Abstract
In this paper, we study a class of compatimental epidemiological models consisting of Susceptible, Infected, and Removed (SIR) individuals with a perturbation factor or exterior effects such as noise, climate change, pollution, etc. We prove the existence and uniqueness of a limit cycle confined in a nonempty closed and convex set by relying on a recent result of Lobanova and Sadovskii. Moreover, we study the existence of Hopf and Bogdanov-Takens bifurcations by applying respectively Poincare-Andronov-Hopf bifurcation theorem and Bogdanov-Takens theorem. Eventually, using Scilab, we illustrate the validity of our results with numerical simulations and also interpret them.
Recommended Citation
Degbo, Seyive J. and Degla, Guy A.
(2022).
(R2023) Analysis of the Auto-Oscillation of a Perturbed SIR Epidemiological Model,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 19,
Iss.
1, Article 10.
Available at:
https://digitalcommons.pvamu.edu/aam/vol19/iss1/10