Method for allocating medical supplies for infectious diseases

Abstract

The application establishes a kind of infectious disease medical material distribution method S1, according to health status, the residents in infectious disease research area are classified;In the case of considering cross-regional travel, the disease transmission rule is established, and the influence of internal management measures and entry and exit management measures is quantified;S2, according to the disease transmission rule, the dynamic model of multi-region transmission of infectious disease is established under the implementation of internal management measures and entry and exit management measures;S3, the dynamic model described in S2 is used to establish a limited medical resource allocation model, and the dynamic optimal medical resource allocation scheme of the infectious disease research area is obtained. With the help of the application, the relevant departments can make more reasonable and accurate emergency medical material allocation scheme, so as to more effectively control the development trend of infectious diseases and improve the ability to cope with epidemic infectious diseases in the region.

Description

TECHNICAL FIELD

[0001] The present application relates to a medical material distribution method, in particular to an infectious disease medical material distribution method. BACKGROUND

[0002] In public health events such as infectious diseases, the distribution of special emergency medical materials such as antibiotics, vaccines, treatment drugs and disinfectants is particularly important; once the decision is wrong, it will cause serious social problems and economic losses. Therefore, in order to reduce the social impact of major infectious diseases and improve the overall public health event response capability of society, an effective emergency management system needs to be established to accurately and quickly distribute special medical materials.

[0003] An emergency medical resource distribution method based on multi-objective optimization (application number CN202010738486.4) sets two optimization targets of high-risk population and infection degree and models, and solves it through particle swarm method, so as to balance the distribution of emergency medical resources in different regions and recommend reasonable emergency medical resource distribution scheme for each region. An emergency medical management system and method for urban public health events (application number CN202210617810.6) sets model construction module, data acquisition module, event classification module, prevention and control command module and rescue taking module in the management system, constructs classification model based on urban public health event data, which is used to judge the danger level of public health event and timely develop emergency plan and take rescue measures. These two inventions provide a reference solution for the distribution of special medical materials, but both lack consideration of population flow and management measures. The present application can help the relevant departments to develop more reasonable and accurate special medical material distribution scheme by considering cross-regional travel, implementation of internal management measures and entry-exit management measures, so as to effectively control the development trend of infectious diseases. SUMMARY

[0004] The application establishes an infectious disease emergency medical material distribution method considering management measures, which is used for designing a dynamic distribution scheme of limited medical materials in a public health emergency. According to the health status, the residents in the infectious disease research area are divided into susceptible, infected, treated and recovered, and the disease transmission rule is established by considering the cross-regional travel. In combination with internal management measures and entry and exit management measures, the application establishes a multi-region discrete SIQR infectious disease model. Based on the multi-region SIQR infectious disease model, the application establishes a limited medical resource distribution model under the condition of limited medical material reserves, and obtains the dynamic optimal medical resource distribution scheme of the infectious disease research area in the research period by solving the model. With the application, the relevant departments can make a more reasonable and precise special emergency medical material distribution scheme, so as to more effectively control the development trend of infectious diseases and improve the ability to cope with epidemic infectious diseases in the region.

[0005] The application provides an infectious disease medical material distribution method, which comprises the following processes:

[0006] S1, according to the health status, the residents in the infectious disease research area are classified; the disease transmission rule is established by considering the cross-regional travel, and the influence of internal management measures and entry and exit management measures is quantified;

[0007] S2, according to the disease transmission rule, a dynamic model of disease transmission in multiple regions is established under the condition of implementing internal management measures and entry and exit management measures;

[0008] S3, a limited medical resource distribution model is established based on the dynamic model in S2, and the dynamic optimal medical resource distribution scheme of the infectious disease research area is obtained by solving.

[0009] Further, the specific process of S1 is that the residents in the infectious disease research area are divided into susceptible, infected, treated and recovered;

[0010] Let Ω represent the infectious disease research area, divide the area Ω into multiple regions, let i represent any region, i.e. i∈Ω; let |Ω| represent the number of divided regions; let N i represent the population of residents in region i∈Ω;

[0011] Region i is divided into four sub-regions, namely susceptible, infected, treated and recovered; let S i , I i , Q i and R i represent the number of susceptible, infected, treated and recovered in region i;

[0012] In the absence of infectious diseases, the population growth of region i is positive, and the population growth is a constant Λi represents, Λ i >0; when the infectious disease occurs, the sub-area S i , I i , Q i and R i The population mortality rate is non-negative, respectively with constant and represent, and

[0013] Let β i represent the incidence rate of region i; then in region i, the standard incidence rate of susceptible is β i S i I i / N i ; the recovery rate of infected and treated in region i is constant, respectively represented by constants α i , ε i ;

[0014] In addition to the treated, the constant proportion of residents of region i traveling to any other region j∈Ω\{i} is g ij ; let g i represent the constant proportion of residents of region i traveling to external regions, g i =∑ j∈Ω\{i} g ij ;

[0015] Through internal management measures, the number of infected in region i decreases at a rate of η i I i , that is, the number of infected in region i decreases per unit time is η i I i ;

[0016] The number of infected traveling from region i to any other region j∈Ω\{i} is g ij I i ; through entry and exit management measures, the number of treated leaving region i is The number of treated entering region j is Therefore, only infected can enter region j from region i and freely move;

[0017] Thus, the effects of internal management measures and entry and exit management measures are quantified.

[0018] Further, characterized in that S2 establishes a dynamic model of the spread of infectious diseases in multiple regions; that is, a multi-region discrete SIQR infectious disease model;

[0019] The multi-region SIQR infectious disease model established is:

[0020] Let N i (t), S i (t), I i (t), Q i (t), R i (t) represent the number of N i , S i , I i , Q i , R i at time t, i.e. the variable N i , S i , I i , Q i , R i as a function of time t; the actual meaning of N i (t), S i (t), I i (t), Q i (t), R i (t) is the same as N i , S i , I i , Q i , R i ;

[0021] For the susceptible S i in region i, the number has the following relationship:

[0022] Number of susceptibles = population growth - number of sick - population deaths - number of people leaving + number of people entering

[0023] The mathematical expression of this relationship is:

[0024]

[0025] For the infected I i in region i, the number has the following relationship:

[0026] Number of infected = number of sick - number of recovered - number of internal treatment - population deaths - number of people leaving + number of people entering

[0027] The mathematical expression of this relationship is:

[0028]

[0029] For the treated Q i in region i, the number has the following relationship:

[0030] Number of treated = number of internal treatment - population deaths - number of recovered + number of people leaving + number of people entering

[0031] The mathematical expression of the relationship is:

[0032]

[0033] For the restorer Q of region i i , the number has the following relationship:

[0034] The number of restorers = the total number of recovered people - the number of population deaths - the number of outbound people + the number of inbound people

[0035] The mathematical expression of the relationship is:

[0036]

[0037] For region i, at the initial time t = 0, the sum of the number of residents in the four subareas is equal to the total number of residents in the region, and the number of residents in each subarea is greater than 0; that is:

[0038] S i (0)>0,I i (0)>0,Q i (0)>0,R i (0)>0

[0039] N i (0)=S i (0)+I i (0)+Q i (0)+R i (0)(5)

[0040] And at the initial time, there is a condition:

[0041]

[0042] In summary, under the implementation of internal management measures and entry and exit management measures, the following multi-region discrete SIQR infectious disease model is established:

[0043]

[0044] In the formula, the first four rows respectively represent the ordinary differential equations of the number of residents in the four subareas S i , I i , Q i , R i change with time; the fifth and sixth rows represent the initial conditions of the SIQR model;

[0045] Let represent the vector solution of the SIQR model; S, I, Q, and R are all vectors with dimension |Ω|. represents the number of susceptible people in each region in the region Ω; Let Ii(t) denote the number of infected people in region i at time t, i.e. Let Tt(t) denote the number of treated people in region i at time t, i.e. Let Rr(t) denote the number of recovered people in region i at time t, i.e.

[0046] Let Θ denote the feasible region of the solution of the SIQR model, Θ is a feasible set, specifically:

[0047]

[0048] Further, the limited medical resource allocation model established by S3 is specifically:

[0049] Divide the research period into multiple time periods to form a set T; let t denote any time period in T, i.e. t∈T; let denote the number of available medical resources in region i at time t; f i t denote the number of medical resources distributed by the emergency center to region i at time t; then denote the total amount of medical resources available to region i at time t; let c denote the amount of medical resources consumed by each treated person per unit time; then for the treated people in region i, the medical resources consumed at any time period t∈T is cQ i (t), all of which cannot exceed the total amount of medical resources available to the region, i.e.

[0050]

[0051] Let denote the number of medical resources reserved by the emergency center at time t; for the research region Ω, at any time period, the number of medical resources distributed by the emergency center to all regions in Ω is∑ i∈Ω f i t , all of which cannot exceed the number of medical resources reserved by the emergency center at this time, i.e.

[0052]

[0053] Let denote the control parameter of the internal management measures of region i at time t; for the infected people I i in region i, at any time period t∈T, the sum of the number of recovered people, treated people, deaths, and people traveling to external regions cannot exceed the number of people who have fallen ill in region i, i.e.

[0054]

[0055] When residents travel between regions i and j, let denote the control parameter of the entry-exit management measures of region i at time t, let denotes the control parameter of the entry-exit management measure in region j at time period t; the total number of infected persons traveling from region i to region j is g ij I i ; the number of treated infected persons leaving region i at time period t through the entry-exit management measure is the number of treated infected persons entering region j is At any time period t∈T, the number of treated infected persons in regions i, j should not exceed the total number of infected persons traveling between regions i, j, that is:

[0056]

[0057] When residents travel between regions i, j, let denote the set of control parameters of the entry-exit management measure in region i. Let Γ i denote the set of control parameters of the internal management measure in region i; then the set elements have the following relationship:

[0058]

[0059] In addition, the variable f i t is non-negative and discrete, that is:

[0060]

[0061] Based on the multi-region SIQR infectious disease model, the following finite medical allocation model is established by minimizing the total number of untreated infected persons in the region Ω and taking into account the above constraints:

[0062]

[0063] s.t.

[0064]

[0065] Further, the solution of the finite medical allocation model adopts the dynamic programming method, and the gurobi commercial solver is called to solve the multi-level linear allocation problem. The solution of the model needs to apply the dynamic programming method. By solving the finite medical allocation model, the dynamic optimal medical resource allocation scheme of the infectious disease research region Ω in the research period T can be obtained.

[0066] The present application enables the relevant departments to develop more reasonable and precise infectious disease emergency medical material allocation schemes, thereby more effectively controlling the development trend of infectious diseases and improving the ability of the region to cope with epidemic infectious diseases. BRIEF DESCRIPTION OF DRAWINGS

[0067] Figure 1A schematic diagram of the transmission process of infectious diseases in a certain region;

[0068] Figure 2 A flowchart of the method of the present application;

[0069] Figure 3 A schematic diagram of the values of infectious disease-related parameters in the study region of infectious diseases;

[0070] Figure 4 A schematic diagram of the dynamic optimal medical resource allocation scheme of the study region Ω of infectious diseases in the study period T. DETAILED DESCRIPTION

[0071] The present application will be further described below in conjunction with examples and the accompanying drawings.

[0072] The present application provides an infectious disease medical material allocation method, as shown in the accompanying drawings, comprising the following processes: Figure 2

[0073] (1) According to the health status, the residents in the study region of infectious diseases are divided into susceptible, infected, treated and recovered. In consideration of cross-regional travel, the transmission rule of infectious diseases is established, and the influence of internal management measures and entry and exit management measures is quantified.

[0074] The study region Ω of infectious diseases can be divided into three regions, i.e. Ω = {1, 2, 3}, |Ω| = 3; let i represent any region, i.e. i ∈ Ω. Let N i represent the number of residents in region i ∈ Ω.

[0075] Region i is divided into four sub-regions, i.e. susceptible, infected, treated and recovered. Among them, the susceptible are healthy but susceptible to infection; the infected have the disease but have not been treated individually; the treated have the disease and have been treated individually; the recovered have recovered and are immune. Let S i , I i , Q i and R i represent the number of susceptible, infected, treated and recovered in region i, respectively.

[0076] Let S, I, Q, R represent vectors with dimension |Ω|. Among them, represents the number of susceptible in each region in region Ω; represents the number of infected in each region in region Ω; represents the number of treated in each region in region Ω; ​This represents the number of recoveries in each region within the study area Ω. Initially, the study area Ω contains: S(0) = (20000, 12000, 11000), I(0) = (1000, 0, 0), Q(0) = (0, 0, 0), and R(0) = (0, 0, 0).

[0077] In the absence of infectious diseases, the population growth in region i is positive, expressed as a constant Λ. i It means, Λ i >0. The population growth rates of the three regions within region Ω are: Λ1 = 200, Λ2 = 150, and Λ3 = 100.

[0078] When an infectious disease occurs, partition S i I i Q i and R i The population mortality rates are all non-negative, expressed as constants. and It means, and The mortality rates for each sub-region within region Ω are as follows:

[0079] Aside from those receiving treatment, the constant proportion of residents of region i traveling to any other region j∈Ω\{i} is g. ij Let g i Let g represent a constant proportion of residents in region i traveling to other regions. i =∑ j∈Ω\{i} g ij The constant proportions of resident travel between different areas within region Ω are as follows: g 12 =0.015, g 21 =0.025, g 23 =0.025, g 32 =0.04, g 13 =0.015, g 31 =0.04. Therefore, the constant proportion of residents from each region within region Ω traveling to other regions is: g1 = g 12 +g 13 =0.015+0.015=0.03, g2=g 21 +g 23 =0.025+0.025=0.05, g3=g 31 +g 32 =0.04 + 0.04 = 0.08.

[0080] Diseases can only be transmitted from an infected person to a susceptible person. i Let β represent the incidence rate in region i; then, within region i, the standard incidence rate among susceptible individuals is β. i Si I i / N i Meanwhile, the recovery rates of both infected and treated individuals within region i remain constant, expressed as constants α. i ε i Let β = 0.3, α = 0.03, and ε = 0.4. Within region Ω, the incidence rates in each region are β1 = β2 = β3 = 0.3, the recovery rates of infected individuals in each region are α1 = α2 = α3 = 0.03, and the recovery rates of treated individuals in each region are ε1 = ε2 = ε3 = 0.4.

[0081] Because the travel time is short, it is not possible to immediately determine the infection status of residents during cross-regional travel (multiple regions within region Ω), so it is not considered.

[0082] When an infectious disease occurs, regions can implement internal management measures and entry / exit management measures. Let η and θ represent the control parameters for internal management measures and entry / exit management measures, respectively. Since the level of medical resources limits the number of infected individuals that can be treated individually, the control parameters for both types of management measures are related to medical resources: the more severe the shortage of medical resources, the lower the estimated values ​​of the control parameters.

[0083] Through internal management measures, the number of infected individuals in region i decreased at a rate η i I i The decrease, i.e., the reduction in the number of infected persons in region i per unit time, is η. i I i .

[0084] The number of infected individuals traveling from region i to any other region j ∈ Ω\{i} is g. ij I i The number of patients receiving treatment who exited from region i through immigration control measures was [number missing]. The number of patients entering region j for treatment was Therefore, in the end only An infected person is able to move freely from region i to region j.

[0085] (2) Based on the transmission patterns of infectious diseases, and under the implementation of internal management measures and entry and exit management measures, a dynamic model of the spread of infectious diseases in multiple regions is established, namely, the multi-region discrete SIQR (susceptible-infected-quarantined-recovered) infectious disease model.

[0086] Let N i (t), S i (t), I i (t), Q i (t), R i(t) represent N respectively i S i I i Q i R i The value at time t, i.e., the variable N. i S i I i Q i R i The form of change with time t. N i (t), S i (t), I i (t), Q i (t), R i The actual meaning of (t) is respectively related to N i S i I i Q i R i same.

[0087] For susceptible individuals S in region i i In terms of quantity, the following relationship exists:

[0088] Number of susceptible individuals = Population growth - Number of infected individuals - Number of deaths - Number of people leaving the country + Number of people entering the country

[0089] The mathematical expression for this relationship is:

[0090]

[0091] For infected persons in region i i In terms of quantity, the following relationship exists:

[0092] Number of infected persons = Number of infected persons - Number of recovered persons - Number of persons receiving in-house treatment - Number of deaths - Number of persons leaving the country + Number of persons entering the country

[0093] The mathematical expression for this relationship is:

[0094]

[0095] For the patient Q in region i i In terms of quantity, the following relationship exists:

[0096] Number of people receiving treatment = Number of people receiving internal treatment - Number of deaths - Number of recovered patients + Number of people leaving the country + Number of people entering the country

[0097] The mathematical expression for this relationship is:

[0098]

[0099] For the restorer Q in region i iIn terms of quantity, the following relationship exists:

[0100] Number of recovered patients = Total number of recovered patients - Number of deaths - Number of people leaving the country + Number of people entering the country

[0101] The mathematical expression for this relationship is:

[0102]

[0103] For region i, at the initial time t=0, the sum of the populations of the four sub-regions equals the total population of the region, and the population of each sub-region is greater than 0. That is:

[0104] S i (0)>0,I i (0)>0,Q i (0)>0,R i (0)>0

[0105] N i (0)=S i (0)+I i (0)+Q i (0)+R i (0)

[0106] And the initial conditions exist:

[0107]

[0108] Based on the above conditions, and under the implementation of internal management measures and entry / exit management measures, the following multi-regional discrete SIQR infectious disease model (hereinafter referred to as SIQR model) is established:

[0109]

[0110] In the formula, the first four rows represent S respectively. i I i Q i R i The ordinary differential equations for the change of the number of residents in these four zones over time; lines 5 and 6 both represent the initial conditions of the SIQR model.

[0111] make Let S, I, Q, and R represent the vector solutions of the SIQR model; S, I, Q, and R are all vectors of dimension |Ω|. This represents the number of susceptible individuals in each region within region Ω. This represents the number of infected individuals in each region within region Ω; This represents the number of patients treated in each region within region Ω. This represents the number of recoveries in each region of region Ω.

[0112] Let Θ denote the feasible region of the solution to the SIQR model, where Θ is the feasible set, specifically:

[0113]

[0114] (3) Based on the multi-region SIQR infectious disease model, under the conditions of limited medical resource reserves, implementation of internal management measures and entry and exit management measures, a limited medical resource allocation model is established, and the dynamic optimal medical resource allocation scheme of the infectious disease research area is obtained by solving the problem.

[0115] Suppose the medical resources to be allocated are antibiotics, with the unit being boxes. The research period is set to 30 days, which is divided into 30 equal time periods, forming a set T; each time period is 1 day, T = {1, 2, ..., 30}, |T| = 30. Let t represent any time period in T, i.e., t ∈ T.

[0116] make This indicates the quantity of medicines available in region i during time period t, and is set as follows: Let f i t This represents the quantity of medicines distributed by the emergency center to region i during time period t; then... This represents the total amount of medicine that region i can use during time period t.

[0117] Let c represent the amount of medicine consumed by each patient per unit time. Set c = 1, meaning each patient consumes 1 box of medicine per unit time. Then, for a patient in region i, the amount of medicine consumed by cQ at any given time period is... i (t) must not exceed the total amount of medicines that can be used in the region, that is:

[0118]

[0119] make This indicates the quantity of medicines stored in the emergency center during time period t, and is set as follows: For the study area Ω, at any given time, the number of medicines distributed by the emergency center to all areas within Ω ∑ i∈Ω f i t The quantity of medicines purchased must not exceed the amount currently stored in the emergency center, that is:

[0120]

[0121] make This represents the control parameters for internal management measures in region i during time period t. For infected person I in region i... i Specifically, in any time period t∈T, the sum of the number of recovered patients, the number of patients treated, the number of deaths, and the number of people traveling to other regions must not exceed the number of cases in region i, that is:

[0122]

[0123] When residents travel between regions i and j, Let represent the control parameters for entry and exit management measures in region i during time period t. This represents the control parameters for entry and exit management measures in region j during time period t. The total number of infected individuals traveling from region i to region j is g. ij I i Through entry and exit management measures, during time period t, the number of treated infected individuals departing from region i was [number missing]. The number of infected individuals who entered region j and received treatment was In any time period t∈T, the number of infected individuals treated in regions i and j must not exceed the total number of infected individuals traveling between regions i and j, that is:

[0124]

[0125] When residents travel between regions i and j, This represents the set of control parameters for entry and exit management measures in region i, and is set as follows: Let Γ i This represents the set of control parameters for the internal management measures of region i, and Γ is set. i ={0.007β,0.014β,…,0.07β}, β = β1 = β2 = β3 = 0.3. Then the set element relation is:

[0126]

[0127] In addition, variable f i t Non-negative and discrete, that is:

[0128]

[0129] Taking into account the above constraints, and with the objective of minimizing the total number of untreated infected individuals in region Ω, a limited medical care allocation model is established based on a multi-region SIQR infectious disease model as follows:

[0130]

[0131] st

[0132]

[0133] The model can be solved using dynamic programming. The model was programmed on the Python platform using the odeint and gurobipy modules from the scipy library, and a commercial solver was called to solve the multilevel linear assignment problem.

[0134] By solving the finite medical resource allocation model, the dynamic optimal allocation scheme of medical resources in the infectious disease research area Ω within the research period T can be obtained. Figure 4 This represents the optimal drug allocation scheme for the three regions of region Ω at various time periods within the study period T. The above embodiments are merely preferred embodiments of the present invention. It should be noted that those skilled in the art can make several improvements and equivalent substitutions without departing from the principle of the present invention, and these improvements and equivalent substitutions to the claims of the present invention all fall within the protection scope of the present invention.

Claims

1. A method for distributing medical supplies for infectious diseases, characterized in that, The method includes the following steps: S1. Classify residents within the infectious disease research area based on their health status; establish disease transmission patterns while considering cross-regional travel, and quantify the impact of internal management measures and entry / exit management measures. S2. Based on the transmission patterns of infectious diseases, and under the premise of implementing internal management measures and entry-exit management measures, establish a dynamic model of the spread of infectious diseases in multiple regions; S3. Based on the dynamic model described in S2, establish a limited medical resource allocation model and solve for the dynamic optimal medical resource allocation scheme in the infectious disease research area. The specific process of S1 is as follows: residents within the infectious disease research area are divided into susceptible individuals, infected individuals, those receiving treatment, and recovered individuals; Let Ω represent the infectious disease research area. Divide the area Ω into multiple regions, and let i represent any one of these regions, i.e., i∈ Ω; Let IΩI represent the number of regions to be divided; Let N i This represents the population of region i∈Ω; Region i is divided into four zones: susceptible individuals, infected individuals, those receiving treatment, and recovered individuals. Let S i I i Q i and R i These represent the number of susceptible individuals, infected individuals, treated individuals, and recovered individuals within region i, respectively. In the absence of infectious diseases, the population growth in region i is positive, expressed as a constant Λ. i It means, Λ i >0; when infectious diseases After it occurs, partition -S i I i Q i and R i The population mortality rates are all non-negative, expressed as constants. and It means, and Let β i Let β represent the incidence rate in region i; then, within region i, the standard incidence rate among susceptible individuals is β. i S i I i / N i Within region i, the recovery rates of both infected individuals and treated individuals are constant, expressed as constants α. i ε i express; Aside from those receiving treatment, the constant proportion of residents of region i traveling to any other region j∈Ω\{i} is g. ij Let g i Let g represent a constant proportion of residents in region i traveling to other regions. i =Σ j∈Ω\ { i }g ij ; Through internal management measures, the number of infected individuals in region i decreased at a rate η i I i The decrease, i.e., the reduction in the number of infected persons in region i per unit time, is η. i I i ; The number of infected individuals traveling from region i to any other region j ∈ Ω\{i} is g. ij I i ; The number of patients receiving treatment who exited from region i through entry and exit management measures was [number missing]. The number of patients entering region j for treatment was Therefore, in the end only One infected person was able to move freely from region i to region j; Thus, the impact of internal management measures and immigration control measures can be quantified; S2 establishes a dynamic model of the spread of infectious diseases in multiple regions; namely, a multi-region discrete SIQR infectious disease model. The established multi-region SIQR infectious disease model is as follows: Let N i (t), S i (t), I i (t), Q i (t), R i (t) represent N respectively i S i I i Q i R i The value at time t, i.e., the variable N. i S i I i Q i R i The form of change of N with time t; i (t), S i (t), I i (t), Q i (t), R i The actual meaning of (t) is respectively related to N i S i I i Q i R i same; For susceptible individuals S in region i i In terms of quantity, the following relationship exists: The mathematical expression for the relationship between the number of susceptible individuals and the population growth rate is: (Population growth - Number of infected individuals - Number of deaths - Number of people leaving the country + Number of people entering the country). For infected persons in region i i In terms of quantity, the following relationship exists: The mathematical expression for the relationship between the number of infected individuals and the number of recovered individuals is: Number of infected individuals = Number of recovered individuals - Number of individuals receiving internal treatment - Number of deaths - Number of people leaving the country + Number of people entering the country. For the patient Q in region i i In terms of quantity, the following relationship exists: The mathematical expression for the relationship between the number of people receiving treatment and the number of deaths and recoveries is: Number of people receiving internal treatment = Number of deaths - Number of recoveries + Number of people leaving the country + Number of people entering the country. For the restorer Q in region i i In terms of quantity, the following relationship exists: Number of recovered patients = Total number of recovered patients - Number of deaths - Number of people leaving the country + Number of people entering the country The mathematical expression for this relationship is: For region i, at the initial time t=0, the sum of the number of residents in the four sub-regions is equal to the total number of residents in the region, and the number of residents in each sub-region is greater than 0. Right now: S i (0)>0,I i (0)>0,Q i (0)>0,R i (0)>0 N i (0)=S i (0)+I i (0)+Q i (0)+R i (0)(5) And the initial conditions exist: Based on the above conditions, and under the implementation of internal management measures and entry / exit management measures, the following multi-regional discrete SIQR infectious disease model is established: In the formula, the first four rows represent S respectively. i I i Q i R i The ordinary differential equations for the change in the number of residents in these four zones over time; Lines 5 and 6 both represent the initial conditions of the SIQR model; make Let S, I, Q, and R represent the vector solutions of the SIQR model; S, I, Q, and R are all vectors of dimension IΩI; where, This represents the number of susceptible individuals in each region within region Ω. This represents the number of infected individuals in each region within region Ω; R represents the number of patients treated in each region within region Ω; R = (S1, ..., S2) IΩI )∈R + IΩI , representing the number of recoveries in each region of region Ω; Let Θ denote the feasible region of the solution to the SIQR model, where Θ is the feasible set, specifically: The specific model for allocating limited medical resources established by S3 is as follows: The research period is divided into multiple time periods, forming a set T; let t represent any time period in T, i.e., t∈T; let D i t f represents the amount of medical resources available in region i during time period t; i t D represents the amount of medical resources distributed by the emergency center to region i during time period t; i t +f i t Let C represent the total amount of medical resources available to region i during time period t; let C represent the amount of medical resources consumed by each patient per unit time; then, for a patient in region i, the amount of medical resources consumed by them in any time period is CQ. i (t) must not exceed the total amount of medical resources available in the region, that is: make This represents the quantity of medical resources stored in the emergency center during time period t; for the study area Ω, this represents the quantity of medical resources Σ distributed by the emergency center to all areas within Ω at any given time period. i∈Ω f i t The quantity of medical resources stored at the emergency center at this time must not exceed the quantity of medical resources currently available. make This represents the control parameters for internal management measures in region i during time period t; for infected person I in region i... i Specifically, in any time period t∈T, the sum of the number of recovered patients, the number of patients treated, the number of deaths, and the number of people traveling to other regions must not exceed the number of cases in region i, that is: When residents travel between regions i and j, Let represent the control parameters for entry and exit management measures in region i during time period t. This represents the control parameters for entry and exit management measures in region j during time period t; the total number of infected individuals traveling from region i to region j is g. ij I i Through entry and exit management measures, during time period t, the number of treated infected individuals departing from region i was [number missing]. The number of infected individuals who entered region j and received treatment was In any time period t∈T, the number of infected individuals treated in regions i and j must not exceed the total number of infected individuals traveling between regions i and j, that is: When residents travel between regions i and j, Let Γ represent the set of control parameters for entry and exit management measures in region i; i Let i represent the set of control parameters for internal management measures in region i; then the set element relationship is as follows: In addition, variable f i t Non-negative and discrete, that is: Taking into account the above constraints, and with the objective of minimizing the total number of untreated infected individuals in region Ω, a limited medical care allocation model is established based on a multi-region SIQR infectious disease model as follows: 。 2. The method for distributing medical supplies for infectious diseases according to claim 1, characterized in that, The finite medical allocation model is solved by applying dynamic programming and calling the commercial gurobi solver to solve the multi-level linear allocation problem.

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