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Periodic solution and ergodic stationary distribution of two stochastic SIQS epidemic systems

Author

Listed:
  • Qi, Haokun
  • Zhang, Shengqiang
  • Meng, Xinzhu
  • Dong, Huanhe

Abstract

This paper proposes two stochastic SIQS epidemic models with periodic parameters and Markov switching. We first prove that the stochastic non-autonomous periodic system has a nontrivial positive periodic solution by using the Khasminskii’s theory. Then the sufficient conditions for extinction of the disease are obtained. Furthermore, we construct suitable stochastic Lyapunov functions with regime switching to prove the existence of ergodic stationary distribution of the stochastic SIQS epidemic model. At last, some rigorous numerical simulations are presented to illustrate our theoretical results.

Suggested Citation

  • Qi, Haokun & Zhang, Shengqiang & Meng, Xinzhu & Dong, Huanhe, 2018. "Periodic solution and ergodic stationary distribution of two stochastic SIQS epidemic systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 223-241.
    • Handle: RePEc:eee:phsmap:v:508:y:2018:i:c:p:223-241
    DOI: 10.1016/j.physa.2018.05.075
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    References listed on IDEAS

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    2. Li, Yan & Zhang, Qimin, 2020. "The balanced implicit method of preserving positivity for the stochastic SIQS epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    3. Lin Hu & Lin-Fei Nie, 2022. "Dynamics of a Stochastic HIV Infection Model with Logistic Growth and CTLs Immune Response under Regime Switching," Mathematics, MDPI, vol. 10(19), pages 1-20, September.
    4. Okita, Kouki & Tatsukawa, Yuichi & Utsumi, Shinobu & Arefin, Md. Rajib & Hossain, Md. Anowar & Tanimoto, Jun, 2023. "Stochastic resonance effect observed in a vaccination game with effectiveness framework obeying the SIR process on a scale-free network," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).

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