infectious period of asymptomatic carriers; This represents the probability that an individual in age group a with an overt infection will develop severe or critical illness. This indicates the average infectious period for mild to moderate cases; This indicates the average recovery time for cases under routine isolation. This indicates the average infectious period for severe and critically ill cases; This indicates the average time from isolation to hospitalization for severe and critically ill cases; This represents the percentage of critically ill patients among severe cases in age group a; This indicates whether patients in age group 'a' who require general hospitalization will receive routine medical intervention. Recovery rate under certain conditions; This refers to cases in age group a requiring ICU treatment, and whether or not they receive ICU medical intervention. Recovery rate under certain conditions; This indicates whether cases in age group a requiring general hospitalization receive routine medical intervention. The mortality rate under certain conditions; This refers to cases in age group a requiring ICU treatment, and whether or not they receive ICU medical intervention. The mortality rate under certain conditions; When the age group a is divided into three age groups, they are defined as age group A, age group B and age group C, respectively, wherein age group : 0-14 years, age group : 15-64 years, age group : 65 years or older; The probability of susceptible individuals in age group a being infected per unit time is: ； where p denotes the probability of transmission from a susceptible to an infected individual by one close contact; denotes the relative susceptibility of the age group a compared to adults; the variable is in one-to-one correspondence with the variable , , , denotes the corresponding variable value for age group j, denotes the number of contacts per time unit of a susceptible individual in city c of age group a with all individuals of age group j. The average number of age group a infected by an infected individual in age group j in city c during its infectious period is: ； wherein, Pj represents the probability of developing severe and critical illness for dominant infected individuals in age group j; Pj represents the probability of developing severe and critical illness for dominant infected individuals in age group j; Pj represents the probability of developing severe and critical illness for dominant infected individuals in age group j; The basic reproduction number of city c in an age-heterogeneous population is the generation matrix the maximum of the real parts of all eigenvalues The generation matrix is: ； Recall Then , the operator denotes the maximum value of the real part of the eigenvalues of the matrix; The elements in the matrix are given by: denotes the average number of people in age class a that an infected person in age class j in city c infects during its infectious period, where ; .

2. The method of claim 1, wherein the method comprises: The parameter values in the dynamic model are as follows: Synthesized with Tencent migration observation data; synthesized using a chemical synthesis; The value of P is estimated by MCMC; ; estimated using MCMC; Estimated using MCMC; Take 2.9 days; Take 0.8; Take 2.3 days; Take 5.2 days; For ; ; Take 2.9 days; and ; Take 2.9 days; and ; For : ; For : , ; ; ; time, ; ; ; For : , ; ; ; , ; ; ; For : time, ; ; ; time, ; ; ; ; For : time, ; .

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