Threshold behaviour of a triple-delay SIQR stochastic epidemic model with Lévy noise perturbation

Yubo Liu; Daipeng Kuang; Jianli Li; Yubo Liu; Daipeng Kuang; Jianli Li

doi:10.3934/math.2022903

AIMS Mathematics

2022, Volume 7, Issue 9: 16498-16518. doi: 10.3934/math.2022903

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Research article

Threshold behaviour of a triple-delay SIQR stochastic epidemic model with Lévy noise perturbation

College of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan 410081, China

Received: 11 March 2022 Revised: 03 July 2022 Accepted: 05 July 2022 Published: 08 July 2022
MSC : 37A50, 37H10, 37N25, 74A15

In this paper, the dynamical behavior of a delayed SIQR stochastic epidemic model with Lévy noise is presented and studied. First, we prove the existence and uniqueness of positive solution. Then, we establish the threshold $ R_0^l $ as a sufficient condition for the extinction and persistence in mean of the disease. Finally, some numerical simulations are presented to support our theoretical results and we infer that the white and Lévy noises affect the transmission dynamics of the system.
- threshold,
- Lévy jumps,
- delay,
- persistence,
- extinction
Citation: Yubo Liu, Daipeng Kuang, Jianli Li. Threshold behaviour of a triple-delay SIQR stochastic epidemic model with Lévy noise perturbation[J]. AIMS Mathematics, 2022, 7(9): 16498-16518. doi: 10.3934/math.2022903

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Abstract

In this paper, the dynamical behavior of a delayed SIQR stochastic epidemic model with Lévy noise is presented and studied. First, we prove the existence and uniqueness of positive solution. Then, we establish the threshold $ R_0^l $ as a sufficient condition for the extinction and persistence in mean of the disease. Finally, some numerical simulations are presented to support our theoretical results and we infer that the white and Lévy noises affect the transmission dynamics of the system.

References

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