Individual migration-based epidemic first arrival time prediction method and application thereof

Abstract

The invention discloses an epidemic first arrival time prediction method based on individual migration and application thereof, and belongs to the technical field of epidemic prediction. In order to accurately predict the first arrival time of the sub-population, a sub-population reaction diffusion process model of the epidemic disease is constructed; based on the obtained sub-population reaction diffusion process model of the epidemic disease, establishing a dual-population structure epidemic disease first arrival time prediction method; based on the obtained sub-population reaction diffusion process model of the epidemic disease and a dual-population structure epidemic disease first arrival time prediction method, establishing a hub structure epidemic disease first arrival time prediction method; establishing a one-dimensional linear structure epidemic first arrival time prediction method; and establishing a multi-path structure epidemic first arrival time prediction method. According to the method, the epidemic first arrival time between any sub-populations on a general composite population network can be accurately predicted.

Description

Technical Field

[0001] The present invention belongs to the technical field of epidemic prediction, and in particular relates to a method for predicting the first arrival time of an epidemic based on individual migration and an application thereof. Background Art

[0002] The development of science and technology has led to the innovation of transportation modes, which has brought convenience to people's travel, but also promoted the global spread of epidemics. Since 1980, the complex population network model based on the aviation network has become the main tool for studying the spread of epidemics. For the spread of epidemics, people are no longer concerned about questions such as "is it possible", but are more concerned about when the epidemic will break out. The first arrival time characterizes the process of endogenous transmission through contact between internal individuals in a subpopulation of all susceptible individuals after the emergence of foreign seed infected individuals. Through the study of the first arrival time, we can answer the question of "how much time do countries, cities and hospitals have to prepare, and how to respond to crises."

[0003] At present, the research on first arrival time mainly starts from two aspects. On the one hand, by performing numerical simulations on complex population network models, the high complexity of epidemic spread can be reasonably reproduced. Unfortunately, such a model itself becomes a black box, and the object can only be studied and analyzed through expensive simulations. On the other hand, algebraic methods lay a solid foundation for drawing general conclusions and provide numerical tools that are superior to direct simulations in terms of time complexity, prediction stability, etc.

[0004] Starting from a two-population network, Gautreau et al. approximated the probability distribution of the first arrival time as a Gumbel distribution, and assumed that the dynamic process of epidemic spread in a composite population network is controlled by a set of most likely trajectories. Under this assumption, the first arrival time from the epidemic source center to the target subpopulation can be represented by the minimum value of all paths, and is calculated by accumulating the first arrival time of two adjacent subpopulations. Brockmann et al. proposed to replace the traditional geographical distance with a probability-driven "effective distance". The complexity of epidemic spread can be understood as a circular wave that spreads from the epidemic source center to all other subpopulations in the network at a constant speed. Numerical simulation results show that the first arrival time from the epidemic source center to the target subpopulation is highly correlated with the effective distance. Wang et al. regarded the migration process of individuals between subpopulations as a non-homogeneous Poisson process and derived a first arrival time prediction method on the global aviation network. The above studies provide theoretical insights into the spread process of epidemics, but there is still a large gap between the calculated first arrival time and the actual situation, and it can only reflect the order in which subpopulations are infected. Summary of the invention

[0005] The problem to be solved by the present invention is to accurately predict the first arrival time of a subpopulation, and a method for predicting the first arrival time of an epidemic based on individual migration and its application are proposed.

[0006] To achieve the above object, the present invention is implemented through the following technical solutions: A method for predicting the first arrival time of an epidemic based on individual migration includes the following steps: S1. Construct a subpopulation reaction-diffusion process model of the epidemic; S2. Based on the subpopulation reaction diffusion process model of the epidemic obtained in step S1, a dual-population structure epidemic first arrival time prediction method is established; S3. Based on the subpopulation reaction diffusion process model of the epidemic obtained in step S1 and the dual-population structure epidemic first arrival time prediction method in step S2, a hub structure epidemic first arrival time prediction method is established; S4. Based on the subpopulation reaction diffusion process model of the epidemic obtained in step S1 and the dual-population structure epidemic first arrival time prediction method in step S2, a one-dimensional linear structure epidemic first arrival time prediction method is established; S5. Based on the subpopulation reaction diffusion process model of the epidemic obtained in step S1 and the dual-population structure epidemic first arrival time prediction method in step S2, a multi-path structure epidemic first arrival time prediction method is established.

[0007] Furthermore, the specific implementation method of step S1 includes the following steps: S1.1. The complex population network is used as the carrier of epidemic transmission. The reaction process of the epidemic within the sub-population is described by the susceptible-infected SI model, which is expressed as: (1) in, i for n Any one of Subpopulation population size, is the number of subpopulations, and Respectively i The number of infected and susceptible people in a subpopulation, is the infection rate; S1.2. In addition to local dynamics, individuals diffuse between subpopulations according to the mobility equation, expressed as: (2) in, for Placeholder for For i Subpopulation to jThe migration rate of each subpopulation, For time; Then, the reaction process of infected individuals within the sub-population and the diffusion process model between sub-populations are obtained, and the expression is: (3).

[0008] Furthermore, the specific implementation method of step S2 includes the following steps: S2.1. In constructing a dual population structure, set i The sub-population is the epidemic center sub-population, j The subpopulation is the target subpopulation; At the initial moment When i subpopulation, i The number of infected people in the initial moment of each subpopulation is set as , , and the first i subpopulation, j The epidemic transmission rate in each subpopulation is set to , is the number of infected people; S2.2. In the initial stage of an epidemic, i The number of infected individuals in a subpopulation is a small fraction of the total population. , the initial stage of the epidemic outbreak is obtained by the mean field approximation equation i The number of infected individuals in a subpopulation ; Assume that from Time starts to When the epidemic first emerged from i The subpopulation spreads to the j subpopulations, the expression is as follows: (4) in, The epidemic first started i The subpopulation spreads to the j The time spent by a subpopulation is Equal to j The first arrival time of each subpopulation; According to the approximate conditions , and the first arrival time of the epidemic in the dual population structure is obtained The expression is: (5) When i The initial number of infected individuals in a subpopulation When , equation (5) approximates the mean value of the Gumbel distribution ,in, is the Euler constant.

[0009] Furthermore, the specific implementation method of step S3 includes the following steps: S3.1. In the hub structure, set i The subpopulation is the epidemic center subpopulation, with directly connected subpopulations, j for k Any one of j The subpopulation is the target subpopulation; Because the i The infected individuals within the first sub-population migrate to other sub-populations, thereby delaying the spread of infected individuals to the first sub-population. j The phenomenon that the hub structure delays the first arrival of the epidemic is called the hub effect. S3.2. The structure of the hub i Subpopulation to j The infection rate of a subpopulation The expression is: ; The first arrival time from the epidemic source sub-population to the target sub-population under the hub structure is The expression is: (6).

[0010] Furthermore, the specific implementation method of step S4 includes the following steps: S4.1. Set up a one-dimensional linear structure using the path Indicates that, among them, setting i The sub-population is the epidemic center sub-population, j The sub-population is the target sub-population, and the sub-population at the epidemic source passes through other sub-populations in turn. spread of the epidemic to a target subpopulation; S4.2. Set the subpopulation of the epidemic source under given initial conditions Existence Infected people, Represents subpopulation To subpopulation The mobility of represents the infection rate of each subpopulation; use Represents subpopulation From infected people to infected sub-populations The time elapsed is then the subpopulation The first arrival time is recorded as ; S4.3. Path Indicates that the epidemic is from a subpopulation The propagation process from propagation to subpopulation 1 to propagation to subpopulation 2 is expressed as: (7) in It can be obtained from equation (5), and then the time from the appearance of an infected person in subpopulation 1 to the appearance of an infected person in subpopulation 2 can be obtained by numerical solution: ; Considering the path , we can obtain from equations (5,7) and ; S4.4. Using the idea of ​​path reduction, assuming that the subpopulation There is a direct edge between subpopulation 2 and subpopulation and the migration rate of subpopulation 2 is expressed as , let Equation (5) ,get (8) Depend on: (9) The time interval from the appearance of an infected person in subpopulation 2 to the appearance of an infected person in subpopulation 3 is obtained as ; S4.5. Iterate the above process to obtain a one-dimensional linear structure target subpopulation First arrival time The expression is: (10).

[0011] Furthermore, the specific implementation method of step S5 includes the following steps: S5.1. In setting up the multipath structure, set i The sub-population is the epidemic center sub-population, j subpopulation is the target subpopulation; there is usually shortest paths, using the path reduction idea, reduce these paths to Strips and subpopulations The directly connected paths have their adjusted mobility recorded as ; S5.2. Set the first arrival time from the epidemic center sub-population to the target sub-population in the multi-path structure as : (11) Right now (12) Since the first arrival time of an epidemic is largely determined by the shortest path, the shortest path set traversal / superposition algorithm is used to obtain the The set of shortest paths , and use to approximate all propagation paths.

[0012] An application of an epidemic first arrival time prediction method based on individual migration is implemented based on the aforementioned epidemic first arrival time prediction method based on individual migration, and is used for first arrival time prediction under a susceptible-infected-recovered SIR model, a susceptible-latent-infected-recovered SEIR model, and a general epidemic complex population network model.

[0013] Beneficial effects of the present invention: The method for predicting the first arrival time of an epidemic based on individual migration described in the present invention innovatively divides the basic propagation structures on a complex population network into four types, namely, a dual population structure, a hub structure, a one-dimensional linear structure, and a multi-path structure.

[0014] The method for predicting the first arrival time of an epidemic based on individual migration described in the present invention innovatively proposes for the first time a twin population prediction technology, a hub adjustment technology for a hub structure, a path reduction algorithm for a one-dimensional linear structure, and a path traversal / superposition algorithm for a multiple path structure to form an epidemic first arrival time prediction algorithm on a general complex population network, which can accurately predict the first arrival time of an epidemic between any sub-populations on a general complex population network. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 Schematic diagram of a complex population network model with SI epidemic-reaction diffusion (RD) process; Figure 2 Schematic diagram of the basic propagation structure on the composite population network of the present invention, where (a) is a dual population structure, (b) is a hub structure, (c) is a one-dimensional linear structure, and (d) is a multi-path structure; Figure 3 The present invention is a flowchart of a method for predicting the first arrival time of an epidemic based on individual migration. DETAILED DESCRIPTION

[0016] In order to make the purpose, technical solution and advantages of the present invention more clear, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention, that is, the specific embodiments described are only part of the embodiments of the present invention, rather than all of the specific embodiments. The components of the specific embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations, and the present invention can also have other embodiments.

[0017] Therefore, the following detailed description of the specific embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents the selected specific embodiments of the present invention. Based on the specific embodiments of the present invention, all other specific embodiments obtained by those skilled in the art without making creative work are within the scope of protection of the present invention.

[0018] In order to further understand the content, features and effects of the present invention, the following specific implementation methods are given as examples, and the attached Figure 1 -Attached Figure 3 The detailed instructions are as follows:

[0019] Embodiment 1: A method for predicting the first arrival time of an epidemic based on individual migration includes the following steps: S1. Construct a subpopulation reaction-diffusion process model of the epidemic; Furthermore, the specific implementation method of step S1 includes the following steps: S1.1. The complex population network is used as the carrier of epidemic transmission. The reaction process of the epidemic within the sub-population is described by the susceptible-infected SI model, which is expressed as: (1) in, i for n Any one of Subpopulation population size, is the number of subpopulations, and Respectively i The number of infected and susceptible people in a subpopulation, is the infection rate; S1.2. In addition to local dynamics, individuals diffuse between subpopulations according to the mobility equation, expressed as: (2) in, for Placeholder for For i Subpopulation to j The migration rate of each subpopulation, For time; Then, the reaction process of infected individuals within the sub-population and the diffusion process model between sub-populations are obtained, and the expression is: (3).

[0020] S2. Based on the subpopulation reaction diffusion process model of the epidemic obtained in step S1, a dual-population structure epidemic first arrival time prediction method is established; Furthermore, the specific implementation method of step S2 includes the following steps: S2.1. In constructing a dual population structure, set i The sub-population is the epidemic center sub-population, j The subpopulation is the target subpopulation; At the initial moment When i subpopulation, i The number of infected people in the initial moment of each subpopulation is set as , , and the first i subpopulation, j The epidemic transmission rate in each subpopulation is set to , is the number of infected people; S2.2. In the initial stage of an epidemic, i The number of infected individuals in a subpopulation is a small fraction of the total population. , the initial stage of the epidemic outbreak is obtained by the mean field approximation equation i The number of infected individuals in a subpopulation ; Assume that from Time starts to When the epidemic first emerged from i The subpopulation spreads to the j subpopulations, the expression is as follows: (4) in, The epidemic first started i The subpopulation spreads to the j The time spent by a subpopulation is Equal to j The first arrival time of each subpopulation; According to the approximate conditions , and the first arrival time of the epidemic in the dual population structure is obtained The expression is: (5) When i The initial number of infected individuals in a subpopulation When , equation (5) approximates the mean value of the Gumbel distribution ,in, is the Euler constant.

[0021] S3. Based on the subpopulation reaction diffusion process model of the epidemic obtained in step S1 and the dual-population structure epidemic first arrival time prediction method in step S2, a hub structure epidemic first arrival time prediction method is established; Furthermore, the specific implementation method of step S3 includes the following steps: S3.1. In the hub structure, set i The subpopulation is the epidemic center subpopulation, with directly connected subpopulations, j for k Any one of j The subpopulation is the target subpopulation; Because the i The infected individuals within the first sub-population migrate to other sub-populations, thereby delaying the spread of infected individuals to the first sub-population. j The phenomenon that the hub structure delays the first arrival of the epidemic is called the hub effect. S3.2. The structure of the hub i Subpopulation to j The infection rate of a subpopulation The expression is: ; The first arrival time from the epidemic source sub-population to the target sub-population under the hub structure is The expression is: (6).

[0022] S4. Based on the subpopulation reaction diffusion process model of the epidemic obtained in step S1 and the dual-population structure epidemic first arrival time prediction method in step S2, a one-dimensional linear structure epidemic first arrival time prediction method is established; Furthermore, the specific implementation method of step S4 includes the following steps: S4.1. Set up a one-dimensional linear structure using the path Indicates that, among them, setting i The sub-population is the epidemic center sub-population, jThe sub-population is the target sub-population, and the sub-population at the epidemic source passes through other sub-populations in turn. spread of the epidemic to a target subpopulation; S4.2. Set the subpopulation of the epidemic source under given initial conditions Existence Infected people, Represents subpopulation To subpopulation The mobility of represents the infection rate of each subpopulation; use Represents subpopulation From infected people to infected sub-populations The time elapsed is then the subpopulation The first arrival time is recorded as ; S4.3. Path Indicates that the epidemic is from a subpopulation The propagation process from propagation to subpopulation 1 to propagation to subpopulation 2 is expressed as: (7) in It can be obtained from equation (5), and then the time from the appearance of an infected person in subpopulation 1 to the appearance of an infected person in subpopulation 2 can be obtained by numerical solution: ; Considering the path , we can obtain from equations (5,7) and ; S4.4. Using the idea of ​​path reduction, assuming that the subpopulation There is a direct edge between subpopulation 2 and subpopulation and the migration rate of subpopulation 2 is expressed as , let Equation (5) ,get (8) Depend on: (9) The time interval from the appearance of an infected person in subpopulation 2 to the appearance of an infected person in subpopulation 3 is obtained as ; S4.5. Iterate the above process to obtain a one-dimensional linear structure target subpopulation First arrival time The expression is: (10).

[0023] S5. Based on the subpopulation reaction diffusion process model of the epidemic obtained in step S1 and the dual-population structure epidemic first arrival time prediction method in step S2, a multi-path structure epidemic first arrival time prediction method is established.

[0024] Furthermore, the specific implementation method of step S5 includes the following steps: S5.1. In setting up the multipath structure, set i The sub-population is the epidemic center sub-population, j subpopulation is the target subpopulation; there is usually shortest paths, using the path reduction idea, reduce these paths to Strips and subpopulations The directly connected paths have their adjusted mobility recorded as ; S5.2. Set the first arrival time from the epidemic center sub-population to the target sub-population in the multi-path structure as : (11) Right now (12) Since the first arrival time of an epidemic is largely determined by the shortest path, the shortest path set traversal / superposition algorithm is used to obtain the The set of shortest paths , and use to approximate all propagation paths.

[0025] Embodiment 2: An application of an epidemic first arrival time prediction method based on individual migration is implemented based on the epidemic first arrival time prediction method based on individual migration described in Example 1, and is used for first arrival time prediction under a susceptible-infected-recovered SIR model, a susceptible-latent-infected-recovered SEIR model, and a general epidemic complex population network model.

[0026] Furthermore, the SIR model is taken as an example to illustrate how to use the method of the present invention to predict the first arrival time.

[0027] In the SIR model, the epidemic dynamics within the subgroup can be described by the ODE system shown in formula (13): (13) In the early stages of dissemination, , so there is Established; solving this differential equation yields ,in The endogenous exponential growth process in the early stage of the epidemic was controlled; Therefore, combined with equation (5), the expression of the first arrival time of the epidemic under the SIR model is: (14) Adjust the infection rate to , and then we can get the first arrival time of the epidemic under the hub structure by substituting equation (14) into equation (7) and equation (8) to reduce the path. By continuously iterating equation (9), the first arrival time of the epidemic under the one-dimensional linear structure can be obtained by equation (10). Path reduction is performed on each path in the multi-path structure to obtain the adjusted migration rate , and put it into formula (12) to get the result after path superposition.

[0028] It should be noted that relational terms such as "first" and "second" are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "comprise a ..." do not exclude the existence of other identical elements in the process, method, article or device including the elements.

[0029] Although the present application has been described above with reference to specific embodiments, various modifications may be made thereto and parts thereof may be replaced with equivalents without departing from the scope of the present application. In particular, as long as there is no structural conflict, the various features in the specific embodiments disclosed in the present application may be used in combination with each other in any manner, and the fact that these combinations are not exhaustively described in this specification is only for the sake of omitting space and saving resources. Therefore, the present application is not limited to the specific embodiments disclosed herein, but includes all technical solutions falling within the scope of the claims.

Claims

1. A method for predicting the first arrival time of an epidemic based on individual migration, characterized in that: The steps include: S1. Construct a subpopulation reaction-diffusion process model of the epidemic; S2. Based on the subpopulation reaction diffusion process model of the epidemic obtained in step S1, a dual-population structure epidemic first arrival time prediction method is established; S3. Based on the subpopulation reaction diffusion process model of the epidemic obtained in step S1 and the dual-population structure epidemic first arrival time prediction method in step S2, a hub structure epidemic first arrival time prediction method is established; S4. Based on the subpopulation reaction diffusion process model of the epidemic obtained in step S1 and the dual-population structure epidemic first arrival time prediction method in step S2, a one-dimensional linear structure epidemic first arrival time prediction method is established; S5. Based on the subpopulation reaction diffusion process model of the epidemic obtained in step S1 and the dual-population structure epidemic first arrival time prediction method in step S2, a multi-path structure epidemic first arrival time prediction method is established.

2. The method for predicting the first arrival time of an epidemic based on individual migration according to claim 1, characterized in that: The specific implementation method of step S1 includes the following steps: S1.

1. The complex population network is used as the carrier of epidemic transmission. The reaction process of the epidemic within the sub-population is described by the susceptible-infected SI model, which is expressed as: (1) in, i for n Any one of Subpopulation population size, is the number of subpopulations, and Respectively i The number of infected and susceptible people in a subpopulation, is the infection rate; S1.

2. In addition to local dynamics, individuals diffuse between subpopulations according to the mobility equation, expressed as: (2) in, for Placeholder for For i Subpopulation to j The migration rate of each subpopulation, For time; Then, the reaction process of infected individuals within the sub-population and the diffusion process model between sub-populations are obtained, and the expression is: (3)。 3. The method for predicting the first arrival time of an epidemic based on individual migration according to claim 2, characterized in that: The specific implementation method of step S2 includes the following steps: S2.

1. In constructing the dual population structure, set i The sub-population is the epidemic center sub-population, j The subpopulation is the target subpopulation; At the initial moment When i subpopulation, i The number of infected people in the initial moment of each subpopulation is set as , , and the first i subpopulation, j The epidemic transmission rate in each subpopulation is set to , is the number of pathogenic subpopulations in the initial situation. infected people; S2.

2. In the initial stage of an epidemic, i The number of infected individuals in a subpopulation is a small fraction of the total population. , the initial stage of the epidemic outbreak is obtained by the mean field approximation equation i The number of infected individuals in a subpopulation ; Assume that from Time starts to When the epidemic first emerged i The subpopulation spreads to the j subpopulations, the expression is as follows: (4) in, The epidemic first started i The subpopulation spreads to the j The time spent by a subpopulation is Equal to j The first arrival time of each subpopulation; According to the approximate conditions , and the first arrival time of the epidemic in the dual population structure is obtained The expression is: (5) When i The initial number of infected individuals in a subpopulation When , equation (5) approximates the mean value of the Gumbel distribution ,in, is the Euler constant.

4. The method for predicting the first arrival time of an epidemic based on individual migration according to claim 3, characterized in that: The specific implementation method of step S3 includes the following steps: S3.

1. In the hub structure, set i The subpopulation is the epidemic center subpopulation, with directly connected subpopulations, j for k Any one of j The subpopulation is the target subpopulation; Because the i The infected individuals within the first sub-population migrate to other sub-populations, thereby delaying the spread of infected individuals to the first sub-population. j The phenomenon that the hub structure delays the first arrival of the epidemic is called the hub effect. S3.

2. The structure of the hub i Subpopulation to j The infection rate of a subpopulation The expression is: ； The first arrival time from the epidemic source sub-population to the target sub-population under the hub structure is The expression is: (6)。 5. The method for predicting the first arrival time of an epidemic based on individual migration according to claim 4, characterized in that: The specific implementation method of step S4 includes the following steps: S4.

1. Set up a one-dimensional linear structure using the path Indicates that, among them, setting i The sub-population is the epidemic center sub-population, j The sub-population is the target sub-population, and the sub-population at the epidemic source passes through other sub-populations in turn. spread of the epidemic to a target subpopulation; S4.

2. Set the subpopulation of the epidemic source under given initial conditions Existence Infected people, Represents subpopulation To subpopulation The mobility of represents the infection rate of each subpopulation; use Represents subpopulation From infected people to infected sub-populations The time elapsed is then the subpopulation The first arrival time is recorded as ; S4.

3. Path Indicates that the epidemic is from a subpopulation The propagation process from propagation to subpopulation 1 to propagation to subpopulation 2 is expressed as: (7) in It can be obtained from equation (5), and then the time from the appearance of an infected person in subpopulation 1 to the appearance of an infected person in subpopulation 2 can be obtained by numerical solution: ; Considering the path , we can obtain from equations (5,7) and ; S4.

4. Using the idea of ​​path reduction, assuming that the subpopulation There is a direct edge between subpopulation 2 and subpopulation and the migration rate of subpopulation 2 is expressed as , let Equation (5) ,get (8) Depend on: (9) The time interval from the appearance of an infected person in subpopulation 2 to the appearance of an infected person in subpopulation 3 is obtained as ; S4.

5. Iterate the above process to obtain a one-dimensional linear structure target subpopulation First arrival time The expression is: (10)。 6. The method for predicting the first arrival time of an epidemic based on individual migration according to claim 5, characterized in that: The specific implementation method of step S5 includes the following steps: S5.

1. In setting up the multipath structure, set i The sub-population is the epidemic center sub-population, j subpopulation is the target subpopulation; there is usually shortest paths, using the path reduction idea, reduce these paths to Strips and subpopulations The directly connected paths have their adjusted mobility recorded as ; S5.

2. Set the first arrival time from the epidemic center sub-population to the target sub-population in the multi-path structure as : (11) Right now (12) Since the first arrival time of an epidemic is largely determined by the shortest path, the shortest path set traversal / superposition algorithm is used to obtain the The set of shortest paths , and use to approximate all propagation paths.

7. An application of a method for predicting the first arrival time of an epidemic based on individual migration, which is implemented by relying on a method for predicting the first arrival time of an epidemic based on individual migration as described in any one of claims 1 to 6, characterized in that: Used for first arrival time prediction under susceptible-infected-recovered SIR model, susceptible-latent-infected-recovered SEIR model, and general epidemic complex population network model.

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