Disease modeling and resource sharing

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Wang, Yifan
Keskinocak, Pinar
Kim, Seong-Hee
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This thesis makes contributions to three research topics: shared-resource allocation, disease modeling, and evaluation of intervention methods. In Chapter 2, we consider a problem of allocating shared resources among multiple classes when a customer from a different class may require a different number of resources and give a different amount of rewards when leaving the system after service completion. A customer is rejected if the number of available resources at the time of her arrival is smaller than the number of resources required for the customer. In this chapter, we find a customer admission control policy that maximizes the long-run average total reward throughput with constraints on secondary performance measures. Our problem is different from the existing literature because we consider a deteriorating service speed depending on the total workload in the system, multiple classes with different reward amounts and different resource requirements, and constraints on secondary performance measures. For a small-scale problem, we calculate the long-run average reward throughput and other performance measures by solving balance equations directly from a multi-class M/G/C/C state dependent queueing model. For a large-scale problem, as balance equations cannot be solved analytically, we use simulation to estimate performance measures and use a Bayesian optimization algorithm based on the Gaussian process to find an optimal allocation among a large number of possible allocations quickly with and without constraints on secondary performance measures. We test the performance of our procedure on a highway access control problem and a server capacity allocation problem of an online retail store. Agent-based simulation is a form of computer-based modeling that provides an intuitive and flexible approach to representing complex systems. It has been used in a wide range of health care applications. In Chapter 3, we develop an agent-based simulation with mosquito and human populations to model the spread of malaria in sub-Saharan Africa countries. We propose and test various strategies for allocating limited resources to evaluate and maximize the impact of proactive community case management (Pro-CCM). The simulation model utilizes ordinary differential equations and incorporates temporal climate information, disease transmission from mosquitoes to humans, and the progression of the disease in infected humans. The model is validated using data from Senegal, a west African country in the Sahel with highly seasonal transmission. We test numerous scenarios to understand how the number and the frequency of sweeps impact the effectiveness of ProCCM. In Chapter 4, we build a multi-water-source (MWS) agent-based simulation model, based on [43], to model the Guinea Worm (GW) disease transmission among dogs in Chad, as well as in each domestic clusters. This model contains three connected single-water-source (SWS) models, partitioning the majority part of Chad based on clustering results. Each SWS model adopts the general framework of the previous stochastic simulation model, which is used to simulate the life cycle of GW and daily interactions between the dogs, worms, and water source over multiple years. Each SWS model is validated using infection data within the corresponding cluster after parameter calibrations. Three SWS models were then connected into an MWS model using geographic information and local human characteristic data. Our MWS model was used to test the effectiveness and fairness of various intervention strategies. We searched for optimal solutions using the Cross-Entropy (CE) Method under various capacity and allocation constraints.
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