Abstract

A SIR EPIDEMIC MODEL WITH CONSTANT VACCINATION WITH SATURATED TREATMENT

Bakare E.A.1, Are E.B.1, Osanyinlusi Samuel 1,2

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Abstract If sufficient and quick steps are taken in the course of an epidemic several infectious diseases will be driven towards eradication. Many mathematical models have been used to explore the dynamics of Susceptible-Infected-Recovered (SIR) transmission but those that considered saturated treatment are quite scarce. A deterministic model for the dynamics of an infectious disease is proposed in the presence of a constant vaccination and saturated treatment. The SIR model, which assumes a mass action incidence rate is analysed qualitatively to examine the stability of the equilibria while the basic reproduction number was also determined. Numerical simulations, to verify our analytical findings were performed. Keywords: Asymptotic transmission, Basic reproduction number, Disease free equilibrium, Next generation matrix, Numerical simulation.

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