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

Document Type: Full Length Article

Authors

1 Department of Mathematics, Faculty of Science, Ekiti State University, Nigeria

2 Department of Mathematics, Ekiti-State University (EKSU), Ado-Ekiti. Ekiti-State, Nigeria

Abstract

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 (R0) is greater than
unity. The results obtained from the simulations were analyzed and discussed.

Keywords