An influenza optimized epidemic prevention method based on population flow network

Abstract

The application discloses an influenza optimized epidemic prevention method based on a population flow network. The method comprises the following steps: acquiring population flow data among multiple cities and influenza prevention and control related data of each city; constructing a population flow network according to the population flow data, wherein cities are taken as nodes, and population flow relations among the cities are taken as directed edges; identifying a key city set for blocking an influenza cross-city circulation propagation path by using a greedy feedback vertex set algorithm based on the population flow network; generating baseline epidemic prevention measures, such as an isolation rate, a detection rate and a vaccination rate, according to the influenza prevention and control data; and optimizing the epidemic prevention measures of the key cities according to a preset epidemic prevention target and an epidemic prevention cost. The method can identify key cities in influenza prevention and control under the condition that city traffic is not completely cut off, and provide a decision basis for cross-city influenza prevention and control and public health resource allocation.

Description

Technical Field

[0001] This invention relates to an optimized influenza prevention and control method based on population flow networks, belonging to the field of control technology based on complex networks. Background Technology

[0002] In the real world, the prediction and control of infectious disease transmission systems is a common challenge in public health management, with influenza emerging as another major public health threat. These systems often exhibit nonlinear dynamics and involve complex interactions between spatial mobility and time-varying transmission factors, making their dynamic behavior inherently unpredictable. Therefore, a deeper understanding of the complex mechanisms of pathogen transmission to mitigate socioeconomic impacts remains a top priority.

[0003] Furthermore, existing infectious disease prevention and control prediction systems are mostly based on homogeneous assumptions, constructing classic compartmentalization models (such as SIR or SEIR). These models often treat the entire province or large region as a uniformly mixed whole, ignoring the spatial heterogeneity caused by population movement between different cities. Meanwhile, in actual public health management, medical resources (such as vaccine reserves, nucleic acid testing capacity, and isolation facility configuration) are subject to strict upper limits. Traditional epidemic prevention strategies mostly adopt uniform control measures applied across the entire province / nation. This approach not only leads to a serious waste of medical resources in low-risk areas but also fails to effectively suppress key cities at transmission hubs, making it difficult to maximize the marginal benefits of prevention and control under resource constraints. Summary of the Invention

[0004] Purpose of the invention: One objective of this invention is to provide an optimized influenza prevention and control method based on population flow networks, so as to achieve optimal prevention and control during the peak influenza season under limited resources.

[0005] Technical solution: The influenza prevention and control optimization method based on population flow network described in this invention includes the following steps:

[0006] S1. Obtain population flow data between multiple cities and influenza prevention and control data for each city. The population flow data is used to reflect population flow relationships, and the influenza prevention and control data is used to identify the influenza transmission environment and transmission development patterns.

[0007] S2. Construct a directed population flow network based on the population flow data, where cities are nodes and the population flow relationships between cities are directed edges.

[0008] S3. Based on the directed population flow network, a greedy feedback vertex set algorithm is used to identify a set of key cities, which is used to block the cyclical spread of influenza in the urban network.

[0009] S4. Generate baseline epidemic prevention measures based on influenza prevention and control data: isolation rate, testing rate, and vaccination rate. The baseline epidemic prevention measures are used to identify the default epidemic prevention settings in non-key cities and serve as the initial parameters for optimizing the intensity of epidemic prevention measures in key cities.

[0010] S5. Based on the preset epidemic prevention goals and costs, optimize the epidemic prevention measures of each city in the set of key cities. The optimization algorithm is used to identify the key city epidemic prevention measures that meet the preset influenza suppression goals and to solve for the key city epidemic prevention measures with the minimum epidemic prevention cost as the optimization goal.

[0011] Furthermore, the population flow data includes the average daily number of people moving between cities, transportation data, migration intensity data, or other data that can reflect the population flow relationship between cities; the influenza prevention and control related data includes, but is not limited to, the population size of each city, the number of initial infections, the number of latent infections, the number of people in isolation, the vaccination rate, testing capacity, isolation capacity, the quantity of epidemic prevention resources, and epidemic prevention cost parameters.

[0012] Furthermore, if there exists from the first The flow of the city to the first Population flow in a city is established from the first city. The city points to the first Directed edges of cities, matrix If there is no population flow in that direction, then no corresponding directed edge is established, and the matrix... The inter-city population flow relationships are represented as a directed network topology, and the adjacency matrix is ​​obtained. .

[0013] Furthermore, the greedy feedback vertex set algorithm includes:

[0014] a) Set the maximum number of sub-network nodes ;

[0015] b) Select from the current directed population flow network Each node forms a local directed subnetwork;

[0016] c) Search for directed cycles in the local directed subnetwork;

[0017] If the local directed subnetwork is initially acyclic, the nodes pointed to by the nodes in the population flow network are roughly classified as feedback vertices and placed into the set of key cities. The population flow network removes all nodes and their associated edges from the local directed subnetworks.

[0018] If the local directed subnetwork initially contains a cycle, calculate the number of directed cycles each node participates in, i.e., the number of directed cycles reduced by deleting that node; identify the node with the largest number of cycles as the feedback vertex and add it to the set of key cities. Remove the feedback vertex and its associated directed edges from the current local directed subnetwork and directed population flow network; repeat the current step until the local directed subnetwork is finally acyclic.

[0019] d) Repeat the steps of selecting local directed subnetworks, searching for directed cycles, determining feedback vertices, and deleting nodes and related edges until there are no directed cycles in the current directed population flow network or all nodes have been processed, thus obtaining the set of key cities. .

[0020] Furthermore, the baseline epidemic prevention measures are used as the default epidemic prevention settings for non-key cities and as initial parameters for optimizing the intensity of epidemic prevention measures in key cities; the epidemic prevention measures are one of isolation, testing, and vaccination; wherein, isolation measures are used to increase the isolation rate of infected or suspected infected individuals, testing measures are used to increase the detection rate of latent or infected individuals, and vaccination measures are used to increase the immune protection rate of susceptible individuals; based on parameters such as city population size, infection level, quantity of epidemic prevention resources, epidemic prevention capacity, and epidemic prevention cost, baseline isolation measures, baseline testing measures, and baseline vaccination measures are set for the city.

[0021] The aforementioned optimization of epidemic prevention measures specifically includes:

[0022] a) First, input the set of key cities. Basic epidemic prevention measures parameter settings and urban population flow network topology;

[0023] b) Set the epidemic prevention parameters for non-key cities as the baseline epidemic prevention measures, and set the feedback vertex set. The epidemic prevention parameters of key cities in China are used as variables to be optimized.

[0024] c) With the preset influenza suppression target as a constraint and the minimum epidemic prevention cost as the optimization objective, solve for the epidemic prevention measures in key cities respectively;

[0025] d) Output the optimal isolation parameters for key cities. Optimal detection parameters and optimal inoculation parameters .

[0026] Beneficial effects:

[0027] This invention proposes a key city-wide influenza prevention method to address influenza transmission under population mobility, significantly reducing social prevention costs and breaking through the traditional "one-size-fits-all" prevention and control strategy. It also points out that implementing intensive self-isolation in key cities can achieve rapid suppression of citywide influenza outbreaks with extremely low social operation and medical costs. Attached Figure Description

[0028] Figure 1 This is a flowchart of the method of the present invention;

[0029] Figure 2 The graph for the greedy feedback vertex set algorithm;

[0030] Figure 3 To optimize the algorithm graph;

[0031] Figure 4 Identify key cities;

[0032] Figure 5 A diagram illustrating the optimal influenza suppression effect of isolation, testing, and vaccination. Detailed Implementation

[0033] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments, but the scope of the present invention is not limited thereto.

[0034] like Figure 1 As shown, this invention provides an optimized influenza prevention and control method based on a population flow network, comprising the following steps: acquiring population flow data between multiple cities and influenza prevention and control related data for each city; constructing a population flow network based on the population flow data, wherein cities are nodes and the population flow relationships between cities are directed edges; identifying a set of key cities for blocking the cross-city circular transmission path of influenza based on the population flow network using a greedy feedback vertex set algorithm; generating baseline prevention and control measures based on influenza prevention and control data: isolation rate, testing rate, and vaccination rate; and optimizing the prevention and control measures for key cities based on preset prevention and control goals and costs.

[0035] The steps are described below:

[0036] S1. First, acquire population flow data between multiple cities and influenza prevention and control data for each city. The population flow data can include the average daily number of people moving between cities, transportation data, migration intensity data, or other data that reflects population flow relationships between cities. The influenza prevention and control data includes, but is not limited to, the population size of each city, the initial number of infections, the number of latent cases, the number of people in quarantine, the vaccination rate, testing capacity, quarantine capacity, the quantity of epidemic prevention resources, and epidemic prevention cost parameters. After preprocessing, the above data is used to construct an urban population flow network and generate key city epidemic prevention measure configuration plans.

[0037] S2. Based on the population flow data, cities are used as nodes and the population flow relationships between cities are used as directed edges to construct a directed population flow network.

[0038] In the directed population flow network, if there exists a flow from the first... The flow of the city to the first Population flow in a city is established from the first city. The city points to the first Directed edges of cities, matrix If there is no population flow in that direction, then no corresponding directed edge is established, and the matrix... Therefore, the inter-city population flow relationship is represented as a directed network topology, and the adjacency matrix is ​​obtained. .

[0039] S3. Based on the directed population flow network and adjacency matrix A greedy feedback vertex set algorithm was used to identify the set of key cities for blocking the cross-city circular transmission of influenza. The algorithm flow is as follows: Figure 2 .

[0040] First, the matrix The permanence of ,in It is a set All possible permutations. Equivalent to calculating using Laplace expansion And all product terms have a sign of +1. Because Each product term in the equation is... The underlying directed graph contains directed cycles or disjoint directed cycles, therefore, the matrix... If all elements are represented by 0 and 1, then yes The number of expansion terms represents the number of unions of cycles and disjoint directed cycles in the underlying directed graph.

[0041] definition matrix

[0042] (1)

[0043] This represents the number of unions of cycles and disjoint directed cycles in the bottom-level directed graph. express Delete the Liede The matrix after the row, Indicates deletion of the first The number of cycles and unions of disjoint directed cycles in the underlying directed graph after each node. Represents a node Included The set is the union of directed cycles and disjoint directed cycles. The specific process of the greedy feedback vertex set algorithm is as follows:

[0044] (i) Before selecting the original network A small network consisting of nodes;

[0045] (ii) Search for rings in small networks;

[0046] If the smaller network is acyclic, and any node in the smaller network has an edge originating from a node in the original network, then it can be roughly classified as a feedback vertex and placed into the network. The original network removes all nodes and their associated edges from the smaller network;

[0047] If the small network has a cycle, choose the largest one. Place the corresponding node And delete these nodes and their related edges (the original network synchronously deletes nodes and edges), repeat the current step until the small network is acyclic, then jump to step (iii).

[0048] (iii) Repeat steps (i)-(ii) until all nodes in the network have been traversed, then terminate the algorithm and output the result. .

[0049] S4. Generate baseline epidemic prevention measures based on influenza prevention and control data: isolation rate, testing rate, and vaccination rate.

[0050] The baseline epidemic prevention measures are used as the default epidemic prevention settings for non-key cities and as initial parameters for optimizing the intensity of epidemic prevention measures in key cities. The epidemic prevention measures are one of isolation, testing, and vaccination. Isolation measures are used to increase the isolation rate of infected or suspected infected individuals; testing measures are used to increase the detection rate of latent or infected individuals; and vaccination measures are used to increase the immunization protection rate of susceptible populations. Baseline isolation, testing, and vaccination measures are set based on parameters such as city population size, infection level, quantity of epidemic prevention resources, epidemic prevention capacity, and epidemic prevention costs.

[0051] S5. Optimize epidemic prevention measures in key cities based on preset epidemic prevention goals and costs. The optimization algorithm flow is described below. Figure 3 The specific process is as follows:

[0052] (i) Input the set of key cities ,matrix Total number of cities Upper and lower boundaries , and initial epidemic parameters ;

[0053] (2)

[0054] Among them, when vaccination is not mandatory, During mandatory vaccination, , . For the first Vaccination rates in individual cities For the first Vaccine failure rates in some cities For the first Recovery rate of each city For the first Infection rate of vaccinated individuals in each city For the first Infection rate of unvaccinated individuals in each city For the first Conversion rate of individuals in the incubation period in a city For the first The rate of individual isolation during the incubation period in each city For the first The testing rate in each city For the first The rate of individual isolation in infected individuals in each city For the first Total population of each city For the city to the city Population movement. For the first The probability of individual vaccination in a city For the first The probability of infection among unvaccinated individuals in a city. For the first The probability of infection among vaccinated individuals in each city.

[0055] (3)

[0056] (4)

[0057] (5)

[0058] in, For the first Number of people vaccinated in each city For the first Number of people in the incubation period in each city For the first Number of infected people in each city.

[0059] (ii) According to sum matrix Constructing auxiliary matrix and ;

[0060] (6)

[0061] (7)

[0062] (iii) Define the constraint matrix ;

[0063] (iv) Define the weight vector , , ; ,but ; , , ;

[0064] (v) Solve constrained optimization problems.

[0065]

[0066] (8)

[0067] in, , ;

[0068] (vi) Obtain optimization parameters ;

[0069] (vii) For each node Calculate the optimal strength ;

[0070] (b) Non-mandatory vaccination,

[0071] Optimal self-isolation measures (9)

[0072] Optimal detection measures (10)

[0073] (b) Compulsory vaccination

[0074] Optimal vaccination measures (11)

[0075] (viii) Output the optimal measure.

[0076] Finally, the set of key cities and their corresponding epidemic prevention and control measures configuration schemes are output. The epidemic prevention and control measures configuration schemes include key city numbers, key city names, epidemic prevention and control measure types, and epidemic prevention and control measure strengths. Considering the following influenza parameters and city network topology, a greedy feedback vertex set algorithm is used to identify key cities, and an optimization algorithm is used to output the epidemic prevention and control measures for key cities. The simulation takes Jiangsu Province, China as the research object. This corresponds to the 13 prefecture-level cities under the jurisdiction of Jiangsu Province, namely Nanjing, Wuxi, Xuzhou, Changzhou, Suzhou, Nantong, Lianyungang, Huai'an, Yancheng, Yangzhou, Zhenjiang, Taizhou, and Suqian. The population flow of the urban network of the 13 cities in Jiangsu Province is shown in matrix (12).

[0077] (12)

[0078] Matrix (12) Line number The element is The unit is Humans. A greedy feedback vertex set algorithm is used to identify key cities in the simulation. ,See Figure 4 The influenza fitting parameters are shown in Table 1. The optimal self-isolation strategy for key cities obtained through the algorithm is as follows: , , , , , , , , , The optimal detection strategy is , , , , , , , , and The optimal vaccination strategy is , , , , , , , , , .

[0079] Table 1 Influenza parameters

[0080]

[0081] Figure 4 It shows the key cities for epidemic prevention and control in the urban network. Figure 5 (a) refers to the original epidemic prevention measures. Figure 5 Figures (b)-(d) respectively demonstrate the inhibitory effects on the incubation period and the infected population after adopting optimal self-isolation, testing, and vaccination in key cities. Figure 5 It can be seen that the proposed prevention and control methods can all suppress the spread of influenza, causing the incubation period and the number of infected people to gradually decrease towards zero. Furthermore, a comparison... Figure 5 The four subgraphs present the original settings, optimal self-isolation, detection, and vaccination suppression effects, showing that self-isolation has better epidemic prevention performance.

[0082] The specific embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above-described scenario. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. An optimized influenza prevention and control method based on population mobility networks, characterized in that, Includes the following steps: S1. Obtain population flow data between multiple cities and influenza prevention and control data for each city. The population flow data is used to reflect population flow relationships, and the influenza prevention and control data is used to identify the influenza transmission environment and transmission development patterns. S2. Construct a directed population flow network based on the population flow data, where cities are nodes and the population flow relationships between cities are directed edges. S3. Based on the directed population flow network, a greedy feedback vertex set algorithm is used to identify a set of key cities, which is used to block the cyclical spread of influenza in the urban network. S4. Generate baseline epidemic prevention measures based on influenza prevention and control data: isolation rate, testing rate, and vaccination rate. The baseline epidemic prevention measures are used to identify the default epidemic prevention settings in non-key cities and serve as the initial parameters for optimizing the intensity of epidemic prevention measures in key cities. S5. Based on the preset epidemic prevention goals and costs, optimize the epidemic prevention measures of each city in the set of key cities. The optimization algorithm is used to identify the key city epidemic prevention measures that meet the preset influenza suppression goals and to solve for the key city epidemic prevention measures with the minimum epidemic prevention cost as the optimization goal.

2. The influenza prevention and control optimization method based on population flow networks according to claim 1, characterized in that, In step S1, the population flow data includes the average daily number of people moving between cities, transportation data, migration intensity data, or other data that can reflect the population flow relationship between cities; the influenza prevention and control related data includes, but is not limited to, the population size of each city, the number of initial infections, the number of latent infections, the number of people in isolation, the vaccination rate, testing capacity, isolation capacity, the quantity of epidemic prevention resources, and epidemic prevention cost parameters.

3. The influenza prevention and control optimization method based on population flow networks according to claim 1, characterized in that, In step S2, if there exists from the first The flow of the city to the first Population flow in a city is established from the first city. The city points to the first Directed edges of cities, matrix If there is no population flow in that direction, then no corresponding directed edge is established, and the matrix... The inter-city population flow relationships are represented as a directed network topology, and the adjacency matrix is ​​obtained. .

4. The influenza prevention and control optimization method based on population flow networks according to claim 3, characterized in that, In step S3, the greedy feedback vertex set algorithm includes: a) Set the maximum number of sub-network nodes ; b) Select from the current directed population flow network Each node forms a local directed subnetwork; c) Search for directed cycles in the local directed subnetwork; If the local directed subnetwork is initially acyclic, the nodes pointed to by the nodes in the population flow network are roughly classified as feedback vertices and placed into the set of key cities. The population flow network removes all nodes and their associated edges from the local directed subnetworks; If the local directed subnetwork initially contains a cycle, calculate the number of directed cycles each node participates in, i.e., the number of directed cycles reduced by deleting that node; identify the node with the largest number of cycles as the feedback vertex and add it to the set of key cities. Remove the feedback vertex and its associated directed edges from the current local directed subnetwork and directed population flow network; repeat the current step until the local directed subnetwork is finally acyclic; d) Repeat the steps of selecting local directed subnetworks, searching for directed cycles, determining feedback vertices, and deleting nodes and related edges until there are no directed cycles in the current directed population flow network or all nodes have been processed, thus obtaining the set of key cities. .

5. The influenza prevention and control optimization method based on population flow networks according to claim 1, characterized in that, In step S4, the baseline epidemic prevention measures are used as the default epidemic prevention settings for non-key cities and as initial parameters for optimizing the intensity of epidemic prevention measures in key cities. The epidemic prevention measures are one of isolation, testing, and vaccination. Among them, isolation measures are used to increase the isolation rate of infected or suspected infected people, testing measures are used to increase the detection rate of latent or infected people, and vaccination measures are used to increase the immune protection rate of susceptible people. Based on the city's population size, infection level, quantity of epidemic prevention resources, epidemic prevention capacity, and epidemic prevention cost parameters, the city's baseline isolation measures, baseline testing measures, and baseline vaccination measures are set.

6. The influenza prevention and control optimization method based on population flow networks according to claim 1, characterized in that, In step S5, the optimization of the epidemic prevention measures includes: a) First, input the set of key cities. Basic epidemic prevention measures parameter settings and urban population flow network topology; b) Set the epidemic prevention parameters for non-key cities as the baseline epidemic prevention measures, and set the feedback vertex set. The epidemic prevention parameters of key cities in China are used as variables to be optimized. c) With the preset influenza suppression target as a constraint and the minimum epidemic prevention cost as the optimization objective, solve for the epidemic prevention measures in key cities respectively; d) Output the optimal isolation parameters for key cities. Optimal detection parameters and optimal inoculation parameters .

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