Optimal time-varying vaccine allocation amid pandemics with uncertain immunity ratios

Abstract

There is a concerted effort to develop vaccines to combat the public health crisis caused by COVID-19. Health experts are raising questions concerning the clinical trials, price and distribution of the vaccines among the public. Policymakers must design regulations to allocate vaccines equitably based on epidemiological as well as economic considerations. Allocation strategies must factor in the extent and duration of immunity the vaccines yield from future infections. We present a time-varying linear optimization-based approach, which incorporates epidemiological factors, such as population density, susceptible count and infected ratio as well as transportation costs, to disseminate vaccines among zones. Our approach also employs an update rule on the epidemiological statistics spawning from the SEIRD model to learn the extent of immunity provided by the vaccines. Our experiments are performed on the map of New York State with realistic mobility using spatial and ordinary differential equation-based SEIRD models. We show that the proposed approach allocates vaccines optimally while preventing zones from resource starvation. It adapts its vaccine recommendation to meet the prespecified epidemiological and economic policy requirements of zones, and is highly amenable to accommodate multiple immunity ratios, vaccine types and the time-span of acquired vaccine immunity. Moreover, we demonstrate that one can learn the latent immunity ratios of the vaccines to make more informed recommendations with time. Our ordinary differential equation-based analysis on the real demographic and infection data of New York State show that a small fraction of zones tends to exhibit a high resource demand due to their vulnerability to the pandemic spread. Our vaccine allocation strategy incorporates infection ratio as one of the criteria and is applicable to conceive a drug allocation strategy. The results suggest that incorporating the vulnerability score of zones to the epidemic spread into vaccine allocation may enhance recommendations and aid policy making.