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<p>In this work, we investigate the dynamics of infectious diseases that are transmitted directly in the population and through environmental contamination. In this context, we have developed a dynamical model called SIQRE in the form of a stochastic differential equation that considers susceptible, infected, quarantined and recovered population as well as environmental contamination as dynamic variables. We investigate the existence and uniqueness of the global non-negative solution for the model individually in the absence and presence of stochastic noise. In the first scenario, we evaluate the local asymptotic stability of both disease-free and endemic equilibria in the deterministic SIQRE model. We also compute the basic reproduction number <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12190_2025_2507_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">\({{\mathcal {\boldsymbol{R}}}_0}\)</EquationSource> </InlineEquation>. When we consider the stochastic noise in the SIQRE model, we obtain some thresholds that fully determine whether the disease goes extinct or prevails for each size of white noise. To validate the analytical results, we perform some numerical simulations.</p>

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Dynamics of a stochastic epidemic model for infectious diseases: inclusion of the environmental contamination factor

  • 期刊论文

  • 发表日期：

    2025年5月14日

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  • Amir Haghighi,
  • Nemat Nyamoradi

摘要

In this work, we investigate the dynamics of infectious diseases that are transmitted directly in the population and through environmental contamination. In this context, we have developed a dynamical model called SIQRE in the form of a stochastic differential equation that considers susceptible, infected, quarantined and recovered population as well as environmental contamination as dynamic variables. We investigate the existence and uniqueness of the global non-negative solution for the model individually in the absence and presence of stochastic noise. In the first scenario, we evaluate the local asymptotic stability of both disease-free and endemic equilibria in the deterministic SIQRE model. We also compute the basic reproduction number \({{\mathcal {\boldsymbol{R}}}_0}\) . When we consider the stochastic noise in the SIQRE model, we obtain some thresholds that fully determine whether the disease goes extinct or prevails for each size of white noise. To validate the analytical results, we perform some numerical simulations.