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Global bifurcation of the reaction–diffusion epidemic model with advection.

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Title: Global bifurcation of the reaction–diffusion epidemic model with advection.
Authors: Li, Chenglin1 (AUTHOR) chenglinli988@163.com
Source: Zeitschrift für Angewandte Mathematik und Physik (ZAMP). Mar2026, Vol. 77 Issue 3, p1-19. 19p.
Subjects: Bifurcation theory, Epidemiological models, Neumann boundary conditions, Spatiotemporal processes, Transport equation, Endemic diseases, Dispersal (Ecology)
Abstract: 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 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. [ABSTRACT FROM AUTHOR]
Copyright of Zeitschrift für Angewandte Mathematik und Physik (ZAMP) is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Global bifurcation of the reaction–diffusion epidemic model with advection.
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  Data: <searchLink fieldCode="AR" term="%22Li%2C+Chenglin%22">Li, Chenglin</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> chenglinli988@163.com</i>
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  Data: <searchLink fieldCode="DE" term="%22Bifurcation+theory%22">Bifurcation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Epidemiological+models%22">Epidemiological models</searchLink><br /><searchLink fieldCode="DE" term="%22Neumann+boundary+conditions%22">Neumann boundary conditions</searchLink><br /><searchLink fieldCode="DE" term="%22Spatiotemporal+processes%22">Spatiotemporal processes</searchLink><br /><searchLink fieldCode="DE" term="%22Transport+equation%22">Transport equation</searchLink><br /><searchLink fieldCode="DE" term="%22Endemic+diseases%22">Endemic diseases</searchLink><br /><searchLink fieldCode="DE" term="%22Dispersal+%28Ecology%29%22">Dispersal (Ecology)</searchLink>
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  Label: Abstract
  Group: Ab
  Data: 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 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. [ABSTRACT FROM AUTHOR]
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  Group: Ab
  Data: <i>Copyright of Zeitschrift für Angewandte Mathematik und Physik (ZAMP) is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.1007/s00033-026-02748-2
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      – Code: eng
        Text: English
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        PageCount: 19
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    Subjects:
      – SubjectFull: Bifurcation theory
        Type: general
      – SubjectFull: Epidemiological models
        Type: general
      – SubjectFull: Neumann boundary conditions
        Type: general
      – SubjectFull: Spatiotemporal processes
        Type: general
      – SubjectFull: Transport equation
        Type: general
      – SubjectFull: Endemic diseases
        Type: general
      – SubjectFull: Dispersal (Ecology)
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      – TitleFull: Global bifurcation of the reaction–diffusion epidemic model with advection.
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              M: 03
              Text: Mar2026
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              Y: 2026
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