Melnikov analysis of chaos in a simple SIR model with periodically or stochastically modulated nonlinear incidence rate

Yanxiang Shi

doi:10.1080/17513758.2020.1718222

Melnikov analysis of chaos in a simple SIR model with periodically or stochastically modulated nonlinear incidence rate

J Biol Dyn. 2020 Dec;14(1):269-288. doi: 10.1080/17513758.2020.1718222.

Author

Yanxiang Shi¹

Affiliation

¹ School of Mathematical Sciences, Shanxi University, Taiyuan, People's Republic of China.

PMID: 32281489
DOI: 10.1080/17513758.2020.1718222

Abstract

In this paper, Melnikov analysis of chaos in a simple SIR model with periodically or stochastically modulated nonlinear incidence rate and the effect of periodic and bounded noise on the chaotic motion of SIR model possessing homoclinic orbits are detailed investigated. Based on homoclinic bifurcation, necessary conditions for possible chaotic motion as well as sufficient condition are derived by the random Melnikov theorem, and to establish the threshold of bounded noise amplitude for the onset of chaos.

Keywords: 34C23; 34C28; 34F05; 37N25; 65P20; Melnikov theorem; SIR model; chaos; homoclinic orbit.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Communicable Diseases / epidemiology*
Disease Susceptibility / epidemiology*
Humans
Incidence
Models, Biological
Nonlinear Dynamics*
Stochastic Processes*