### AIMS Mathematics

2022, Issue 9: 16498-16518. doi: 10.3934/math.2022903
Research article

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

• 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.

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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• 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.

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