NUMERICAL AND STABILITY ANALYSIS OF THE TRANSMISSION DYNAMICS OF SVIR EPIDEMIC MODEL
WITH STANDARD INCIDENCE RATE
Ogunmiloro O.M., Abedo F.O., Kareem H.A.
Department of Mathematics, Ekiti – State University, Ado – Ekiti, Ekiti State, Nigeria
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ABSTRACT
In this article, a Susceptible – Vaccinated – Infected – Recovered (SVIR) model is formulated and analysed using comprehensive mathematical techniques. The vaccination class is primarily considered as means of controlling the disease spread. The basic reproduction number (Ro) of the model is obtained, where it was shown that if Ro<1, at the model equilibrium solutions when infection is present and absent, the infection- free equilibrium is both locally and globally asymptotically stable. Also, if Ro>1, the endemic equilibrium solution is locally asymptotically stable. Furthermore, the analytical solution of the model was carried out using the Differential Transform Method (DTM) and Runge - Kutta fourth-order method. Numerical simulations were carried out to validate the theoretical results.
Keywords: SVIR epidemic model, Reproduction number, Local stability, Global stability, DTM, Runge-Kutta
Published On: 30 December 2019
