Dynamical analysis of SIR model with Gamma distribution delay driven by Lévy noise and switching

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Abstract

Considering the distributed time delay and the stochastic change of environment, this research primarily studied the dynamical behavior of the gamma-distributed delay SIR model driven by Lévy noise and Markov chain. First, it is proved that there is a unique global positive solution for stochastic model. Second, by constructing appropriate stochastic Lyapunov functions that account for regime switching, we derive a sufficient condition, R_s > 1, indicating the existence of a stationary distribution. This suggests the disease will persist over a long period. Finally, numerical simulations confirm the theoretical findings.

Keywords

SIR model / distributed delay / Markov switching / Lévy noise / stationary distribution

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