Medical resource allocation method based on time sequence complex network and plaque model

Abstract

The invention discloses a medical resource allocation method based on a time sequence complex network and a plaque model, and belongs to the technical field of resource allocation optimization. Aiming at the problem of how to predict the current infectious disease transmission trend and the inter-regional population flow on the medical resource bearing capacity in the region under the population flow condition, the method comprises the following steps: crawling data through Python, and cleaning and preprocessing the data; analyzing and researching the infectious disease evolution trend of each province in a time period through Arcgis software, constructing a time sequence complex network based on a gravitation model, and describing infectious disease transmission; comprehensively evaluating a spatial topological structure and an evolution trend of the infectious disease network by taking network density and a clustering coefficient as global indexes to obtain a'key 'region influencing infectious disease transmission; fitting the number of newly added accumulated patients and the number of hospitalized patients every day by adopting an SEIQHDR plaque model and combining a Monte Carlo algorithm; and a medical resource dynamic configuration model is used to analyze the relationship between population flow and the medical resource condition of the key region, and then resource allocation is optimized.

Description

Technical Field

[0001] The present invention belongs to the technical field of resource allocation optimization, and in particular relates to a medical resource allocation method based on a temporal complex network and a plaque model. Background Art

[0002] Previously, an acute respiratory infectious disease was a global pandemic, which had a huge impact on the social, economic, production and life of various countries. At present, the infectious disease has entered a lower level, but it is far from over, so the study of its transmission mechanism is still of great significance. Previous studies on infectious diseases have focused on the overall trend of a region, but there have been few studies on its internal transmission mechanism. From December 2022 to January 2023, all provinces in my country suffered from the rapid spread of infectious diseases, and the medical system was under tremendous pressure. Although no mandatory restrictions on the flow of people have been taken, the people's conscious implementation of self-protection behaviors such as staying at home and reducing going out has reduced the spread of infectious diseases.

[0003] The transportation network of each province in China is well developed, including road, rail and air transportation, and the province has high population mobility, which significantly increases the risk of infectious disease transmission. The close connection between the regions within the province has become a potential infectious disease risk spillover network, and each region may become a source of spread. At the same time, population mobility has a great impact on cities with tight medical resources. Population migration usually reduces the pressure on the local medical system, but increases the pressure on the place of immigration. During this period, resource allocation in areas with a large number of immigrants should be strengthened. Restricting population migration is not always beneficial. In some provincial capitals, the time of medical resource squeeze increases when there is no migration; while for third- and fourth-tier cities, changes in migration rates have little effect on the duration of medical resource squeeze. The formulation of medical resource allocation and population migration management methods needs to be customized according to specific circumstances. Summary of the invention

[0004] In view of the problem of how to predict the impact of current infectious disease transmission trends and inter-regional population mobility on the carrying capacity of regional medical resources under population mobility, the present invention provides a medical resource allocation method based on a temporal complex network and a plaque model.

[0005] In order to achieve the above object, the present invention adopts the following technical solutions:

[0006] A medical resource allocation method based on a temporal complex network and a plaque model comprises the following steps:

[0007] Step 1: crawl data through Python, and then clean and preprocess the data;

[0008] Step 2: Analyze the evolution trend of infectious diseases in each province during the study period using ArcGIS software, and construct a temporal complex network based on the gravity model to describe the spread of infectious diseases;

[0009] Step 3: Using network density, clustering coefficient and centrality as global indicators, comprehensively evaluate the spatial topological structure and evolution trend of the infectious disease network and derive the “key” areas that affect the spread of infectious diseases;

[0010] Step 4: Based on the “critical” areas, the SEIQHDR patch model is used in combination with the Monte Carlo algorithm to fit the daily cumulative number of new patients and the number of hospitalized patients. The medical resource dynamic configuration model is then used to analyze the relationship between population mobility and the medical resource situation between “critical” areas, thereby optimizing resource allocation.

[0011] Further, the specific operations of step 2 are:

[0012] The research period [T1, T2] is divided into N net time windows to form a segmented timing network, which is expressed as follows:

[0013] {[T1, T1+Δ],[T1+Δ,T2+2Δ],…,[T1+(N net -1)Δ,T2]}

[0014] Among them, Δ represents the window width; T1 is the date when data collection starts; T2 is the date when data collection ends; infectious diseases last for a long time, and it is inappropriate to use the network in the same time period to characterize the spatial characteristics of the spread of infectious diseases. Therefore, a time series network is constructed in stages to characterize the spatial characteristics of the spread of infectious diseases.

[0015] According to the change in the daily total number of newly infected people, the time series network is divided into N net Slice networks; each slice network is recorded as: Among them G t =(V t ,E t )t=1,2,···,N net , V t represents the set of the tth network node, G t is the set of the tth network edge, E t Represents the edge between the tth network node.

[0016] A temporal network is a dynamic network. Different from a network with a static topology, after adding the time dimension, the edges in the network will appear and disappear intermittently over time. Such a network is called a temporal network.

[0017] Furthermore, the specific method of constructing a slice network is:

[0018] The improved gravity model is used to describe the spread of infectious diseases among cities and the evolution of network structure. The gravity model is constructed as follows:

[0019]

[0020] Among them, b ij represents the spatial correlation of infectious disease transmission between cities i and j, and is also a constituent element of the adjacency matrix; ρ ij represents the correlation coefficient of the number of infections between cities i and j in the selected time period; k ij It represents the proportion of the number of infected people in city i to that in cities i and j, and is used to describe the directionality and asymmetry of the spread of infectious diseases between cities; I i represents the number of infected people in city i within a period of time; P i represents the permanent population of city i within a period of time; G i represents the number of highway toll stations in city i within a period of time; D ij represents the actual geographical distance between cities i and j;

[0021]

[0022] B t Represents the adjacency matrix corresponding to time period t.

[0023] Furthermore, the network density in step 3 represents the ratio of the actual connections between network nodes to the theoretically existing edges, and is used to measure the degree of interconnection between nodes in the network; the greater the network density, the more interconnections between nodes, and the denser the edge connections between nodes; the calculation formula for network density is as follows:

[0024]

[0025] Among them, m t represents the actual edges of the t-th slice network, where N is the number of nodes;

[0026] The clustering coefficient in step 3 represents the ratio of the number of edges actually connected between a node and its nearby nodes to the maximum number of edges connected to these nodes, and is used to measure the degree of clustering between a node and its connected nodes. The larger the clustering coefficient, the smaller the network has the small-world characteristic. The calculation formula of the clustering coefficient is as follows:

[0027]

[0028] Among them, k i represents the number of nodes adjacent to node i, E it represents the k of the t-th slice networki The number of edges connecting the nodes.

[0029] Furthermore, the centrality index specifically includes node degree, degree centrality, closeness centrality, betweenness centrality and eigenvector centrality; the centrality index is used to study the regions and relative importance of cities in the province that play a key role in the spread and development of infectious diseases;

[0030] The node degree refers to the number of actual edges between a single node and surrounding nodes. The number of incoming edges of a node is called the node's in-degree, i.e., the point-in degree. The number of outgoing edges of a node is called the node's out-degree, i.e., the point-out degree. In the infectious disease network, the point-out degree is used to measure the number of infectious diseases caused by a city to other cities, and the point-in degree is used to measure the degree of infectious diseases spread by other cities to a city. The calculation formula of the node degree is as follows:

[0031] degree ti =|E ti |,t=1,2,···,N net ; i=1,2,···,N

[0032] Among them, degree ti represents the degree of the i-th node in the t-th slice network, represented by |E ti | indicates;

[0033] The degree centrality indicates the ratio of the actual number of edges a node has to the theoretical number of edges. It is used to measure the number of connections a node has in the network. The greater the degree centrality of a city, the stronger the correlation and the closer the connection between the city and other cities. The calculation formula of degree centrality is as follows:

[0034]

[0035] The closeness centrality is the reciprocal of the average of the shortest paths between a node and all other nodes in the network. The shortest distance refers to the number of edges in the shortest path between two points. If one point is regarded as the starting point and the other point is the k-th neighbor of the point, the shortest distance between the two is k. The larger the closeness centrality value, the closer the node is to other nodes and the more it has the status of a "central actor" in the network. The calculation formula of closeness centrality is as follows:

[0036]

[0037] Among them, d ij represents the shortest path from city i to city j in the tth slice network;

[0038] The betweenness centrality indicates the number of times a node appears in all the shortest paths between other nodes. The greater the betweenness centrality, the greater the role of the city as an intermediary, and the role of a bridge in the spread of infectious diseases. The calculation formula of betweenness centrality is as follows:

[0039]

[0040] Among them, g jk represents the number of shortest paths between city j and city k, and represents the number of paths between city j and city k that pass through node i;

[0041] The eigenvector centrality is used to measure the influence or importance of a node in a network. In a graph, nodes influence each other. A node receives influence from neighboring nodes through incoming edges. Therefore, the eigenvector centrality score of a node depends not only on the number of incoming edges, but also on the importance of the incoming edge neighbors. The larger the score of a node, the greater its influence. The calculation formula of the eigenvector centrality is as follows:

[0042] EC ti =x i ,t=1,2,···,N net ; i=1,2,···,N

[0043] Among them, x i Represents the i-th component of the eigenvector corresponding to the maximum eigenvalue of the adjacency matrix of the t-th slice network.

[0044] Furthermore, the model assumptions of the SEIQHDR plaque model in step 4 are as follows: (1) recovered patients will not be infected again during the study period; (2) the total population N of each city i (1) The number of asymptomatic infections and their transmission to susceptible persons will remain unchanged during the study period; (2) Asymptomatic infections and their transmission to susceptible persons are not considered; (3) Asymptomatic infections and their transmission to susceptible persons are not considered; (4) As patients are inactive during home quarantine, they are not contagious during home quarantine; (5) As long as there are beds, there will be sufficient medical staff and medical equipment; even in periods of medical stress, although there may be challenges in accommodating all patients, hospitalized patients can receive adequate treatment; (6) As most people do not undergo nucleic acid testing after control is lifted, people with similar symptoms are regarded as new cases; (7) Changes in the number of hospital beds are quantitative indicators that reflect the dynamic changes in medical resources; the increase and decrease in the number of hospital beds is used as a quantitative indicator to reflect the dynamic allocation of medical resources.

[0045] Furthermore, the transfer relationship of the population is: susceptible person S i There is a chance to become a latent infected person; Lurker E i After the incubation period, there is a chance that the patient will develop into a symptomatic infection. iThere is a chance of recovery or death due to lack of timely treatment, most of whom will enter home quarantine; those at home Q i There is a chance that the condition will worsen and require hospitalization i , or there is a chance of recovery R i , there is also a certain risk of death; hospitalized patients H i Chance of death D i or discharged from hospital after recovery; ci (t) represents the hospital bed capacity in region i at time t, reflecting medical resources; susceptible, latent, infected, hospitalized, and recovered people can migrate between region i and region j;

[0046] Further, the SEIQHDR plaque model is expressed as:

[0047]

[0048] Where i = 1 to n, and

[0049] The contact rate is a function that decreases with time t and is expressed as:

[0050]

[0051] Among them, c 0i represents the contact rate at the initial time, c 0i =c i (0);c bi Represents the minimum contact rate given the current control strategy δ 1i It means that the contact rate decreases in an exponential manner.

[0052] Furthermore, the dynamic configuration model of medical resources is: using a logistic growth model to simulate the change in the number of beds, expressed as:

[0053]

[0054] Among them, δ i represents the production and allocation capacity of medical resources, H mi Indicates the maximum number of beds available during an epidemic;

[0055] According to the different stages of disease development, a piecewise function is used to calculate the number of beds per day, expressed as:

[0056]

[0057] Among them, H 0i represents the initial bed capacity for novel coronavirus patients during an infectious disease outbreak, T irepresents the critical moment when the city begins to increase medical resources (including hospital beds); therefore, the daily potential number of empty beds is calculated as H ji (t) = max{H ci (t)-θ i Q i ,0}.

[0058] Furthermore, the specific operations of step 4 are: firstly perform model parameter estimation and data fitting, use Latin hypercube sampling and Markov chain Monte Carlo simulation to estimate unknown parameters, and use SEIQHDR plaque model to fit the daily new cases and number of hospitalizations; use the ode45 function in MATLAB software, use the network density formula and clustering coefficient formula to calculate the number of available beds per day and perform sensitivity analysis, and then use the dynamic configuration model of medical resources to analyze the relationship between population mobility and medical resources between "key" areas.

[0059] Compared with the prior art, the present invention has the following advantages:

[0060] The present invention tests Shanxi Province, treating it as 11 independent patches (also called "nodes"), and studies the limitations of population mobility between patches on the impact of infectious diseases, as well as the impact of these limitations on the final number of infections, the number of hospitalizations, and medical resources (indicated by available hospital beds). In addition, the present invention also discusses the impact of population mobility on cities with tight medical resources, and how to shorten the time of medical resource runs through macroeconomic regulation. For the first time, the present invention uses 11 prefecture-level cities in Shanxi Province as research units, and identifies areas that play a "key" role in the spread of infectious diseases through network structure and node centrality attributes. The present invention innovatively explores how population mobility between key nodes affects the scale of infectious diseases and the allocation of medical resources within the nodes. This study is of great significance for understanding and controlling the spread of infectious diseases, and also provides a valuable reference for the rational allocation of medical resources. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 It is a schematic diagram of the transformation relationship of the crowd status;

[0062] Figure 2 It is a schematic flow diagram of the method of the present invention;

[0063] Figure 3 This is a diagram showing the curve of the number of new infections in Shanxi Province every day;

[0064] Figure 4 This is the evolution chart of the cumulative number of new coronavirus infections in 11 cities in Shanxi Province over five periods;

[0065] Figure 5 This is a graph showing the changes in degree centrality, closeness centrality, betweenness centrality, and eigenvector centrality over time for 11 cities in Shanxi Province;

[0066] Figure 6 is the parameter estimate for Taiyuan and Jinzhong, where a and b represent the parameters β1, β2, and c of the Markov chain realized with 10,000 samples. 01 and c 02 ; c, d are bar graphs.

[0067] Figure 7 Fitting results of the cumulative number of new cases and new hospitalizations in Taiyuan and Jinzhong from December 9, 2022 to January 13, 2023. The circles and triangles are the cumulative number of newly reported human cases and hospitalizations, and the curve represents the solution to equation (10).

[0068] Figure 8 are the parameter estimates for Linfen and Yuncheng; a, b represent the simulation results of the parameters β3, β4, β5 and β6 of the Markov chain realized with 10,000 samples; c, d are histograms.

[0069] Fig. 9 Fitting results of the cumulative number of new cases and new hospitalizations in Linfen and Yuncheng from December 9, 2022 to January 13, 2023. The circles and triangles are the cumulative number of newly reported human cases and hospitalizations, and the curve represents the solution to equation (10).

[0070] Fig.10 The graphs of daily vacant beds in Taiyuan and Jinzhong under different population migration scenarios; (a) shows the daily vacant beds in Taiyuan and Jinzhong under different population migration scenarios; (b) shows the daily vacant beds in Jinzhong under different population migration scenarios. The red, green, black, purple and blue solid lines respectively represent the changes in the number of vacant beds when only considering the population migration from Jinzhong to Taiyuan, the actual population migration, 4 / 5 of the actual population migration scale, and no population migration, when only considering the population migration from Taiyuan to Jinzhong.

[0071] Fig.11 The charts of the daily changes in the number of vacant beds in Linfen and Yuncheng are shown below. (a) shows the daily changes in the number of vacant beds in Linfen under different population migration conditions; (b) shows the daily changes in the number of vacant beds in Yuncheng under different population migration conditions. The blue, green, black, purple and red solid lines respectively represent the changes in the number of vacant beds when only considering the population migration from Yuncheng to Linfen, the actual population migration, 4 / 5 of the actual population migration scale, and no population migration, and only considering the population migration from Linfen to Yuncheng. DETAILED DESCRIPTION

[0072] In order to gain a deeper understanding of the present invention, we will provide a comprehensive and detailed description of the present invention. However, the present invention has multiple implementations and is not limited to the specific examples listed herein. The presentation of these examples is intended to deepen the comprehensive understanding of the disclosure of the present invention.

[0073] Table 1 Model symbol explanation table

[0074]

[0075]

[0076] Among them, i and j represent regions

[0077] Example 1

[0078] This embodiment takes Shanxi Province as an example, a medical resource allocation method based on a temporal complex network and a plaque model includes the following steps:

[0079] Step 1: crawl data through Python, and then clean and preprocess the data;

[0080] The data on the number of newly infected people per day were collected from the infection rates of various cities provided by Shanxi Medical University and Shanxi Provincial Center for Disease Control and Prevention, and were calculated by "local total population × incidence rate". The data on hospitalized cases were provided by the Shanxi Provincial Health Commission through the designated hospital monitoring system. The number of beds in the general hospitals of each city in Shanxi Province was obtained from the Shanxi Provincial Medical and Health Service System Plan. The population migration data was obtained after processing through the Baidu Migration Scale Index. The processing process is as follows: First, Python was used to crawl the Baidu Migration Scale Index related data provided by the Baidu Migration Big Data Platform; then the actual number of migrants in a certain place in any direction (in / out) was calculated with the help of the Baidu Migration Scale Index structure inversion.

[0081] The daily data of newly infected people from December 1, 2022 to January 13, 2023 were collected and analyzed using R language. The analysis results are shown in Figure 3 We found that during the study period, the trend of infectious diseases in Shanxi Province can be divided into five stages: slow rise period, rapid rise period, stable period, rapid decline period and slow decline period.

[0082] Step 2: Analyze the evolution trend of infectious diseases in each province during the study period using ArcGIS software, and construct a temporal complex network based on the gravity model to describe the spread of infectious diseases;

[0083] ArcGIS software was used to simulate the evolution of infectious diseases in various cities in Shanxi Province during these five stages. Figure 4The analysis found that the second and third stages were the peak periods of infectious diseases in Shanxi Province, and infectious diseases in Taiyuan, Jinzhong, Luliang, Linfen, Jincheng, Changzhi and Yuncheng were more serious. In order to further explore the role of various cities in the evolution of infectious diseases and evaluate the trend of infectious diseases, this study further subdivided the above five stages into five time slices and constructed an infectious disease association network based on them.

[0084] The research period [T1, T2] is divided into N net time windows to form a segmented timing network, which is expressed as follows:

[0085] {[T1, T1+Δ],[T1+Δ,T2+2Δ],…,[T1+(N net -1)Δ,T2]}

[0086] Among them, Δ represents the window width, which is 5 in this embodiment; T1 is the date when data collection starts; T2 is the date when data collection ends; infectious diseases last for a long time, and it is inappropriate to use the network in the same time period to characterize the spatial characteristics of the spread of infectious diseases, so a time series network is constructed in stages to characterize the spatial characteristics of the spread of infectious diseases.

[0087] According to the change in the daily total number of newly infected people, the time series network is divided into N net Slice networks; each slice network is recorded as: Among them G t =(V t ,E t )t=1,2,···,N net , V t represents the set of the tth network node, G t is the set of the tth network edge, E t Represents the edge between the tth network node and the node. Temporal networks are dynamic networks; different from networks with static topological structures, after adding the time dimension, the edges in the network will appear and disappear intermittently over time. Such networks are called temporal networks.

[0088] Furthermore, the specific method of constructing a slice network is:

[0089] The improved gravity model is used to describe the spread of infectious diseases among cities and the evolution of network structure. The improved gravity model is constructed as follows:

[0090]

[0091] Among them, b ij represents the spatial correlation of infectious disease transmission between cities i and j, and is also a constituent element of the adjacency matrix; ρ ijrepresents the correlation coefficient of the number of infections between cities i and j in the selected time period; k ij It represents the proportion of the number of infected people in city i to that in cities i and j, and is used to describe the directionality and asymmetry of the spread of infectious diseases between cities; I i represents the number of infected people in city i within a period of time; P i represents the permanent population of city i within a period of time; G i represents the number of highway toll stations in city i within a period of time; D ij represents the actual geographical distance between cities i and j;

[0092]

[0093] B t Represents the adjacency matrix corresponding to time period t.

[0094] In the infectious disease network, nodes represent prefecture-level cities. Edges represent that there is correlation between the spread of infectious diseases in two urban areas, and no edges represent that there is no direct correlation between the spread of infectious diseases in two urban areas. The five corresponding network graphs are constructed through the adjacency matrix of the five slice networks to study the evolution of the infectious disease association network and the evolution of infectious disease risks. The greater the correlation between infectious diseases between cities, the more edges there are in the network graph, and the easier it is for infectious diseases to spread.

[0095] In the first period, the growth rate of the number of new infections in each city was relatively small, but the number of edges in the slice network was large, indicating that the correlation between the urban areas already existed and was at a high level at this time, indicating that although the current situation of infectious diseases was not serious at this time, a large-scale outbreak of infectious diseases was imminent. In the second period, the number of new infections in each urban area rose sharply every day, the edges of the slice network became denser, and the correlation of infectious diseases between urban areas increased rapidly. In the third period when the infectious diseases were the most serious, the number of edges in the slice network was the closest, forming a complex infectious disease transmission network. With the reform of policies and the active cooperation and conscious home stay of residents, the growth rate of the number of new infections began to turn negative in the fourth period; it generally showed a downward trend until the fifth period, but due to the robustness of the infectious disease network, government units and residents still need to be highly vigilant to break the small world attribute of the infectious disease network and thus slow down the spread of infectious diseases.

[0096] Step 3: Using network density and clustering coefficient as global indicators, comprehensively evaluate the spatial topological structure and evolution trend of the infectious disease network and derive the “critical” areas that affect the spread of infectious diseases;

[0097] Network density refers to the ratio of the actual connections between network nodes to the theoretically existing edges, and is used to measure the degree of interconnection between nodes in the network. The greater the network density, the more interconnections between nodes, and the denser the edges between nodes. The calculation formula for network density is as follows:

[0098]

[0099] Among them, m t represents the actual edges of the t-th slice network, where N is the number of nodes;

[0100] The clustering coefficient represents the ratio of the number of edges actually connected between a node and its nearby nodes to the maximum number of possible edges between these nodes. It is used to measure the degree of clustering between a node and its connected nodes. The larger the clustering coefficient, the smaller the network has the small-world characteristic. The calculation formula of the clustering coefficient is as follows:

[0101]

[0102] Among them, k i represents the number of nodes adjacent to node i, E it represents the k of the t-th slice network i The number of edges connecting the nodes.

[0103] According to the network density formula and clustering coefficient formula, the infectious disease transmission density and average clustering coefficient in Shanxi from December 1, 2022 to January 13, 2023 were calculated. The results are shown in Table 2.

[0104] Table 2 Overall analysis of infectious disease network in Shanxi Province

[0105]

[0106] Furthermore, the centrality index is used to study the regions and relative importance of cities in the province that play a key role in the spread and development of infectious diseases; the centrality index specifically includes node degree, degree centrality, closeness centrality, betweenness centrality and eigenvector centrality;

[0107] The node degree refers to the number of actual edges between a single node and surrounding nodes. The number of incoming edges of a node is called the node's in-degree, i.e., the point-in degree. The number of outgoing edges of a node is called the node's out-degree, i.e., the point-out degree. In the infectious disease network, the point-out degree is used to measure the number of infectious diseases caused by a city to other cities, and the point-in degree is used to measure the degree of infectious diseases spread by other cities to a city. The calculation formula of the node degree is as follows:

[0108] degree ti =|E ti |,t=1,2,···,N net ; i=1,2,···,N

[0109] Among them, degree ti represents the degree of the i-th node in the t-th slice network, represented by |E ti | indicates;

[0110] The degree centrality indicates the ratio of the actual number of edges a node has to the theoretical number of edges. It is used to measure the number of connections a node has in the network. The greater the degree centrality of a city, the stronger the correlation and the closer the connection between the city and other cities. The calculation formula of degree centrality is as follows:

[0111]

[0112] The closeness centrality is the reciprocal of the average of the shortest paths between a node and all other nodes in the network. The shortest distance refers to the number of edges in the shortest path between two points. If one point is regarded as the starting point and the other point is the k-th neighbor of the point, the shortest distance between the two is k. The larger the closeness centrality value, the closer the node is to other nodes and the more it has the status of a "central actor" in the network. The calculation formula of closeness centrality is as follows:

[0113]

[0114] Among them, d ij represents the shortest path from city i to city j in the tth slice network;

[0115] The betweenness centrality indicates the number of times a node appears in all the shortest paths between other nodes. The greater the betweenness centrality, the greater the role of the city as an intermediary, and the role of a bridge in the spread of infectious diseases. The calculation formula of betweenness centrality is as follows:

[0116]

[0117] Among them, g jk represents the number of shortest paths between city j and city k, and represents the number of paths between city j and city k that pass through node i;

[0118] The eigenvector centrality is used to measure the influence or importance of a node in a network. In a graph, nodes influence each other. A node receives influence from neighboring nodes through incoming edges. Therefore, the eigenvector centrality score of a node depends not only on the number of incoming edges, but also on the importance of the incoming edge neighbors. The larger the score of a node, the greater its influence. The calculation formula of the eigenvector centrality is as follows:

[0119] EC ti =x i ,t=1,2,···,N net; i=1,2,···,N

[0120] Among them, x i Represents the i-th component of the eigenvector corresponding to the maximum eigenvalue of the adjacency matrix of the t-th slice network.

[0121] The individual node network characteristics of 11 cities in Shanxi Province from December 1, 2022 to January 13, 2023 include: degree centrality, node degree (out-degree, in-degree), closeness centrality, proximity centrality, and eigenvector centrality. The results are shown in Table 3.

[0122] Table 3 Analysis of the centrality of infectious disease network in Shanxi Province

[0123]

[0124] ① Degree centrality

[0125] The data in Table 3 show that the average degree centrality of the 11 urban areas is 0.4982. Taiyuan and Jinzhong are located in the central urban agglomeration of Shanxi Province. As the provincial capital, Taiyuan has a large flow of people and a dense population, while Shanxi University City is located there. These factors together have led to the fact that the spread of infectious diseases in these two areas is significantly higher than in other areas. In the degree centrality ranking, Linfen and Yuncheng, located in the southeastern urban agglomeration of Shanxi Province, rank high among the southern cities of Shanxi Province. These two cities have large economic aggregates, large populations, and large flow of people.

[0126] ②Out-degree and in-degree

[0127] The analysis in Table 3 shows that the average values ​​of the out-degree and in-degree of the 11 urban areas under investigation are both 4.9818. The out-degree of Jinzhong City and Taiyuan City during the epidemic period far exceeded the average level, indicating that these cities played an "overflow" role in the spread of infectious diseases. The in-degree of Shuozhou City and Datong City is nearly twice their out-degree, indicating that during this epidemic, these two urban areas mainly played the role of receiving the inflow of infectious diseases from other urban areas. Yuncheng and Linfen City, located in the southeastern urban agglomeration of Shanxi Province, ranked high in the region, indicating that these cities played an "overflow" role in the spread of infectious diseases in the southeastern urban agglomeration.

[0128] ③ Closeness to center

[0129] As shown in Table 3, the average proximity centrality of the 11 urban areas is 0.6132. The proximity centrality of the six prefecture-level cities in Shanxi is higher than the average. However, the proximity centrality of Datong City and Shuozhou City in the north, Yuncheng City and Jincheng City in the south, and Yangquan City in the east is lower than the average. This shows that during this epidemic, the internal areas of Shanxi had more direct connections with other areas and had the status of "central actors" in the network, while the peripheral areas played the role of "marginal actors".

[0130] ④ Betweenness centrality

[0131] In the infectious disease risk network, the intermediary centrality describes the "hub" nature of the regional node in the associated network and is the intermediary of the infectious disease transmission network. As shown in Table 3, the average intermediary centrality of the 11 urban areas is 3.6751. In the central urban agglomeration of Shanxi Province, the sum of the intermediary centralities of Taiyuan and Jinzhong is 15.79, so the two cities occupy an absolute position in the infectious disease transmission network in the central cities of Shanxi Province. Among the cities in the southeast of Shanxi Province, the sum of the intermediary centralities of Linfen and Yuncheng is 3.89, so the two cities occupy an absolute position in the infectious disease transmission network in the southeast of Shanxi Province.

[0132] ⑤Eigenvector centrality

[0133] The eigenvector centrality indicates the importance of the regional nodes connected to the node. As shown in Table 3, the average eigenvector centrality of the 11 urban areas is 0.2744. Taiyuan City and Jinzhong City are the two regions with the highest eigenvector centrality in Shanxi Province. These two urban areas are also the two regions with the largest number of people initially infected by this infectious disease. In the entire infectious disease risk network, they are the source of risk transmission, as well as traditional intermediaries and hubs. In southeastern Shanxi, Linfen and Yuncheng have the highest eigenvector centrality, which are the source of regional risk transmission, as well as traditional intermediaries and hubs.

[0134] Step 4: Based on the “key” areas, the SEIQHDR patch model is used in combination with the Monte Carlo algorithm to fit the daily cumulative number of new patients and the number of hospitalized patients; the medical resource dynamic configuration model is then used to analyze the relationship between population mobility and the medical resource situation between “key” areas, thereby optimizing resource allocation;

[0135] Centrality analysis shows that the key areas for the spread of infectious diseases in Shanxi Province are: Taiyuan, Jinzhong, Linfen and Yuncheng. The simulation results show that changes in the population migration rate have a significant impact on the run on medical resources. If the population only migrates from Jinzhong to Taiyuan, the run on medical resources in Taiyuan will occur earlier and be prolonged; if the population only migrates from Taiyuan to Jinzhong, the run on medical resources in Jinzhong will be prolonged. If the migration rate of the two places drops to 4 / 5 of the original level, the situation in Taiyuan remains unchanged, and the run on Jinzhong will end earlier. When there is no migration, the run time in Taiyuan increases, while that in Jinzhong decreases. The situations in Linfen and Yuncheng are similar, which also shows the direct impact of population mobility on the run on medical resources.

[0136] The SEIQHDR plaque model assumes that: (1) recovered patients will not be infected again during the study period; (2) the total population N of each city i(1) The number of asymptomatic infections and their transmission to susceptible persons will remain unchanged during the study period; (2) Asymptomatic infections and their transmission to susceptible persons are not considered; (3) Asymptomatic infections and their transmission to susceptible persons are not considered; (4) As patients are inactive during home quarantine, they are not contagious during home quarantine; (5) As long as there are beds, there will be sufficient medical staff and medical equipment; even in periods of medical stress, although there may be challenges in accommodating all patients, hospitalized patients can receive adequate treatment; (6) As most people do not undergo nucleic acid testing after control is lifted, people with similar symptoms are regarded as new cases; (7) Changes in the number of hospital beds are quantitative indicators that reflect the dynamic changes in medical resources; the increase and decrease in the number of hospital beds is used as a quantitative indicator to reflect the dynamic allocation of medical resources.

[0137] The transfer relationship of the population is: susceptible person S i There is a chance to become a latent infected person; Lurker E i After the incubation period, there is a chance that the patient will develop into a symptomatic infection. i There is a chance of recovery or death due to lack of timely treatment, most of whom will enter home quarantine; those at home Q i There is a chance that the condition will worsen and require hospitalization i , or there is a chance of recovery R i , there is also a certain risk of death; hospitalized patients H i Chance of death D i or discharged from hospital after recovery; ci (t) represents the hospital bed capacity in region i at time t, reflecting medical resources; susceptible, latent, infected, hospitalized, and recovered people can migrate between region i and region j;

[0138] The SEIQHDR patch model is expressed as:

[0139]

[0140] Where i = 1 to n, and

[0141] The contact rate is a function that decreases with time t and is expressed as:

[0142]

[0143] Among them, c 0i represents the contact rate at the initial time, c 0i =c i (0);c bi Represents the minimum contact rate given the current control strategy δ 1i It means that the contact rate decreases in an exponential manner.

[0144] The dynamic configuration model of medical resources is: using the logistic growth model to simulate the change in the number of beds, expressed as:

[0145]

[0146] Among them, δ i represents the production and allocation capacity of medical resources, H mi Indicates the maximum number of beds available during an epidemic;

[0147] According to the different stages of disease development, a piecewise function is used to calculate the number of beds per day, expressed as:

[0148]

[0149] Among them, H 0i represents the initial bed capacity for novel coronavirus patients during an infectious disease outbreak, T i represents the critical moment when the city begins to increase medical resources (including hospital beds); therefore, the daily potential number of empty beds is calculated as H ji (t) = max{H ci (t)-θ i Q i ,0}.

[0150] Latin hypercube sampling and Markov chain Monte Carlo simulation were used to estimate unknown parameters, and the SEIQHDR plaque model was used to fit the daily number of new cases and hospitalizations. The ode45 function in MATLAB software was used to calculate the number of available beds per day using the network density formula and clustering coefficient formula, and a sensitivity analysis was performed.

[0151] Empirical study of SEIQHDR patch model based on population mobility

[0152] 1. Data fitting and prediction results

[0153] In this study, by analyzing the centrality of the time series network, we identified the four cities of Taiyuan, Jinzhong, Linfen, and Yuncheng with the highest degree centrality and proximity centrality as "key" nodes for the spread of infectious diseases. Based on the processed Baidu Migration Index data, we observed that the proportion of population migration between Taiyuan and Jinzhong (Linfen and Yuncheng) was significantly higher than that with other cities during the studied period. Therefore, this study selected Taiyuan-Jinzhong and Linfen-Yuncheng in Shanxi Province as two groups of research cases, collected data on the number of infections and hospitalizations from December 10, 2022 to January 13, 2023, and fitted these data, while simulating and predicting the number of vacant beds for medical resources.

[0154] The Monte Carlo method (MCMC) was used to simulate formula (10) 4000 times, and the parameter estimates of the Taiyuan-Jinzhong group and the Linfen-Yuncheng group were obtained. The specific results are shown in Figure 6 and Figure 8 In addition, the solutions and confidence intervals of the two groups of cities for formula (10) are obtained. Figure 7 and Fig. 9 All the parameter values ​​related to the calculation are listed in Tables 4 and 5. The relationship between the actual population migration and the dynamic changes in the number of vacant beds in medical resources is Fig.10 and Fig.11 In Taiyuan, the run on medical resources began on December 21 and lasted for 4 days. In contrast, the same situation in Jinzhong started on December 19 and lasted for 13 days. The run on medical resources in Taiyuan occurred later and lasted for a shorter period of time, indicating that its medical conditions were more adequate than those in Jinzhong. In Linfen, the run on medical resources began on December 15 and lasted for 69 days. In contrast, the same situation in Yuncheng started on December 10 and lasted for 64 days. Compared with Taiyuan and Jinzhong, Linfen and Yuncheng have poor medical resource reserves and weaker allocation capabilities.

[0155] Table 4 Parameters of Taiyuan (i=1) Jinzhong (j=2)

[0156]

[0157] Table 5 Linfen (i = 3) Yuncheng (j = 4) parameter table

[0158]

[0159]

[0160] 2. Analysis of the relationship between population migration and medical resource allocation

[0161] The impact of population migration rate on the allocation of medical resources. The duration of medical resource run is used as an indicator to measure the status of medical resources. The medical run is quantified by the number of vacant beds and their available time. Medical resource run is defined as a state with no vacant beds.

[0162] Then, the changes in the number of vacant beds and their duration were analyzed, and the relevant results were shown under different scenarios of population migration rates. The results are as follows: Fig.10 and Fig.11 The study constructed three scenarios: one-way migration, migration scale reduced to 4 / 5 of the original, and no migration at all. The study found that:

[0163] (1) If the population migration occurs only from Jinzhong to Taiyuan, the time of occurrence of the medical resource run in Taiyuan will remain unchanged and the end time will be advanced to January 5, 2023, while the time of occurrence of the medical resource run in Jinzhong will be postponed to December 16, 2022 and the end time will be postponed to January 20, 2023, which means the run time will be increased by 9 days compared with the actual situation. On the contrary, if the population migrates only from Taiyuan to Jinzhong, the start time of the medical resource run in Taiyuan will not change and the end time will be postponed to January 11, 2023, while the run in Jinzhong will start from December 17, 2022 and end in advance to December 26, 2022. If the population migration rates of the two places drop to 4 / 5 of the original level at the same time, the medical resource run in Taiyuan will remain unchanged, but the run in Jinzhong will end two days earlier than the actual situation. In the absence of population migration, the time of occurrence of the medical resource run in Taiyuan will remain unchanged compared to the actual situation, and the end time will be postponed to January 9, 2023; the start time of the medical resource run in Jinzhong City will be delayed to December 17, 2022, and the end time will be advanced to December 28, and the number of days of the run will be reduced by 15 days.

[0164] (2) If population migration occurs only from Yuncheng to Linfen, the end time of the medical resource run in Linfen will be advanced to January 1, 2023, and the time of the run will remain unchanged; while the medical resource run in Yuncheng will be delayed to January 12, 2023. If the population migrates only from Linfen to Yuncheng, the end time of the medical resource run in Linfen will be postponed to January 6, 2023, and the run in Yuncheng will be advanced to January 1, 2023. If the population migration rates of the two places are reduced to 4 / 5 of the original level at the same time, the medical resource run in Linfen will not change, but the run in Yuncheng will be delayed by one day. In the absence of population migration, the end time of the medical resource run in Linfen will be advanced to January 2, 2023, and the overall run duration will be reduced by one day compared with the actual situation; the medical resource run in Yuncheng will be delayed by two days to January 6, 2023.

[0165] Judging from the results, population migration will affect the duration of medical resource runs. Generally speaking, population outflow will ease the pressure on the local medical system and increase the pressure on the medical system in the place of migration. Therefore, it is necessary to strengthen resource allocation in areas with a large influx of population when infectious diseases break out. However, restrictions on population migration are not always beneficial. For example, assuming that there is no population migration, the duration of medical runs in Taiyuan City has increased instead; it may also be ineffective. For example, for Yuncheng City, no matter how the population migration rate changes, the duration of medical runs changes very little. This also reflects the need to formulate appropriate medical resource allocation and population migration restriction policies according to local conditions.

[0166] In summary, the present invention firstly uses an improved gravity model to construct an adjacency matrix for the spread of infectious diseases, and on this basis establishes a time-series slice threshold network. By analyzing the evolution of the spatial topological structure of the network, the following phenomena are observed: the changing trends of the graph density and clustering coefficient show that after the residents spontaneously stay at home, these indicators first rise and then fall, and finally reach an inflection point. This trend reflects that the conscious home behavior of residents helps to reduce the flow of population between nodes, thereby reducing the connectivity of the network, effectively curbing the spread of infectious diseases, and significantly reducing the demand for anti-epidemic resources. Through the analysis of the centrality index, it is found that Taiyuan City, Jinzhong City, Linfen City, and Yuncheng City rank high in terms of proximity centrality and intermediary centrality, indicating that these cities play a key role as "central actors" and "bridges" in the infectious disease network. Therefore, the study regards Taiyuan City and Jinzhong City, as well as Linfen City and Yuncheng City as key areas for infectious disease management, and quantitatively analyzes the impact of population mobility on infectious diseases in these areas.

[0167] The results show that the run on medical resources in Taiyuan started on December 17 and lasted for 22 days, while the run on medical resources in Jinzhong started on December 10 and lasted for 27 days. Taiyuan has stronger medical resources and allocation capabilities than Jinzhong. The runs on medical resources in Linfen and Yuncheng started on December 14, 2022 and December 13, 2022, respectively, and lasted for 21 days and 23 days, respectively, reflecting the inadequacy of these regions in terms of medical resource reserves and allocation capabilities. In addition, the study also explored the impact of population mobility on the allocation of medical resources. The results show that population migration can reduce the pressure on the local medical system, but at the same time it will increase the burden on the medical system of the place of migration. Therefore, during the high incidence of infectious diseases, for areas with more population migration, it is necessary to strengthen the allocation of medical resources. However, according to case analysis, it is found that restrictions on population migration are not always beneficial, and appropriate strategies for the allocation of medical resources and population migration restrictions should be formulated according to specific circumstances.

[0168] The present invention regards each of the 11 cities in Shanxi Province as an independent node, constructs a network topology, and explores the dynamic evolution of the spread of infectious diseases in the 11 cities when only residents consciously implement self-protection behaviors such as staying at home and reducing going out. Taking into account the factors that affect the spread of infectious diseases, such as population density, number of infected people, correlation between cities in Shanxi Province, and road traffic, the classic gravity model is innovatively improved to more accurately describe the interaction between cities, analyze the various indicators of various cities in Shanxi Province in the spread of infectious diseases, and determine the areas that play a "key" role in the spread of infectious diseases. Taking into account the complexity of actual infectious diseases, the classic SEIR model is improved, and the SEIQHDR plaque model is established. Combined with the results of the network topology model, the medical resource situation in various cities in Shanxi is predicted and warned, and the relationship between population mobility and medical resource allocation is analyzed, and corresponding optimization is made to reduce the duration of medical runs and optimize medical resource allocation.

[0169] The contents not described in detail in the specification of the present invention belong to the prior art known to the professional and technical personnel in the field. Although the illustrative specific embodiments of the present invention are described above to facilitate the understanding of the present invention by the technical personnel in the field, it should be clear that the present invention is not limited to the scope of the specific embodiments. For the ordinary technical personnel in the field, as long as various changes are within the spirit and scope of the present invention defined and determined by the attached claims, these changes are obvious, and all inventions and creations using the concept of the present invention are protected.

Claims

1. A medical resource allocation method based on temporal complex network and plaque model, characterized in that: The following steps are involved: Step 1: crawl data through Python, and then clean and preprocess the data; Step 2: Analyze the evolution trend of infectious diseases in each province during the study period using ArcGIS software, and construct a temporal complex network based on the gravity model to describe the spread of infectious diseases; Step 3: Using network density, clustering coefficient and centrality as global indicators, comprehensively evaluate the spatial topological structure and evolution trend of the infectious disease network and derive the "key" areas that affect the spread of infectious diseases; Step 4: Based on the "key" areas, the SEIQHDR patch model is used in combination with the Monte Carlo algorithm to fit the daily cumulative number of new patients and the number of hospitalized patients; the dynamic configuration model of medical resources is then used to analyze the relationship between population mobility and the medical resource situation between "key" areas, thereby optimizing resource allocation.

2. According to claim 1, a medical resource allocation method based on temporal complex network and plaque model is characterized by: The specific operations of step 2 are: The research period [T1, T2] is divided into N net time windows to form a segmented timing network, which is expressed as follows: {[T1,T1+Δ],[T1+Δ,T2+2Δ],…,[T1+(N net -1)D,T2]} Where, Δ represents the window width; T1 is the date when data collection starts; T2 is the date when data collection ends; According to the change in the daily total number of newly infected people, the time series network is divided into N net Slice networks; each slice network is recorded as: Among them G t =(V t ,E t )t=1,2,···,N net , V t represents the set of the tth network node, G t is the set of the tth network edge, E t Represents the edge between the tth network node.

3. The medical resource allocation method based on temporal complex network and plaque model according to claim 2 is characterized by: The specific method of building a slice network is: The improved gravity model is used to describe the spread of infectious diseases among cities and the evolution of network structure. The improved gravity model is constructed as follows: Among them, b ij represents the spatial correlation of infectious disease transmission between cities i and j, and is also a constituent element of the adjacency matrix; ρ ij represents the correlation coefficient of the number of infections between cities i and j in the selected time period; k ij It represents the proportion of the number of infected people in city i to that in cities i and j, and is used to describe the directionality and asymmetry of the spread of infectious diseases between cities; I i represents the number of infected people in city i within a period of time; P i represents the permanent population of city i within a period of time; G i represents the number of highway toll stations in city i within a period of time; D ij represents the actual geographical distance between cities i and j; B t Represents the adjacency matrix corresponding to time period t.

4. The medical resource allocation method based on temporal complex network and plaque model according to claim 1, characterized in that: The network density in step 3 represents the ratio of the actual connections between network nodes to the theoretically existing edges, and is used to measure the degree of interconnection between nodes in the network. The greater the network density, the more interconnections between nodes, and the denser the edges between nodes. The calculation formula of network density is as follows: Among them, m t represents the actual edges of the t-th slice network, where N is the number of nodes; The clustering coefficient in step 3 represents the ratio of the number of edges actually connected between a node and its nearby nodes to the maximum number of edges connected to these nodes, and is used to measure the degree of clustering between a node and its connected nodes. The larger the clustering coefficient, the smaller the network has the small-world characteristic. The calculation formula of the clustering coefficient is as follows: Among them, k i represents the number of nodes adjacent to node i, E it represents the k of the t-th slice network i The number of edges connecting the nodes.

5. The medical resource allocation method based on temporal complex network and plaque model according to claim 1, characterized in that: The centrality index specifically includes node degree, degree centrality, closeness centrality, betweenness centrality and eigenvector centrality; The node degree refers to the number of actual edges between a single node and surrounding nodes. The number of incoming edges of a node is called the node's in-degree, i.e., the point-in degree. The number of outgoing edges of a node is called the node's out-degree, i.e., the point-out degree. In the infectious disease network, the point-out degree is used to measure the number of infectious diseases caused by a city to other cities, and the point-in degree is used to measure the degree of infectious diseases spread by other cities to a city. The calculation formula of the node degree is as follows: degree ti =|E ti |,t=1,2,···,N net ;i=1,2,···,N Among them, degree ti represents the degree of the i-th node in the t-th slice network, represented by |E ti | indicates; The degree centrality indicates the ratio of the actual number of edges a node has to the theoretical number of edges. It is used to measure the number of connections a node has in the network. The greater the degree centrality of a city, the stronger the correlation and the closer the connection between the city and other cities. The calculation formula of degree centrality is as follows: The closeness centrality is the reciprocal of the average of the shortest paths between a node and all other nodes in the network. The shortest distance refers to the number of edges in the shortest path between two points. If one point is regarded as the starting point and the other point is the k-th neighbor of the point, the shortest distance between the two is k. The larger the closeness centrality value, the closer the node is to other nodes and the more it has the status of a "central actor" in the network. The calculation formula of closeness centrality is as follows: Among them, d ij represents the shortest path from city i to city j in the tth slice network; The betweenness centrality indicates the number of times a node appears in all the shortest paths between other nodes. The greater the betweenness centrality, the greater the role of the city as an intermediary, and the role of a bridge in the spread of infectious diseases. The calculation formula of betweenness centrality is as follows: Among them, g jk represents the number of shortest paths between city j and city k, and represents the number of paths between city j and city k that pass through node i; The eigenvector centrality is used to measure the influence or importance of a node in a network. In a graph, nodes influence each other. A node receives influence from neighboring nodes through incoming edges. Therefore, the eigenvector centrality score of a node depends not only on the number of incoming edges, but also on the importance of the incoming edge neighbors. The larger the score of a node, the greater its influence. The calculation formula of the eigenvector centrality is as follows: EC ti =x i ,t=1,2,···,N net ;i=1,2,···,N Among them, x i Represents the i-th component of the eigenvector corresponding to the maximum eigenvalue of the adjacency matrix of the t-th slice network.

6. The medical resource allocation method based on temporal complex network and plaque model according to claim 1 is characterized by: The model assumption of the SEIQHDR plaque model in step 4 is: (1) The recovered patients will not be infected again during the study period; (2) Total population of each city N i unchanged during the study period; (3) Asymptomatic infections and their transmission to susceptible individuals are not considered; (4) Since patients are inactive during their stay at home, they are not contagious during their stay at home; (5) As long as there are beds, there will be enough medical staff and medical equipment; even during times of medical stress, although there may be challenges in accommodating all patients, hospitalized patients can receive adequate treatment; (6) Since most people do not undergo nucleic acid testing after the control is lifted, people with similar symptoms are considered new cases; (7) The change in the number of hospital beds is a quantitative indicator that reflects the dynamic changes in medical resources; the increase and decrease in the number of hospital beds is used as a quantitative indicator to reflect the dynamic allocation of medical resources.

7. The medical resource allocation method based on temporal complex network and plaque model according to claim 1 is characterized by: The transfer relationship of the population is: susceptible S i There is a chance to become a latent infected person; Lurker E i After the incubation period, there is a chance that the patient will develop into a symptomatic infection. i There is a chance of recovery or death due to lack of timely treatment, most of whom will enter home quarantine; those at home Q i There is a chance that the condition will worsen and require hospitalization i , or there is a chance of recovery R i , there is also a certain risk of death; hospitalized patients H i Chance of death D i or discharged from hospital after recovery; ci (t) represents the hospital bed capacity of region i at time t, reflecting the medical resources; susceptible, latent, infected, hospitalized and recovered people can migrate between region i and region j.

8. The medical resource allocation method based on temporal complex network and plaque model according to claim 1, characterized in that: The SEIQHDR plaque model is expressed as: Where i = 1 to n, and The contact rate is a function that decreases with time t and is expressed as: Among them, c 0i represents the contact rate at the initial time, c 0i =c i (0);c bi Represents the minimum contact rate given the current control strategy δ 1i It means that the contact rate decreases in an exponential manner.

9. The medical resource allocation method based on temporal complex network and plaque model according to claim 1, characterized in that: The dynamic configuration model of medical resources is: using the logistic growth model to simulate the change in the number of beds, expressed as: Among them, δ i represents the production and allocation capacity of medical resources, H mi Indicates the maximum number of beds available during an epidemic; According to the different stages of disease development, a piecewise function is used to calculate the number of beds per day, expressed as: Among them, H 0i represents the initial bed capacity for novel coronavirus patients during an infectious disease outbreak, T i represents the critical moment when the city begins to increase medical resources; therefore, the daily potential number of empty beds is calculated as H ji (t) = max{H ci (t)-θ i Q i ,0}.

10. The medical resource allocation method based on temporal complex network and plaque model according to claim 1, characterized in that: The specific operations of step 4 are: firstly perform model parameter estimation and data fitting, use Latin hypercube sampling and Markov chain Monte Carlo simulation to estimate unknown parameters, and use SEIQHDR plaque model to fit the daily new cases and number of hospitalizations; use the ode45 function in MATLAB software, use the network density formula and clustering coefficient formula to calculate the number of available beds per day and perform sensitivity analysis, and then use the medical resource dynamic configuration model to analyze the relationship between population mobility and medical resource conditions between "key" areas.

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