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A delayed vaccinated epidemic model with nonlinear incidence rate and Lévy jumps

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  • Fan, Kuangang
  • Zhang, Yan
  • Gao, Shujing
  • Chen, Shihua

Abstract

A stochastic susceptible–infectious–recovered epidemic model with nonlinear incidence rate is formulated to discuss the effects of temporary immunity, vaccination, and Le.́vy jumps on the transmission of diseases. We first determine the existence of a unique global positive solution and a positively invariant set for the stochastic system. Sufficient conditions for extinction and persistence in the mean of the disease are then achieved by constructing suitable Lyapunov functions. Based on the analysis, we conclude that noise intensity and the validity period of vaccination greatly influence the transmission dynamics of the system.

Suggested Citation

  • Fan, Kuangang & Zhang, Yan & Gao, Shujing & Chen, Shihua, 2020. "A delayed vaccinated epidemic model with nonlinear incidence rate and Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 544(C).
    • Handle: RePEc:eee:phsmap:v:544:y:2020:i:c:s0378437119318898
    DOI: 10.1016/j.physa.2019.123379
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    References listed on IDEAS

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    Cited by:

    1. El Attouga, Sanae & Bouggar, Driss & El Fatini, Mohamed & Hilbert, Astrid & Pettersson, Roger, 2023. "Lévy noise with infinite activity and the impact on the dynamic of an SIRS epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 618(C).
    2. Liu, Chao & Tian, Yilin & Chen, Peng & Cheung, Lora, 2024. "Stochastic dynamic effects of media coverage and incubation on a distributed delayed epidemic system with Lévy jumps," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    3. Zhang, Ge & Li, Zhiming & Din, Anwarud, 2022. "A stochastic SIQR epidemic model with Lévy jumps and three-time delays," Applied Mathematics and Computation, Elsevier, vol. 431(C).

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