  Vaccines have proven effective in mitigating the threat of severe infections
and deaths during outbreaks of infectious diseases. However, vaccine hesitancy
(VH) complicates disease spread prediction and healthcare resource assessment
across regions and populations. We propose a modeling framework that integrates
an epidemiological compartmental model that captures the spread of an
infectious disease within a multi-stage stochastic program (MSP) that
determines the allocation of critical resources under uncertainty. The proposed
compartmental MSP model adaptively manages the allocation of resources to
account for changes in population behavior toward vaccines (i.e., variability
in VH), the unique patterns of disease spread, and the availability of
healthcare resources over time and space. The compartmental MSP model allowed
us to analyze the price of fairness in resource allocation. Using real COVID-19
vaccination and healthcare resource data from Arkansas, U.S. (January-May
2021), our findings include: (i) delaying the initial deployment of additional
ventilators by one month could lead to an average increase in the expected
number of deaths by 285.41/month, highlighting the importance of prompt action;
(ii) each additional ventilator in the initial stockpile and in supply leads to
a decrease in the expected number of deaths by 1.09/month and 0.962/month,
respectively, emphasizing the importance of maintaining a large stockpile and
scalable production response; (iii) the cost of ensuring equitable resource
allocation varies over time and location, peaking during the peak of a disease
outbreak and in densely populated areas. This study emphasizes the importance
of flexible, informed public health decision-making and preparedness, providing
a model for effective resource allocation in public health emergencies.
