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

Jing Yang; Shaojuan Ma; Dongmei Wei; Jing Yang; Shaojuan Ma; Dongmei Wei

doi:10.3934/era.2025138

Electronic Research Archive

2025, Volume 33, Issue 5: 3158-3176. doi: 10.3934/era.2025138

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

1.
School of Mathematics and Information Science, North Minzu University, Yinchuan 750021, China
2.
Ningxia Key Laboratory of Intelligent Information and Big Data Processing, Yinchuan 750021, China
3.
Ningxia Basic Science Research Center of Mathematics, Yinchuan 750021, China

Received: 23 January 2025 Revised: 19 March 2025 Accepted: 25 April 2025 Published: 21 May 2025

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.
- SIR model,
- distributed delay,
- Markov switching,
- Lévy noise,
- stationary distribution
Citation: Jing Yang, Shaojuan Ma, Dongmei Wei. Dynamical analysis of SIR model with Gamma distribution delay driven by Lévy noise and switching[J]. Electronic Research Archive, 2025, 33(5): 3158-3176. doi: 10.3934/era.2025138

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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.

References

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