Optimal vaccination strategy for an SIRS model with imprecise parameters and Lévy noise

Abstract

Parameters of mathematical models are often imprecise due to various uncertainties. How parameter imprecision and sudden environmental changes influence the optimal control of dynamical systems remains unclear. In this paper, we formulate an Susceptible-Infected-Recovered-Susceptible (SIRS) epidemic model that includes imprecise parameters, Lévy jumps, and vaccination control. We use the model to investigate the near-optimal control problem in the setting of vaccination. We obtain priori estimates of the susceptible, infected and recovered populations. We establish sufficient and necessary conditions for the near-optimality of the model using Pontryagin stochastic maximum principle. We also develop an algorithm for the near-optimal control problem and perform numerical simulations to illustrate the effect of vaccination and Lévy noise.