A multi-region collaborative planning and scheduling method for infectious disease emergency resources

Abstract

The present invention establishes a multi-region collaborative planning and scheduling method for infectious disease emergency resources. The present invention models the travel process of residents within the scope of infectious disease research and characterizes the propagation characteristics of infectious diseases in the transportation network. By organically combining the two, the present invention establishes a multi-region infectious disease diffusion model to predict the dynamic demand for infectious disease emergency resources. Based on the multi-region infectious disease diffusion model and with the minimization of system costs as the optimization goal, the present invention constructs a multi-region collaborative planning and scheduling model for infectious disease emergency resources; by introducing appropriate auxiliary variables to solve the model, the present invention obtains a multi-region collaborative planning and scheduling scheme for infectious disease emergency resources. The present invention can help formulate a more reasonable and effective multi-region collaborative planning and scheduling scheme for infectious disease emergency resources, and more quickly and accurately suppress the development trend of infectious diseases, thereby improving the ability to respond to public health emergencies in multiple regions.

Description

Technical Field

[0001] The present invention belongs to the field of resource planning and scheduling, and in particular relates to a multi-region collaborative planning and scheduling method for infectious disease emergency resources. Background Art

[0002] Major infectious diseases often occur quickly, affect a wide range of people, and are characterized by high infectiousness and morbidity. Furthermore, the rapid spread of viral infections is closely linked to high-density, long-distance travel and logistics. Therefore, to address major infectious diseases, it is necessary to establish a multi-regional coordinated planning and dispatching mechanism for emergency resources such as antibiotics and disinfectants, forming a robust and comprehensive public health emergency management system to enhance society's overall response capacity to public health emergencies.

[0003] The existing disclosed patent is an infectious disease prediction method and system based on big data (application number CN202211146616.0). Based on the total personnel information and sick personnel information of each region, a negative binomial distribution model is established to predict the probability trend of the number of cases in each region, and a linear regression model is established to predict the user's probability of illness. A new infectious disease monitoring and response system based on big data (application number CN202211022345.8) predicts the probability trend of the disease based on the collected data, and determines whether it is a risk disease. At the same time, it determines whether the number of infected people in the current area exceeds the warning baseline, so as to take corresponding measures, thereby achieving rapid positioning and timely response to emerging infectious diseases. Both inventions provide effective solutions for the prediction and control of infectious diseases, but they are mainly aimed at the prevention and control of infectious diseases within the region, and do not consider cross-regional collaborative prevention and control of infectious diseases. The present invention combines the travel process of residents and the characteristics of infectious disease transmission to establish a multi-regional infectious disease diffusion model to predict the dynamic demand for infectious disease emergency resources; on this basis, with the minimization of system cost as the optimization goal, a multi-regional collaborative planning and scheduling model for infectious disease emergency resources is established and solved to obtain a reasonable and effective multi-regional collaborative planning and scheduling plan for emergency resources, thereby quickly and accurately suppressing the development trend of infectious diseases and improving the region's ability to respond to public health emergencies. Summary of the Invention

[0004] Technical problem: The present invention establishes a multi-region collaborative planning and scheduling method for infectious disease emergency resources, which is used to predict the dynamic demand for emergency resources considering cross-regional travel in the context of infectious diseases, and to realize the collaborative planning and scheduling of emergency resources in multiple regions. The present invention models the travel process of residents within the scope of infectious disease research, and at the same time characterizes the propagation characteristics of infectious diseases in the transportation network; by organically combining the two, the present invention establishes a multi-region infectious disease diffusion model to predict the dynamic demand for infectious disease emergency resources. Based on the multi-region infectious disease diffusion model and with the minimization of system cost as the optimization goal, the present invention constructs a multi-region collaborative planning and scheduling model for infectious disease emergency resources. The present invention introduces appropriate auxiliary variables to solve the model and obtains a multi-region collaborative planning and scheduling scheme for infectious disease emergency resources. With the help of the present invention, relevant departments formulate more reasonable and effective multi-region collaborative planning and scheduling schemes for infectious disease emergency resources, which can more quickly and accurately suppress the development trend of infectious diseases, thereby improving the region's ability to respond to public health emergencies.

[0005] Technical Solution: To solve the above problems, the present invention proposes a multi-region collaborative planning and scheduling method for infectious disease emergency resources, which includes the following steps:

[0006] (1) Model the travel process of residents within the scope of the infectious disease study to describe the residents' activities within and between regions;

[0007] (2) Consider the spread characteristics of infectious diseases in the transportation network and organically embed these spread characteristics into the residents' travel process;

[0008] (3) Considering the impact of residents’ travel, a multi-regional infectious disease diffusion model was established;

[0009] (4) Predict the dynamic demand for emergency resources of drugs and disinfectants based on a multi-regional infectious disease diffusion model;

[0010] (5) Taking system cost minimization as the optimization goal, a multi-regional collaborative planning and scheduling model for infectious disease emergency resources is constructed;

[0011] (6) Auxiliary variables are introduced to solve the multi-region collaborative planning and scheduling model of infectious disease emergency resources in order to carry out multi-region collaborative planning and scheduling of infectious disease emergency resources.

[0012] Furthermore, in step (1), the travel process of residents within the scope of the infectious disease study is modeled. The specific process is as follows:

[0013] Assume that the set of regions within the scope of infectious disease research is Ω, and there are a total of |Ω| regions;

[0014] make Represents the registered residents of area i∈Ω, and the registered residents are divided into It is divided into 4 parts: residents in area i, residents on the road from area i to area j, residents on the road from area j back to area i, and residents in area j, with N ii 、 N ij Represents, where i, j∈Ω and j≠i, then the following equality exists:

[0015]

[0016] Let g ii express The proportion of trips to other areas is represents the traveling residents in area i;

[0017] Let θ ij express The proportion of trips to area j is:

[0018]

[0019]

[0020] make express The proportion of people arriving from area i to area j; let r ij Indicates N ij The proportion of activities in region j; let express The proportion of people arriving from region j to region i.

[0021] Furthermore, step (2) organically embeds the propagation characteristics of infectious diseases in the transportation network into the residents' travel process. The specific method is as follows:

[0022] According to the SIS infectious disease model, the population N within the study range is divided into susceptible people S and infected people I, N = S ∪ I. Susceptible people refer to healthy people who have not been infected with the disease, and infected people refer to people who have been infected with the disease.

[0023] Combining the residents' travel process with the SIS infectious disease model, the population N at each spatial location ij 、 N ij Divided into S ii 、 S ij , I ii 、 I ij Among these eight states, S ii 、 S ij Corresponding to N ii 、 N ijSusceptible people in I ii 、 I ij Corresponding to N ii 、 N ij Among the infected, there are N ii =S ii ∪I ii , N ij =S ij ∪I ij ;

[0024] For intra-region propagation, S ii Contact I ji , The probability is λ i , the probability of being infected after contact is β i ;

[0025] For inter-regional transmission, let M represent the set of inter-regional travel modes, M = {train, bus}; m represents any travel mode in the set M, m∈M, and let It represents the proportion of people traveling between area i and area j who choose mode m. In the process of traveling in mode m, the number of susceptible people on the road from area i to area j is Contact with infected people on the way from area k to area l The probability of The probability of being infected after contact is The probability that an infected person recovers and becomes susceptible is τ, assuming that the birth rate and death rate of the population are equal, both represented by μ.

[0026] Furthermore, the multi-region infectious disease diffusion model established in step (3) is specifically:

[0027] Let f ii (S,I),f ij (S,I) respectively represent S ii 、S ij The number of people who contracted the disease due to contact with infected people Respectively The number of people who became infected due to contact with infected people during travel is as follows:

[0028]

[0029]

[0030]

[0031]

[0032] S ii The dynamic evolution relationship of the status population is:

[0033]

[0034] Converted into mathematical expression, S ii The dynamic evolution equation of the state population is:

[0035]

[0036] The dynamic evolution relationship of the status population is:

[0037]

[0038] Converted into mathematical expression, The dynamic evolution equation of the state population is:

[0039]

[0040] S ij The dynamic evolution relationship of the status population is:

[0041]

[0042] Converted into mathematical expression, S ii The dynamic evolution equation of the state population is:

[0043]

[0044] The dynamic evolution relationship of the status population is:

[0045]

[0046] Converted into mathematical expression, The dynamic evolution equation of the state population is:

[0047]

[0048] I ii The dynamic evolution relationship of the status population is:

[0049]

[0050] Converted into mathematical expression, I ii The dynamic evolution equation of the state population is:

[0051]

[0052] The dynamic evolution relationship of the status population is:

[0053]

[0054]

[0055] I ij The dynamic evolution relationship of the status population is:

[0056]

[0057] Converted into mathematical expression, S ii The dynamic evolution equation of the state population is:

[0058]

[0059] The dynamic evolution relationship of the status population is:

[0060]

[0061]

[0062] In summary, for any region i∈Ω, the multi-region infectious disease diffusion model considering residents’ travel is as follows:

[0063]

[0064] Furthermore, the multi-regional collaborative planning and scheduling model for infectious disease emergency resources constructed in step (5) is specifically as follows:

[0065] Let P represent the set of all emergency resource warehouses. For any warehouse p∈P, P i represents the set of emergency resource warehouses in region i∈Ω, P=∪ i∈I P i , let T denote the set of time periods for system planning, construction, and operation, and any time period t∈T;

[0066] An optimization model is established with the goal of minimizing system costs, including warehouse location costs, facility construction costs, resource procurement costs, warehousing costs, and shortage costs. The objective function is as follows:

[0067]

[0068] Where c ρ represents the location cost of the resource warehouse p∈P, which is fixed, x p is a 0-1 variable, x p =1 means warehouse p is selected and built, otherwise x p =0,∑ p∈P c p x prepresents the warehouse location cost of the system, ca p represents the facility construction cost of resource warehouse p∈P, y p represents the facility construction scale of warehouse p, ∑ p∈P ca p y p represents the system's facility construction cost, c s represents the purchase cost of resource s per unit quantity, represents the quantity of resource s purchased by region i, represents the system's emergency resource procurement cost, represents the storage cost of resource s per unit quantity in region i, represents the storage quantity of resource s in region i during period t, represents the system's emergency resource storage cost, It represents the shortage cost of resource s per unit in region i or the economic loss caused by the shortage. represents the shortage of resource s in region i, represents the system's emergency resource shortage cost;

[0069] For this optimization model, there are the following constraints:

[0070]

[0071] Where B i represents the emergency budget of region i; b ji represents the emergency assistance provided by other regions j∈Ω\{i} to region i. This constraint states that the cost of planning and building emergency resource warehouses and purchasing resources in region i must not exceed the available emergency budget and emergency assistance.

[0072]

[0073] This constraint indicates whether region i accepts emergency assistance from other regions j∈Ω\{i}. This constraint is an emergency budget cooperation mechanism among multiple regions. If the emergency budget of each region is limited to the use of the region, then b ij =0, j∈Ω\{i},

[0074]

[0075] Where, represents the allowed construction scale of the resource warehouse p∈P. This constraint means that the construction scale of the resource warehouse shall not exceed the allowed construction scale;

[0076]

[0077] Where r sIt represents the storage space required for a unit quantity of resource s. This constraint means that the storage space of resources purchased for warehouse p must not exceed the construction scale of the warehouse.

[0078]

[0079] Where, represents the number of resources s pre-scheduled from region j∈Ω\{i} to region i according to the budget cooperation mechanism at time t=0, η ij represents the conversion rate of emergency resources between region i and region j∈Ω\{i}. This constraint guarantees the total value of emergency resources provided by region j∈Ω\{i} to region i.

[0080]

[0081] Where, represents the demand for resource s in region i during time period t. This constraint represents the equilibrium state of emergency resources in region i, that is, the demand for resource d in region i is equal to the sum of the shortage quantity of resource d in the region and the purchase quantity;

[0082]

[0083] Where, represents the number of resources s that the emergency management center dispatches from region i to region j∈Ω\{i} at t=0; represents the number of resources s that the emergency management center redispatched from region j to region i∈Ω\{j} at t=0; both are resource redispatching variables of the emergency management center, represents the demand of region i for resource s at t = 0. This constraint is the storage constraint of emergency resources, that is, the balance constraint between emergency resource reserves and cross-regional coordination;

[0084]

[0085]

[0086] These two constraints ensure that no cyclic scheduling occurs between regions during the pre-scheduling and re-scheduling process;

[0087]

[0088] This constraint limits the sum of the resources that can be pre-dispatched and re-dispatched between regions to no more than the amount of resources procured by the region;

[0089]

[0090]

[0091]

[0092]

[0093]

[0094]

[0095]

[0096]

[0097] The above constraints represent the types of decision variables, where x p is a 0-1 variable; y p 、 is a non-negative integer, that is, it belongs to the set of non-negative integers is a non-negative continuous variable;

[0098] In summary, the multi-regional collaborative planning and scheduling model for infectious disease emergency resources is:

[0099]

[0100] st

[0101]

[0102]

[0103]

[0104]

[0105]

[0106]

[0107]

[0108]

[0109]

[0110]

[0111]

[0112]

[0113]

[0114]

[0115]

[0116]

[0117]

[0118]

[0119] Furthermore, the specific process of solving the multi-regional collaborative planning and scheduling model for infectious disease emergency resources in step (6) is as follows:

[0120] The multi-regional collaborative planning and scheduling model for infectious disease emergency resources is essentially a mixed-integer nonlinear programming model that includes the following four nonlinear constraints:

[0121]

[0122]

[0123]

[0124]

[0125] Auxiliary variables are introduced to convert these four nonlinear constraints into linear constraints one by one, specifically:

[0126]

[0127]

[0128]

[0129]

[0130] Where, and are all positive infinity, ensuring the auxiliary 0-1 variable φ i 、 It has no effect on the original decision variables. represents the number of resources s pre-scheduled from region j∈Ω\{i} to region i according to the budget cooperation mechanism in time period t, It represents the number of resources s pre-scheduled from region i∈Ω\{j} to region j according to the budget cooperation mechanism in time period t. The converted model is a mixed integer linear programming model, which is solved by Cplex or Gurobi solver.

[0131] Beneficial effects: Compared with the prior art, the technical solution of the present invention has the following beneficial technical effects:

[0132] Combining the travel process of residents and the characteristics of infectious disease transmission, a multi-regional infectious disease diffusion model was established to accurately predict the dynamic demand for infectious disease emergency resources; with the minimization of system cost as the optimization goal, a multi-regional collaborative planning and scheduling model for infectious disease emergency resources was established and solved, which can obtain a reasonable and effective multi-regional collaborative planning and scheduling plan for emergency resources. BRIEF DESCRIPTION OF THE DRAWINGS

[0133] Figure 1 Schematic diagram of the infectious disease diffusion process considering residents' travel.

[0134] Figure 2 Flow chart of the method of the present invention. DETAILED DESCRIPTION

[0135] The present invention will be further described below with reference to examples and accompanying drawings.

[0136] The present invention provides a multi-region collaborative planning and scheduling method for infectious disease emergency resources, such as Figure 2 As shown, the following process is included:

[0137] (1) Model the travel process of residents within the scope of the infectious disease study to characterize the activity status of residents within and between regions.

[0138] There are two regions within the infectious disease research area Ω, that is, |Ω| = 2. Let them be region 1 and region 2, that is, i = 1, 2.

[0139] make represents the registered residents of area i∈Ω. Figure 1 , will register residents According to the spatial location of its activities, it is divided into 4 parts: within area i, on the way from area i to area j, on the way from area j back to area i, and within area j, with N ii 、 N ij Represents, where i, j∈Ω and j≠i. Then there exists the following equality relationship:

[0140]

[0141] Let g ii express The proportion of trips to other areas is represents the number of residents traveling in area i. Among them, area 1 has g 11 =0.05, region 2 has g 22 =0.08.

[0142] Let θ ij express The proportion of trips to region j. Since there are only two regions, θ 12 =θ 21 =1. There are:

[0143]

[0144]

[0145] make express The proportion of people arriving from area i to area j is Let r ij Indicates N ij The proportion of activities in region j is r 12 =0.26,r 21 =0.21. express The proportion of people arriving from area j to area i is

[0146] (2) Consider the propagation characteristics of infectious diseases in the transportation network and organically embed these propagation characteristics into the residents' travel process.

[0147] In the initial stage, the infectious disease only spreads in area 1, while there is no infectious disease in area 2.

[0148] According to the classic SIS infectious disease model, the population N within the study area is divided into susceptible individuals S and infected individuals I, where N = S ∪ I. Susceptible individuals are healthy people who have not yet been infected with the disease, while infected individuals are those who have already been infected with the disease.

[0149] Combining the residents' travel process with the SIS infectious disease model, the population N at each spatial location ii 、 N ij Can be divided into S ii 、 S ij , I ii 、 I ij These eight states. Among them, S ii 、 S ij Corresponding to N ii 、 N ij Susceptible people in I ii 、 I ij Corresponding to N ii 、 N ij Among the infected, there are N ii =S ii ∪Iii , N ij =S ij ∪I ij .

[0150] For intra-region propagation, S ii Contact I ji , The probability is λ i , the probability of being infected after contact is β i .

[0151] For inter-regional transmission, the inter-regional travel mode set M = {train, bus}; m represents any travel mode in the set M, m∈M. Let It represents the proportion of people traveling between area i and area j who choose mode m. In the process of traveling in mode m, Contact The probability of The probability of being infected after contact is

[0152] The probability that an infected person recovers and becomes susceptible is τ. Assume that the birth rate and death rate of the population are equal, both represented by i.

[0153] In the initial stage, the values ​​of relevant parameters for the spread of infectious diseases are shown in Table 1.

[0154] Table 1 Related parameters and values ​​of infectious disease transmission

[0155]

[0156]

[0157] (3) Considering the impact of residents’ travel, a multi-regional infectious disease diffusion model is established.

[0158] Let f ii (S,I),f ij (S,I) respectively represent S ii 、S ij The number of people who contracted the disease due to contact with infected people Respectively The number of people who became infected due to contact with infected people during travel is as follows:

[0159]

[0160]

[0161]

[0162]

[0163] S ii The dynamic evolution relationship of the status population is:

[0164]

[0165] Converted into mathematical expression, S ii The dynamic evolution equation of the state population is:

[0166]

[0167] The dynamic evolution relationship of the status population is:

[0168]

[0169] Converted into mathematical expression, The dynamic evolution equation of the state population is:

[0170]

[0171] S ij The dynamic evolution relationship of the status population is:

[0172]

[0173] Converted into mathematical expression, S ii The dynamic evolution equation of the state population is:

[0174]

[0175] The dynamic evolution relationship of the status population is:

[0176]

[0177] Converted into mathematical expression, The dynamic evolution equation of the state population is:

[0178]

[0179] I ii The dynamic evolution relationship of the status population is:

[0180]

[0181] Converted into mathematical expression, I ii The dynamic evolution equation of the state population is:

[0182]

[0183] The dynamic evolution relationship of the status population is:

[0184]

[0185] Converted into mathematical expression, The dynamic evolution equation of the state population is:

[0186]

[0187] I ij The dynamic evolution relationship of the status population is:

[0188]

[0189] Converted into mathematical expression, S ii The dynamic evolution equation of the state population is:

[0190]

[0191] The dynamic evolution relationship of the status population is:

[0192]

[0193] Converted into mathematical expression, The dynamic evolution equation of the state population is:

[0194]

[0195] In summary, for any region i∈Ω, the multi-region infectious disease diffusion model considering residents’ travel is as follows:

[0196]

[0197] (4) Based on the multi-regional infectious disease diffusion model, predict the dynamic demand for emergency resources such as drugs and disinfectants.

[0198] The emergency resource set S includes two resources: antibiotics and disinfectants, that is, |S| = 2; s∈S represents any resource, s = 1, 2.

[0199] make represents the basic demand of each patient for resource s in each period. The number of infected registered residents in area i is That is, the sum of the number of patients infected within each region and the number of patients infected during inter-regional travel. Therefore, in time period t, the demand for resource s in region i is It can be expressed as:

[0200]

[0201] (5) With the minimization of system cost as the optimization goal, a multi-regional collaborative planning and scheduling model for infectious disease emergency resources is constructed.

[0202] Let P represent the set of all emergency resource warehouses, any warehouse p∈P. i represents the set of emergency resource warehouses in region i∈Ω, P=∪ i∈I P i Region 1 has two alternative emergency resource warehouses, denoted as Warehouse 1 and Warehouse 2, with |P1| = 2 and p = 1, 2. Region 2 has two alternative emergency resource warehouses, denoted as Warehouse 3 and Warehouse 4, with |P2| = 2 and p = 3, 4. Therefore, P = P1 ∪ P2.

[0203] Let T denote the set of time periods for system planning, construction, and operation, and any time period t∈T.

[0204] An optimization model is established with the goal of minimizing system costs, including warehouse location costs, facility construction costs, resource procurement costs, storage costs, and shortage costs. The objective function is as follows:

[0205]

[0206] Where c p represents the location cost of resource warehouse p∈P, and c p =100,000RMB. x p is a 0-1 variable, x p =1 means warehouse p is selected and built, otherwise x p =0.∑ p∈P c p x p Represents the warehouse location cost of the system.

[0207] ca p It represents the facility construction cost of resource warehouse p∈P unit scale, and ca p =5RMB / m 2 .y p Represents the facility construction scale of warehouse p. ∑ p∈P ca p y p Represents the facility construction cost of the system.

[0208] c s The unit price of antibiotics is 4000 yuan per box, and each box contains 10ml*2000 tubes, that is, c 1 = 4000RMB / box; the unit price of disinfectant is 1000RMB / box, each box contains 500ml*20 bottles, i.e. c 2 =1000RMB / box. Represents the quantity of resource s purchased by region i. Represents the system's emergency resource procurement cost.

[0209] It represents the storage cost of resource s per unit quantity in region i. The storage cost of antibiotics per unit quantity is 0.1 yuan / week, that is, The storage fee for disinfection supplies per unit is 0.2 yuan / week, that is, It represents the storage quantity of resource s in region i during period t. Represents the system's emergency resource storage cost.

[0210] It represents the shortage cost of resource s per unit in region i or the economic loss caused by the shortage. The shortage cost of antibiotics is 8,000 yuan per box, that is, The shortage cost of disinfectants is RMB 4,000 per box, i.e. represents the shortage of region i with respect to resource s. Represents the system's emergency resource shortage cost.

[0211] For this optimization model, there are the following constraints:

[0212]

[0213] Where B i The emergency budget of area i is RMB 1 million and that of area 2 is RMB 9 million, i.e. B1 = RMB 1,000,000 and B2 = RMB 9,000,000. ji represents the emergency assistance provided by other regions j∈Ω\{i} to region i. This constraint states that the cost of planning and building emergency resource warehouses and purchasing resources in region i must not exceed the available emergency budget and emergency assistance.

[0214]

[0215] This constraint indicates whether region i accepts emergency assistance from other regions j∈Ω\{i}. This constraint is actually a multi-region emergency budget cooperation mechanism. If the emergency budget of each region is limited to the use of the region, then

[0216]

[0217] Where, Indicates the permitted construction scale of resource warehouse p∈P. Considering the limitation of urban construction land, the permitted construction scale of resource warehouse in area 1 and area 2 is 600m 2 and 200m 2,Right now This constraint indicates that the construction scale of the resource warehouse must not exceed the permitted construction scale.

[0218]

[0219] Where r s The storage space required for a unit quantity of resource s is 0.2 m. The storage space required for a unit quantity of antibiotics and disinfectants is 0.2 m. 2 and 0.5m 2 , that is, r 1 =0.2m 2 , r 2 =0.5m 2 This constraint states that the storage space of resources purchased for warehouse p must not exceed the construction scale of the warehouse.

[0220]

[0221] Where, represents the number of resources s pre-scheduled from region j∈Ω\{i} to region i according to the budget cooperation mechanism at time t=0. ij represents the emergency assistance conversion rate between region i and region j∈Ω\{i}. The emergency assistance conversion rate between regions 1 and 2 is 30%, that is, η 12 =η 21 = 30%. This constraint ensures that the emergency aid from region j∈Ω\{i} to region i is used to purchase emergency resources.

[0222]

[0223] This constraint represents the equilibrium state of emergency resources in region i, that is, the demand for resource s in region i is equal to the sum of the shortage quantity and the purchase quantity of resource s in the region.

[0224]

[0225] Where, represents the number of resources s that the emergency management center dispatches from region i to region j∈Ω\{i} at t=0; Similarly, are all resource rescheduling variables of the emergency management center. This constraint is the storage constraint of emergency resources, that is, the balance constraint between emergency resource reserves and cross-regional coordination.

[0226]

[0227]

[0228] These two constraints ensure that there is no cyclic scheduling between regions during the pre-scheduling and re-scheduling process.

[0229]

[0230] This constraint limits the sum of the resources that can be pre-dispatched and re-dispatched between regions to no more than the amount of resources procured by the region.

[0231]

[0232]

[0233]

[0234]

[0235]

[0236]

[0237]

[0238]

[0239] The above constraints represent the types of decision variables. p is a 0-1 variable; y p 、 is a non-negative integer; b ij 、 is a non-negative continuous variable.

[0240] In summary, the multi-regional collaborative planning and scheduling model for infectious disease emergency resources is:

[0241]

[0242] st

[0243]

[0244]

[0245]

[0246]

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[0249]

[0250]

[0251]

[0252]

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[0260]

[0261] (6) Introduce appropriate auxiliary variables to solve the multi-region collaborative planning and scheduling model for infectious disease emergency resources. The multi-region collaborative planning and scheduling model for infectious disease emergency resources is essentially a mixed integer nonlinear programming (MINLP) model, which includes the following four nonlinear constraints:

[0262]

[0263]

[0264]

[0265]

[0266] To facilitate mathematical solution, appropriate auxiliary variables are introduced to convert these four nonlinear constraints into linear constraints one by one. Specifically:

[0267]

[0268]

[0269]

[0270]

[0271] Where, and are all very large positive numbers, which can ensure the auxiliary 0-1 variable φ i 、 The original decision variables are not affected. The converted model is a mixed integer linear programming (MILP) model, which can be solved by commercial solvers such as Cplex and Gurobi.

[0272] By solving the multi-region collaborative planning and scheduling model of infectious disease emergency resources, a multi-region collaborative planning and scheduling scheme for emergency resources within the infectious disease research scope Ω and the research period T can be obtained, as shown in Table 2.

[0273] Table 2 Multi-regional collaborative planning and dispatching scheme for infectious disease emergency resources

[0274]

[0275] The above embodiments are only preferred implementations of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and equivalent substitutions can be made without departing from the principles of the present invention. These technical solutions after improvements and equivalent substitutions to the claims of the present invention all fall within the scope of protection of the present invention.

Claims

1. A multi-region collaborative planning and scheduling method for infectious disease emergency resources, characterized in that: The method comprises the following steps: (1) Model the travel process of residents within the scope of the infectious disease study to describe the residents' activities within and between regions; (2) Consider the spread characteristics of infectious diseases in the transportation network and organically embed these spread characteristics into the residents' travel process; (3) Considering the impact of residents’ travel, a multi-regional infectious disease diffusion model was established; (4) Predict the dynamic demand for emergency resources of drugs and disinfectants based on a multi-regional infectious disease diffusion model; (5) Taking system cost minimization as the optimization goal, a multi-regional collaborative planning and scheduling model for infectious disease emergency resources is constructed; (6) Introducing auxiliary variables to solve the multi-region collaborative planning and scheduling model of infectious disease emergency resources to carry out multi-region collaborative planning and scheduling of infectious disease emergency resources; In step (1), the travel process of residents within the scope of the infectious disease study is modeled. The specific process is as follows: Assume that the set of regions within the scope of infectious disease research is Ω, and there are a total of |Ω| regions; make Represents the registered residents of area i∈Ω, and the registered residents are divided into It is divided into 4 parts: residents in area i, residents on the road from area i to area j, residents on the road from area j back to area i, and residents in area j, with N ii 、 N ij Represents, where i, j∈Ω and j≠i, then the following equality exists: Let g ii express The proportion of trips to other areas is represents the traveling residents in area i; Let θ ij express The proportion of trips to area j is: make express The proportion of people arriving from area i to area j; let r ij Indicates N ij The proportion of activities in region j; let express The proportion of people arriving from region j to region i; Step (2) organically embeds the spread characteristics of infectious diseases in the transportation network into the residents' travel process. The specific method is as follows: According to the SIS infectious disease model, the population N within the study range is divided into susceptible people S and infected people I, N = S ∪ I. Susceptible people refer to healthy people who have not been infected with the disease, and infected people refer to people who have been infected with the disease. Combining the residents' travel process with the SIS infectious disease model, the population N at each spatial location ii 、 N ij Divided into S ii 、 S ij , I ii 、 I ij Among these eight states, S ii 、 S ij Corresponding to N ii 、 N ij Susceptible people in I ii 、 I ij Corresponding to N ii 、 N ij Among the infected, there are N ii =S ii ∪I ii , N ij =S ij ∪I ij ; For intra-region propagation, S ii Contact The probability is λ i , the probability of being infected after contact is β i ;S ij Contact The probability is λ j , the probability of being infected after contact is β j ; For inter-regional transmission, let M represent the set of inter-regional travel modes, M = {train, bus}; m represents any travel mode in the set M, m∈M, and let It represents the proportion of people traveling between area i and area j who choose mode m. In the process of traveling in mode m, the number of susceptible people on the road from area i to area j is Contact with infected people on the way from area k to area l The probability of The probability of being infected after contact is The probability that an infected person recovers and becomes susceptible is τ, assuming that the birth rate and death rate of the population are equal, both represented by μ; The multi-region infectious disease diffusion model established in step (3) is specifically: Let f ii (S,I),f ij (S,I) respectively represent S ii 、S ij The number of people who contracted the disease due to contact with infected people Respectively The number of people who became infected due to contact with infected people during travel is as follows: S ii The dynamic evolution relationship of the status population is: Converted into mathematical expression, S ii The dynamic evolution equation of the state population is: The dynamic evolution relationship of the status population is: Converted into mathematical expression, The dynamic evolution equation of the state population is: S ij The dynamic evolution relationship of the status population is: Converted into mathematical expression, S ii The dynamic evolution equation of the state population is: The dynamic evolution relationship of the status population is: Converted into mathematical expression, The dynamic evolution equation of the state population is: I ii The dynamic evolution relationship of the status population is: Converted into mathematical expression, I ii The dynamic evolution equation of the state population is: The dynamic evolution relationship of the status population is: Converted into mathematical expression, The dynamic evolution equation of the state population is: I ij The dynamic evolution relationship of the status population is: Converted into mathematical expression, S ii The dynamic evolution equation of the state population is: The dynamic evolution relationship of the status population is: Converted into mathematical expression, The dynamic evolution equation of the state population is: In summary, for any region i∈Ω, the multi-region infectious disease diffusion model considering residents’ travel is as follows: The multi-regional collaborative planning and scheduling model for infectious disease emergency resources constructed in step (5) is specifically as follows: Let P represent the set of all emergency resource warehouses. For any warehouse p∈P, P i represents the set of emergency resource warehouses in region i∈Ω, P=∪ i∈I P i , let T denote the set of time periods for system planning, construction, and operation, and any time period t∈T; An optimization model is established with the goal of minimizing system costs, including warehouse location costs, facility construction costs, resource procurement costs, warehousing costs, and shortage costs. The objective function is as follows: Where c p represents the location cost of the resource warehouse p∈P, which is fixed, x p is a 0-1 variable, x p =1 means warehouse p is selected and built, otherwise x p =0,∑ p∈p c p x p represents the warehouse location cost of the system, ca p represents the facility construction cost of resource warehouse p∈P, y p represents the facility construction scale of warehouse p, ∑ p∈P ca p y p represents the system's facility construction cost, c s represents the purchase cost of resource s per unit quantity, represents the quantity of resource s purchased by region i, represents the system's emergency resource procurement cost, represents the storage cost of resource s per unit quantity in region i, represents the storage quantity of resource s in region i during period t, represents the system's emergency resource storage cost, It represents the shortage cost of resource s per unit in region i or the economic loss caused by the shortage. represents the shortage of resource s in region i, represents the system's emergency resource shortage cost; For this optimization model, there are the following constraints: Where B i represents the emergency budget of region i; b ji represents the emergency assistance provided by other regions j∈Ω\{i} to region i. This constraint states that the cost of planning and building emergency resource warehouses and purchasing resources in region i must not exceed the available emergency budget and emergency assistance. This constraint indicates whether region i accepts emergency assistance from other regions j∈Ω\{i}. This constraint is an emergency budget cooperation mechanism among multiple regions. If the emergency budget of each region is limited to the use of the region, then Where, represents the allowed construction scale of the resource warehouse p∈P. This constraint means that the construction scale of the resource warehouse shall not exceed the allowed construction scale; Where r s It represents the storage space required for a unit quantity of resource s. This constraint means that the storage space of resources purchased for warehouse p must not exceed the construction scale of the warehouse. Where, represents the number of resources s pre-scheduled from region j∈Ω\{i} to region i according to the budget cooperation mechanism at time t=0, η ij represents the conversion rate of emergency resources between region i and region j∈Ω\{i}. This constraint guarantees the total value of emergency resources provided by region j∈Ω\{i} to region i. Where, represents the demand for resource s in region i during time period t. This constraint represents the equilibrium state of emergency resources in region i, that is, the demand for resource s in region i is equal to the sum of the shortage quantity and the purchase quantity of resource s in the region; Where, represents the number of resources s that the emergency management center dispatches from region i to region j∈Ω\{i} at t=0; represents the number of resources s that the emergency management center redispatched from region j to region i∈Ω\{j} at t=0; both are resource redispatching variables of the emergency management center, represents the demand of region i for resource s at t = 0. This constraint is the storage constraint of emergency resources, that is, the balance constraint between emergency resource reserves and cross-regional coordination; These two constraints ensure that no cyclic scheduling occurs between regions during the pre-scheduling and re-scheduling process; This constraint limits the sum of the resources that can be pre-dispatched and re-dispatched between regions to no more than the amount of resources procured by the region; The above constraints represent the types of decision variables, where x p is a 0-1 variable; y p 、 is a non-negative integer, that is, it belongs to the set of non-negative integers b ij 、 is a non-negative continuous variable; In summary, the multi-regional collaborative planning and scheduling model for infectious disease emergency resources is: st The specific process of solving the multi-region collaborative planning and scheduling model of infectious disease emergency resources in step (6) is as follows: The multi-regional collaborative planning and scheduling model for infectious disease emergency resources is essentially a mixed-integer nonlinear programming model that includes the following four nonlinear constraints: Auxiliary variables are introduced to convert these four nonlinear constraints into linear constraints one by one, specifically: Where, and are all positive infinity, ensuring the auxiliary 0-1 variable φ i 、 It has no effect on the original decision variables. represents the number of resources s pre-scheduled from region j∈Ω\{i} to region i according to the budget cooperation mechanism in time period t, It represents the number of resources s pre-scheduled from region i∈Ω\{j} to region j according to the budget cooperation mechanism in time period t. The converted model is a mixed integer linear programming model, which is solved by Cplex or Gurobi solver.

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