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<p>We study the effects of diffusion rates together with boundary outflow on disease persistence in an SIS reaction–diffusion model with Robin boundary conditions. Robin-type boundary terms represent loss of individuals through the habitat boundary, which can destabilize equilibria and suppress disease persistence. Our work concentrates on how dispersion rates shape the existence and structure of positive steady states. We analyze limiting profiles where dispersion coefficients tend to 0 or <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(+\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>+</mo> <mi>∞</mi> </mrow> </math></EquationSource> </InlineEquation>, which show that fast diffusion amplifies boundary loss, driving one or both populations toward extinction. In contrast, slow diffusion confines individuals within the habitat, promoting persistence and supporting endemic equilibria. These findings show the interplay between dispersion and boundary outflow, ensuring that mobility can either enhance or counteract the effects of boundary-induced losses in spatially heterogeneous epidemiological systems.</p>

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Impact of dispersion rates on the positive steady state of an SIS epidemic model with population outflow at the boundary

  • 期刊论文

  • 发表日期：

    2026年5月14日

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  • Salih Djilali

摘要

We study the effects of diffusion rates together with boundary outflow on disease persistence in an SIS reaction–diffusion model with Robin boundary conditions. Robin-type boundary terms represent loss of individuals through the habitat boundary, which can destabilize equilibria and suppress disease persistence. Our work concentrates on how dispersion rates shape the existence and structure of positive steady states. We analyze limiting profiles where dispersion coefficients tend to 0 or \(+\infty \) + ∞ , which show that fast diffusion amplifies boundary loss, driving one or both populations toward extinction. In contrast, slow diffusion confines individuals within the habitat, promoting persistence and supporting endemic equilibria. These findings show the interplay between dispersion and boundary outflow, ensuring that mobility can either enhance or counteract the effects of boundary-induced losses in spatially heterogeneous epidemiological systems.