Title of article
Stability Analysis and Optimal Control of Vaccination and Treatment of a SIR Epidemiological Deterministic Model with Relapse
Author/Authors
Ogunmiloro, O. M Department of Mathematics - Ekiti State University - Ado Ekiti - P.M.B 5363, Nigeria , Fadugba, S. E Department of Mathematics - Ekiti State University - Ado Ekiti - P.M.B 5363, Nigeria , Ogunlade, T. O Department of Mathematics - Ekiti State University - Ado Ekiti - P.M.B 5363, Nigeria
Pages
13
From page
39
To page
51
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
Global stability , Local stability , Lyapunov , Optimal control , Pontryagin maximum principle
Journal title
Astroparticle Physics
Serial Year
2018
Record number
2438716
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