Document Type

Dissertation

Date of Award

8-31-2021

Degree Name

Doctor of Philosophy in Industrial Engineering - (Ph.D.)

Department

Mechanical and Industrial Engineering

First Advisor

Ismet Esra Buyuktahtakin-Toy

Second Advisor

Sanchoy K. Das

Third Advisor

Athanassios K. Bladikas

Fourth Advisor

Wenbo Cai

Fifth Advisor

Kathleen McEnnis

Abstract

This dissertation addresses the resource allocation challenges of fighting against infectious disease outbreaks. The goal of this dissertation is to formulate multi-stage stochastic programming and agent-based models to address the limitations of former literature in optimizing resource allocation for preventing and controlling epidemics and pandemics. In the first study, a multi-stage stochastic programming compartmental model is presented to integrate the uncertain disease progression and the logistics of resource allocation to control a highly contagious infectious disease. The proposed multi-stage stochastic program, which involves various disease growth scenarios, optimizes the distribution of treatment centers and resources while minimizing the total expected number of new infections and funerals due to an epidemic. Two new equity metrics are defined and formulated, namely infection and capacity equity, to explicitly consider equity for allocating treatment funds and facilities for fair resource allocation in epidemics control. The multi-stage value of the stochastic solution (VSS), demonstrating the superiority of the proposed stochastic programming model over its deterministic counterpart, is studied. The first model is applied to the Ebola Virus Disease (EVD) case in West Africa, including Guinea, Sierra Leone, and Liberia. In the following study, the previous model is extended to a mean-risk multi-stage vaccine allocation model to capture the influence of the outbreak scenarios with low probability but high impact. The Conditional Value at Risk (CVaR) measure used in the model enables a trade-off between the weighted expected loss due to the outbreak and expected risks associated with experiencing disastrous epidemic scenarios. A method is developed to estimate the migration rate between each infected region when limited migration data is available. The second study is applied to the case of EVD in the Democratic Republic of the Congo.

In the third study, a new risk-averse multi-stage stochastic epidemics-ventilator-logistics compartmental stochastic programming model is developed to address the resource allocation challenges of mitigating COVID-19. This epidemiological logistics model involves the uncertainty of untested asymptomatic infections and incorporates short-term human migration. Disease transmission is also forecasted through deriving a new formulation of transmission rates that evolve over space and time with respect to various non-pharmaceutical interventions, such as wearing masks, social distancing, and lockdown. In the fourth study, a simulation-optimization approach is introduced to address the vaccination facility location and allocation challenges of the COVID-19 vaccines. A detailed agent-based simulation model of the COVID-19 is extended and integrated with a new vaccination center and vaccine-allocation optimization model. The proposed agent-based simulation-optimization framework simulates the disease transmission first and then minimizes the total number of infections over all the considered regions by choosing the optimal vaccine center locations and vaccine allocation to those centers. Specifically, the simulation provides the number of susceptible and infected individuals in each geographical region for the current time period as an input into the optimization model. The optimization model then minimizes the total number of estimated infections and provides the new vaccine center locations and vaccine allocation decisions for the following time period. Decisions are made on where to open vaccination centers and how many people should be vaccinated at each future stage in each region of the considered geographical location. Then these optimal decision values are imported back into the simulation model to simulate the number of susceptible and infected individuals for the subsequent periods. The agent-based simulation-optimization framework is applied to controlling COVID-19 in the states of New Jersey. The results provide insights into the optimal vaccine center location and vaccine allocation problem under varying budgets and vaccine types while foreseeing potential epidemic growth scenarios over time and spatial locations.

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