Global Stability Analysis of Sir Epidemic Model with Relapse and Immunity Loss
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Date
2016
Journal Title
Journal ISSN
Volume Title
Publisher
International Journal of Applied Science and Mathematical Theory ISSN 2489-009X Vol. 2 No.1 2016 www.iiardpub.org
Abstract
A deterministic mathematical model for the transmission dynamics of infectious disease with
immunity loss and relapse was built and analyzed. The model was shown to exhibit two
equilibria, namely, a disease free equilibrium and an endemic equilibrium. The computated
basic reproductive number (R_0) was used to establish that whenever R_0<1, the disease free
equilibrium is locally asymptotically stable and the endemic equilibrium is locally asymptotically
stable whenever
R_0>1. Furthermore the global stability for the two equilibria was investigated
using Lyapunov function. The model was simulated numerically to validate the analytical results.
Description
Keywords
Epidemic Model, Relapse, Immunity Loss, Equilibria, Global Stability
Citation
Akinyemi, S. T., Ibrahim, M. O., Usman, I. G. and Odetunde, O. (2016). Global Stability Analysis of SIR Epidemic Model with Relapse and Immunity Loss. International Journal of Applied Science and Mathematical Theory Vol. 2 No. 1 2016