Optimal Control Analysis of an SIR Epidemic Model with Constant recruitment

Abstract

A mathematical model of an SIR epidemic model with constant recruitment and two control variables using control terms and a deterministic system of dierential equation is presented and analyzed mathematically and numerically. We intend to control the susceptible and infected individuals with educational campaign and treatment strategies. We analyzed the model by non-dimensionalizing the system of equations of our SIR epidemic model and derived our basic reproduction number.We aim to minimize the total number of infective individuals and the cost associated with the use of educational campaign and treatment on [0; T ]. We used Pontryagin's maximum principle to characterize the optimal levels of the two controls. The resulting optimality system is solved numerically. The results show that the optimal combination of treatment and educational campaign strategy required to achieve the set objective will depend on the relative cost of each of the control measures. The results from our simulation is discussed.

Keywords: Computational simulations, Disease Free Equilibrium, Optimal control, Pontryagin's Maximum Principle, stability theory.