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<p>In this paper, we develop a new stochastic SIRS model for disease transmission under environmental uncertainty, combining a general nonlinear incidence and capacity-limited (saturated) treatment with both Gaussian white noise (Itô diffusion) and telegraph noise represented by a finite-state Markov regime switch. Using stopping time localization and a tailored Lyapunov functional, we establish global existence, positivity, and non-explosion of solutions, and we derive explicit, verifiable conditions for (i) almost-sure extinction and (ii) persistence in the mean. The resulting thresholds clarify how noise intensities, regime statistics, incidence curvature, and treatment saturation interact. Numerical experiments based on the Milstein scheme for regime switching SDEs corroborate the theory and illustrate control trade-offs under capacity constraints. These results provide a rigorous foundation for assessing intervention strategies when transmission and healthcare availability fluctuate across regimes.</p>

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The impact of regime switching on stochastic SIRS dynamics with general incidence and treatment saturation

  • 期刊论文

  • 发表日期：

    2026年7月21日

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  • Jungang Wang,
  • Jie Zhou,
  • Abdulwasea Alkhazzan,
  • Yassine Sabbar,
  • Minjuan Wang

摘要

In this paper, we develop a new stochastic SIRS model for disease transmission under environmental uncertainty, combining a general nonlinear incidence and capacity-limited (saturated) treatment with both Gaussian white noise (Itô diffusion) and telegraph noise represented by a finite-state Markov regime switch. Using stopping time localization and a tailored Lyapunov functional, we establish global existence, positivity, and non-explosion of solutions, and we derive explicit, verifiable conditions for (i) almost-sure extinction and (ii) persistence in the mean. The resulting thresholds clarify how noise intensities, regime statistics, incidence curvature, and treatment saturation interact. Numerical experiments based on the Milstein scheme for regime switching SDEs corroborate the theory and illustrate control trade-offs under capacity constraints. These results provide a rigorous foundation for assessing intervention strategies when transmission and healthcare availability fluctuate across regimes.