Optimal Capacity-Constrained COVID-19 Vaccination for Heterogeneous Populations

COVID-19 and the ensuing vaccine capacity constraints have emphasized the importance of proper prioritization during vaccine rollout. This problem is complicated by heterogeneity in risk levels, contact rates, and network topology which can dramatically and unintuitively change the efficacy of vaccination and must be taken into account when allocating resources. This paper proposes a general model to capture a wide array of network heterogeneity while maintaining computational tractability and formulates vaccine prioritization as an optimal control problem. Pontryagin’s Maximum Principle is used to derive properties of optimal, potentially highly dynamic, allocation policies, providing significant reductions in the set of candidate policies. Extensive numerical simulations of COVID-19 vaccination are used to corroborate these findings and further illicit optimal policy characteristics and the effects of various system, disease, and population parameters.

I. INTRODUCTION

Since its beginning in December 2019, the COVID-19 pandemic has resulted in nearly 500 million infections and over 6 million deaths as of March 2022 [1]. Vaccines have proven to be the most effective countermeasure to the pandemic by limiting further transmission and protecting especially vulnerable populations [2]. During its early stages, the vaccination drive was heavily capacity constrained with demand far outstripping supply and administration capability – a challenge that continues to plague Low- and Middle-Income Countries (LMICs) [3]. This is bound to be the case for vaccines developed for every infectious disease. Under such constraints, governments and public health organization must make the critical choice of whom to vaccinate first: 1) those who are likely to transmit the disease most, 2) those who are at risk for developing a serious form of the disease due to age or comorbidity, or 3) a combination of the first and second set. For COVID-19 most public health bodies opted for the second category first, but was it the optimal choice even if we consider the limited objective of minimizing say only the fatality count?