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<p>This paper is purported to investigate diffusive epidemic model with advection in a bounded domain with the no-flux boundary condition. The sufficient conditions to nonexistence and existence of a nonconstant positive solution are considered for this epidemic system. The results show that there exists spatiotemporal pattern formation when the tendency of infected individuals is strong to move away from the susceptible individuals with <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal {R}_{0}&gt;1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="script">R</mi> <mn>0</mn> </msub> <mo>&gt;</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>, which indicates that there exists endemic disease extensively with the stripe-like or the spotted, while there does not exist spatiotemporal pattern formation when the self-pressure is big enough with a weak repulsive tendency. Furthermore, by using the global bifurcation theory, it is derived that a branch of nonconstant solutions can bifurcate from the positive constant solution when the repulsive tendency is relatively big. </p>

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Global bifurcation of the reaction–diffusion epidemic model with advection

  • 期刊论文

  • 发表日期：

    2026年3月7日

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  • Chenglin Li

摘要

This paper is purported to investigate diffusive epidemic model with advection in a bounded domain with the no-flux boundary condition. The sufficient conditions to nonexistence and existence of a nonconstant positive solution are considered for this epidemic system. The results show that there exists spatiotemporal pattern formation when the tendency of infected individuals is strong to move away from the susceptible individuals with \(\mathcal {R}_{0}>1\) R 0 > 1 , which indicates that there exists endemic disease extensively with the stripe-like or the spotted, while there does not exist spatiotemporal pattern formation when the self-pressure is big enough with a weak repulsive tendency. Furthermore, by using the global bifurcation theory, it is derived that a branch of nonconstant solutions can bifurcate from the positive constant solution when the repulsive tendency is relatively big.