Heterogeneous joint vaccine allocation and quarantine restriction planning under uncertainty: The COVID-19 pandemic

Once effective vaccines are discovered for a pandemic and initial distribution infrastructure, and mechanisms are implemented, the next concern is an optimal vaccination campaign to stop the disease or minimize the casualties. This paper studies the optimization of a Vaccine Distribution Network (VDN) through a single-objective Mixed-Integer Non-Linear Programming (MINLP) model for minimizing the total cost in terms of governmental aid (to maintain the economy), logistics, vaccination, and hospitalization costs. The proposed model develops the optimal joint vaccination-quarantine strategy under equity considerations to (1) determine the optimal allocation of available vaccine stockpiles to different population classes in different regions and (2) seek to impose quarantine restrictions to different regions optimally. The proposed model was applied to a real case study, the vaccine distribution network in France. Through a comprehensive numerical analysis, the optimal vaccine allocation is calculated, and the impact of equity and quarantine on the performance of the distribution network is investigated. Moreover, fractional dosing on the number of infections is examined. The results show that equity considerations, counter-intuitively, lead to an increased number of infections. Furthermore, it is illustrated that fractional dosing helps policymakers to control the pandemic better under a limited supply of vaccines.