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Dynamical behaviors of a stochastic SIS model on Metapopulation Networks with Markovian switching

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  • Jing, Wenjun
  • Cao, Xiaochun
  • Zhang, Juping

Abstract

Considering the impacts of human mobility and telegraph noise on infectious disease transmission, a stochastic SIS model on metapopulation networks with Markovian switching is formulated. By constructing a Lyapunov function, the existence of a unique global positive solution to the model is proved. Moreover, we derive sufficient conditions for the extinction and persistence in mean of the infectious disease. The results reveal the important role of the stationary distribution of Markov chain in determining the threshold conditions. Furthermore, numerical simulations indicate that environmental switching can lead to the potential for multi-wave spread of infectious diseases. When the environment switches at a speed of logarithmic scale, the speed of environmental switching is not directly related to the thresholds, but affects the temporal fluctuations of the epidemic. The slower the speed of environmental switching, the lower the frequency of fluctuation, but the larger the fluctuation amplitude of epidemic spreading. Our work contributes to enrich the theoretical analysis of epidemic dynamics on metapopulation networks.

Suggested Citation

  • Jing, Wenjun & Cao, Xiaochun & Zhang, Juping, 2026. "Dynamical behaviors of a stochastic SIS model on Metapopulation Networks with Markovian switching," Chaos, Solitons & Fractals, Elsevier, vol. 204(C).
    • Handle: RePEc:eee:chsofr:v:204:y:2026:i:c:s0960077925017497
    DOI: 10.1016/j.chaos.2025.117736
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