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Existing compartmental models in epidemiology are limited in terms ofoptimizing the resource allocation to control an epidemic outbreak underdisease growth uncertainty. In this study, we address this core limitation bypresenting a multi-stage stochastic programming compartmental model, whichintegrates the uncertain disease progression and resource allocation to controlan infectious disease outbreak. The proposed multi-stage stochastic programinvolves various disease growth scenarios and optimizes the distribution oftreatment centers and resources while minimizing the total expected number ofnew infections and funerals. We define two new equity metrics, namely infectionand capacity equity, and explicitly consider equity for allocating treatmentfunds and facilities over multiple time stages. We also study the multi-stagevalue of the stochastic solution (VSS), which demonstrates the superiority ofthe proposed stochastic programming model over its deterministic counterpart.We apply the proposed formulation to control the Ebola Virus Disease (EVD) inGuinea, Sierra Leone, and Liberia of West Africa to determine the optimal andfair resource-allocation strategies. Our model balances the proportion ofinfections over all regions, even without including the infection equity orprevalence equity constraints. Model results also show that allocatingtreatment resources proportional to population is sub-optimal, and enforcingsuch a resource allocation policy might adversely impact the total number ofinfections and deaths, and thus resulting in a high cost that we have to payfor the fairness. Our multi-stage stochastic epidemic-logistics model ispractical and can be adapted to control other infectious diseases inmeta-populations and dynamically evolving situations.

A Multi-Stage Stochastic Programming Approach to Epidemic Resource Allocation with Equity Considerations