Optimal vaccination control for COVID-19 in a metapopulation model: a case of the Philippines

Abstract

We investigate a contextual problem of how to distribute a limited supply of vaccines over a period of time in a country where different regions have its own vaccination capacities. Considering that daily vaccination will affect future disease progression, we aim to find a distribution strategy over time that can minimize the total infection and implementation costs. Lagrangian and Eulerian migrations connect our multi-patch COVID-19 model, and vaccination is added as a control measure. An optimal control problem with an isoperimetric constraint is formulated and solved using the Adapted Forward–Backward Sweep Method. In distributing 5 million vaccines in 50 days, simulations showed that the optimal control strategy could lead to a difference of reducing two hundred thousand infections in just one region.