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.

中文翻译：

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带有周期性或随机调制非线性入射率的简单SIR模型中的混沌的Melnikov分析。

本文详细研究了具有周期或随机调制非线性入射率的简单SIR模型中混沌的Melnikov分析，以及周期性和有界噪声对具有等斜轨道的SIR模型混沌运动的影响。基于均斜分叉，通过随机梅尔尼科夫定理推导了可能发生混沌运动的必要条件以及充分条件，并建立了混沌发生时有界噪声幅度的阈值。