  Existing compartmental models in epidemiology are limited in terms of
optimizing the resource allocation to control an epidemic outbreak under
disease growth uncertainty. In this study, we address this core limitation by
presenting a multi-stage stochastic programming compartmental model, which
integrates the uncertain disease progression and resource allocation to control
an infectious disease outbreak. The proposed multi-stage stochastic program
involves various disease growth scenarios and optimizes the distribution of
treatment centers and resources while minimizing the total expected number of
new infections and funerals. We define two new equity metrics, namely infection
and capacity equity, and explicitly consider equity for allocating treatment
funds and facilities over multiple time stages. We also study the multi-stage
value of the stochastic solution (VSS), which demonstrates the superiority of
the proposed stochastic programming model over its deterministic counterpart.
We apply the proposed formulation to control the Ebola Virus Disease (EVD) in
Guinea, Sierra Leone, and Liberia of West Africa to determine the optimal and
fair resource-allocation strategies. Our model balances the proportion of
infections over all regions, even without including the infection equity or
prevalence equity constraints. Model results also show that allocating
treatment resources proportional to population is sub-optimal, and enforcing
such a resource allocation policy might adversely impact the total number of
infections and deaths, and thus resulting in a high cost that we have to pay
for the fairness. Our multi-stage stochastic epidemic-logistics model is
practical and can be adapted to control other infectious diseases in
meta-populations and dynamically evolving situations.
