Optimal Control Analysis of an SIRS Epidemic Model with the Asymptotic Transmission

In this paper, we developed and analysed a SIRS(Susceptible-Infected-Recovered-Susceptible) epidemic model that capturesthe asymptotic transmission in the presence of two controlinterventions (vaccination and treatment). Non-linear deter-ministic system of dierential equations was used to capturethe asymptotic transmission of the SIRS epidemic model andthe basic reproduction number, R0, with the two controlinterventions of the model was computed. Optimal controltheory was applied using the Pontryagin's Maximum Principle(PMP) to investigate optimal strategies for controlling the spreadof the disease using vaccination and treatment as the systemcontrol variables. The result predicted that both treatmentand vaccination strategies are very eective control strategiesto combat the transmission of any disease but in areas oflimited resources treatment only or vaccination only can beapplied to reduce the morbidity and mortality of any disease.Finally, numerical simulations were performed and graphicalresults were presented to illustrate the analytical solution.