A Bicriteria Model to Determine Pareto Optimal Pulse Vaccination Strategies

Abstract

The aim of this paper is to determine approximate Pareto optimal (efficient) pulse vaccination strategies for epidemics modeled by the susceptible-infected-removed (SIR) without population dynamics, characterized by a single epidemic wave. Pulse vaccination is the application of the vaccination campaign over a limited time interval, by vaccinating susceptible individuals at a constant vaccination rate. A pulse vaccination strategy includes the determination of the beginning date and duration of the campaign and the vaccination rate. SIR with vaccination (SIRV) epidemic model is applied during pulse vaccination campaign, resulting in final proportions of removed (Rf) and vaccinated (Vf) individuals at the end of the epidemic. The burden of the epidemic is estimated in terms of Rf and Vf; two criteria are simultaneously minimized: vaccination cost and treatment cost of infected individuals and other economic losses due to sickness that are assumed to be proportional to Vf and Rf, respectively. To find approximate efficient solutions to this bicriteria problem, ODE and genetic algorithm toolboxes of MATLAB are integrated (GA-ODE). In GA-ODE, an augmented weighted Tchebycheff program is used as the evaluation function, calculated by solving the SIRV model and obtaining Rf and Vf values. Sample approximate efficient vaccination strategies are determined for diseases with a basic reproduction number (R0) 1.2 to 2.0. Consequently, obtained strategies are characterized as short-period campaigns that start as early as possible, i.e., as soon as vaccines are available and the vaccination rate increases with the severity of the disease (R0) and the importance weight given to minimization of Rf.