Optimal Vaccination Strategies for a Heterogeneous SIS Model

Abstract. We study in a general mathematical framework the optimal allocation of vaccine in an heterogeneous population. We cast the problem of optimal vaccination as a biobjective minimization problem [Formula: see text], where [Formula: see text] and [Formula: see text] stand, respectively, for the cost and the loss incurred when following the vaccination strategy [Formula: see text], where the function [Formula: see text] represents the proportion of nonvaccinated among individuals of feature [Formula: see text]. To measure the loss, we consider either the effective reproduction number, a classical quantity appearing in many models in epidemiology, or the overall proportion of infected individuals after vaccination in the maximal equilibrium, also called the endemic state. We only make few assumptions on the cost [Formula: see text], which cover the uniform cost, that is, the total number of vaccinated people. The analysis of the biobjective problem is carried out in a general framework, and we check that it is well posed for the SIS model and has Pareto optima, which can be interpreted as the “best” vaccination strategies. We provide properties of the corresponding Pareto frontier given by the outcomes [Formula: see text] of Pareto optimal strategies.