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<p>This paper presents a stochastic <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math> <mi mathvariant="script">SIS</mi> </math></EquationSource> <EquationSource Format="TEX">$\mathcal{SIS}$</EquationSource> </InlineEquation> (Susceptible-Infected-Susceptible) epidemic model with generalized incidence function and two separate Brownian noise sources. Using analytical methods from stochastic calculus, we derive explicit threshold conditions governing disease extinction and endemic persistence. These theoretical results are validated through systematic numerical simulations, including phase-space trajectory analysis under varying epidemiological scenarios. A central contribution is the development of a novel computational-analytic framework to rigorously verify the model’s long-term statistical properties: (i) stationarity through distributional convergence tests, and (ii) ergodicity via empirical moment estimation. The combined analytical-numerical approach provides actionable insights for epidemic modeling while advancing methodology for stochastic dynamical systems.</p>

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A computational-analytic framework for assessing stationarity and ergodicity for a stochastic SIS epidemic model

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月3日

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  • Lahcen Boulaasair,
  • Hassane Bouzahir,
  • Mhamed Eddahbi,
  • Brahim Benaid

摘要

This paper presents a stochastic SIS $\mathcal{SIS}$ (Susceptible-Infected-Susceptible) epidemic model with generalized incidence function and two separate Brownian noise sources. Using analytical methods from stochastic calculus, we derive explicit threshold conditions governing disease extinction and endemic persistence. These theoretical results are validated through systematic numerical simulations, including phase-space trajectory analysis under varying epidemiological scenarios. A central contribution is the development of a novel computational-analytic framework to rigorously verify the model’s long-term statistical properties: (i) stationarity through distributional convergence tests, and (ii) ergodicity via empirical moment estimation. The combined analytical-numerical approach provides actionable insights for epidemic modeling while advancing methodology for stochastic dynamical systems.