Stability Analysis and Optimal Control of Vaccination and Treatment of a SIR Epidemiological Deterministic Model with Relapse

In this paper, we studied and formulated the relapsed SIR model of a constant size population with standard incidence rate. Also, the optimal control problem with treatment and vaccination as controls, subject to the model is formulated. The analysis carried out on the model, clearly showed that the infection free steady state is globally asymptotically stable if the basic reproduction number is less than unity, and the endemic steady state, also, is globally asymptotically stable if the basic reproduction number (R۰) is greater than unity. The results obtained from the simulations were analyzed and discussed.

Keywords:

Global stability , Local stability , Lyapunov , Optimal Control , Pontryagin maximum principle