Optimal ordering strategy and budget allocation for the Covid-19 vaccination planning

Abstract

During the COVID-19 pandemic, the most important thing was to control the overall infection rate. To achieve this goal, social managers can choose to use vaccines with different production cycles and therapeutic effects for epidemic prevention and control under financial budget constraints. In this paper we adopt a two-tier queueing system with reneging to characterize the operation management of COVID-19 vaccine ordering and vaccination, in which a higher–efficacy vaccine queue (HQ) and a lower-efficacy vaccine queue (LQ) are employed to account for two types of vaccines service. In light of this framework, a recursive formula is proposed for deriving the infection rates of residents in both HQ and LQ. Social managers can achieve the lowest total infection rate by selecting appropriate vaccine ordering strategies under fixed service capacity, or by allocating financial budgets reasonably under the investment cost regime. Accordingly, we obtain the socially optimal vaccine ordering strategies and financial budget allocation. Finally, we analyze the sensitivity of various parameters to relevant optimal strategies and discover that utilizing a mixed ordering strategy is socially optimal in most circumstances. However, in some extreme cases, ordering a single type of vaccine (higher- or lower-efficacy) may also result in the lowest societal infection rate.