Epidemic-logistics Modeling: A New Perspective on Operations Research

The goal of this book is to introduce a part of research directions on epidemic dynamics investigated by our research group and our main results during the past several years. Before this, some basic knowledge on epidemic dynamics will be introduced which may be helpful to those readers who are not familiar with the mathematical modeling on epidemiology.

In this chapter, we construct a unique forecasting model for the demand of emergency resources based on the epidemic diffusion rule when suffering a bioterror attack. In what follows, we focus on how to deliver emergency resources to the epidemic areas. We find that both the pure point-to-point delivery mode and the pure multi-depot, multiple traveling salesmen delivery system are difficult to operate in an actual emergency situation. Thus, we propose a mixed-collaborative distribution mode, which can equilibrate the contradiction between these two pure modes. A special time window for the mixed-collaborative mode is designed. A genetic algorithm is adopted to solve the optimization model. To verify the validity and the feasibility of the mixed-collaborative mode, we compare it with these two pure distribution modes from both aspects of total distance and timeliness.

In this chapter, we present a discrete time-space network model for allocating medical resource following an epidemic outbreak. It couples a forecasting mechanism for dynamic demand of medical resource based on an epidemic diffusion model and a multi-stage programming model for optimal allocation and transport of such resource. In this chapter, we present a discrete time-space network model for allocating medical resource following an epidemic outbreak. It couples a forecasting mechanism for dynamic demand of medical resource based on an epidemic diffusion model and a multi-stage programming model for optimal allocation and transport of such resource. At each stage, the linear programming solves for a cost minimizing resource allocation solution subject to a time-varying demand that is forecasted by a recursion model. The rationale that the medical resource allocated in early periods will take effect in subduing the spread of epidemic and thus impact the demand in later periods has been incorporated in such recursion model. We compare the proposed medical resource allocation mode with other operation modes in practice, and find that our model is superior to any of them in less waste of resource and less logistic cost. The results may provide some practical guidelines for a decision-maker who is in charge of medical resource allocation in an epidemics control effort.

This chapter is a continuous work of Chap. 4. In this chapter, we develop a unique time-varying forecasting model for dynamic demand of medical resources based on a susceptible-exposed-infected-recovered (SEIR) influenza diffusion model. In this forecasting mechanism, medical resources allocated in the early period will take effect in subduing the spread of influenza and thus impact the demand in the later period. We adopt a discrete time-space network to describe the medical resources allocation process following a hypothetical influenza outbreak in a region.

As mentioned in the above chapters, the demand of emergency resource is usually uncertain and varies quickly in anti-bioterrorism system. With the consideration of emergency resources allocated to the epidemic areas in the early rescue cycles will affect the demand in the following periods, we construct an integrated and dynamic optimization model with time-varying demand for the emergency logistics network based on the epidemic diffusion rule.

This chapter is a continuous work of Chap. 6. In this chapter, a three-level and dynamic linear programming model for allocating medical resources based on epidemic diffusion model is proposed. The epidemic diffusion model is used to construct the forecasting mechanism for dynamic demand of medical resources. Heuristic algorithm coupled with MATLAB mathematical programming solver is adopted to solve the model. A numerical example is presented for testing the model’s practical applicability. The main contribution of the present study is that a discrete time-space network model to study the medical resources allocation problem when an epidemic outbreak is formulated. It takes consideration of the time evolution and dynamic nature of the demand, which is different from most existing researches on medical resources allocation. In our model, the medicine logistics operation problem has been decomposed into several mutually correlated sub-problems, and then be solved systematically in the same decision scheme. Thus, the result will be much more suitable for real operations. Moreover, in our model, the rationale that the medical resources allocated in early periods will take effect in subduing the spread of the epidemic spread and thus impact the demand in later periods has been for the first time incorporated. A win-win emergency rescue effect is achieved by the integrated and dynamic optimization model. The total rescue cost is controlled effectively, and meanwhile, inventory level in each urban health departments is restored and raised gradually.

This chapter presents a dynamic logistics model for medical resources allocation that can be used to control an epidemic diffusion. It couples a forecasting mechanism, constructed for the demand of a medicine in the course of such epidemic diffusion, and a logistics planning system to satisfy the forecasted demand and minimize the total cost. The forecasting mechanism is a time discretized version of the SEIR model that is widely employed in predicting the trajectory of an epidemic diffusion. The logistics planning system is formulated as a mixed 0–1 integer programming problem characterizing the decision-making at various levels of hospitals, distribution centers, pharmaceutical plants, and the transportation in between them. The model is built as a closed-loop cycle, comprising forecast phase, planning phase, execution phase, and adjustment phase. The parameters of the forecasting mechanism are adjusted in reflection of the real data collected in the execution phase by solving a quadratic programming problem. A numerical example is presented to verify efficiency of the model.

Infectious disease outbreaks have occurred many times in the past decades and are more likely to occur in the future. Recently, Büyüktahtakın et al. [1] proposed a new epidemics-logistics model to control the 2014 Ebola outbreak in West Africa. Considering that different diseases have dissimilar diffusion dynamics and can cause different public health emergencies, we modify the proposed model by changing capacity constraint, and then apply it to control the 2009 H1N1 outbreak in China. We formulate the problem to be a mixed-integer non-linear programming model (MINLP) and simultaneously determine when to open the new isolated wards and when to close the unused isolated wards. The test results reveal that our model could provide effective suggestions for controlling the H1N1 outbreak, including the appropriate capacity setting and the minimum budget required with different intervention start times.

This chapter presents two medicine logistics planning models by using a time-space network approach, one with deterministic variables and the other with stochastic variables. Flow dependent variable costs, random demand and random service time are featured in our models in addressing economies of scale and uncertainties in a real-world medical logistics problem. Effective computational schemes are designed, and an evaluation method is proposed to derive and assess a solution to the models. Numerical tests are conducted and show promising results for applications to a real-world problem.

Medical resources scheduling affects the medical institution’s operation cost, customer satisfaction and medical service quality. Therefore, a lean arrangement of medical resources order and shipment is quite necessary and important. In this chapter, we propose two optimal models for medical resources order and shipment in community health service centers (CHSCs), with a dual emphasis on minimizing the total operation cost and improving the operation level in practice. The first planning model is a deterministic planning model (DM). Systematically, it considers constraints including the lead time of the suppliers, the storage capacity of the medical institutions, and the integrated shipment planning in the dimensions of time and space. The problem is a multi-commodities flow problem and is formulated as a mixed 0–1 integer programming model.

Generally, medicine order and delivery are operated based on the previous experiences. First of all, estimating the average annual demands of hospital storage center. Second, planning a medical goods order and delivery schedule based on the annual average demands as well as establishing the period of ordering and delivering. Third, in the process of operating, medical system supplies goods according to the re-order point and safe stock. In this chapter, we propose three time-space network models for medicine order and shipment, which may help improve the effectiveness when managing the medicine in hospitals.

In this chapter, we present two optimization models for optimizing the epidemic-logistics network. In the first one, we formulate the problem of emergency materials distribution with time windows to be a multiple traveling salesman problem. Knowledge of graph theory is used to transform the MTSP to be a TSP, then such TSP route is analyzed and proved to be the optimal Hamilton route theoretically. Besides, a new hybrid genetic algorithm is designed for solving the problem. In the second one, we propose an improved location-allocation model with an emphasis on maximizing the emergency service level. We formulate the problem to be a mixed-integer nonlinear programming model and develop an effective algorithm to solve the model. In this chapter, we present two optimization models for optimizing the epidemic-logistics network. In the first one, we formulate the problem of emergency materials distribution with time windows to be a multiple traveling salesman problem. Knowledge of graph theory is used to transform the MTSP to be a TSP, then such TSP route is analyzed and proved to be the optimal Hamilton route theoretically. Besides, a new hybrid genetic algorithm is designed for solving the problem. In the second one, we propose an improved location-allocation model with an emphasis on maximizing the emergency service level. We formulate the problem to be a mixed-integer nonlinear programming model and develop an effective algorithm to solve the model.