Analysis on a diffusive SIS epidemic model with logistic source

Analysis on a diffusive SIS epidemic model with logistic source In this paper, we are concerned with an SIS epidemic reaction–diffusion model with logistic source in spatially heterogeneous environment. We first discuss some basic properties of the parabolic system, including the uniform upper bound of solutions and global stability of the endemic equilibrium when spatial environment is homogeneous. Our primary focus is to determine the asymptotic profile of endemic equilibria (when exist) if the diffusion (migration) rate of the susceptible or infected population is small or large. Combined with the results of Li et al. (J Differ Equ 262:885–913, 2017) where the case of linear source is studied, our analysis suggests that varying total population enhances persistence of infectious disease. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Zeitschrift für angewandte Mathematik und Physik Springer Journals

Analysis on a diffusive SIS epidemic model with logistic source

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Publisher
Springer International Publishing
Copyright
Copyright © 2017 by Springer International Publishing AG
Subject
Engineering; Theoretical and Applied Mechanics; Mathematical Methods in Physics
ISSN
0044-2275
eISSN
1420-9039
D.O.I.
10.1007/s00033-017-0845-1
Publisher site
See Article on Publisher Site

Abstract

In this paper, we are concerned with an SIS epidemic reaction–diffusion model with logistic source in spatially heterogeneous environment. We first discuss some basic properties of the parabolic system, including the uniform upper bound of solutions and global stability of the endemic equilibrium when spatial environment is homogeneous. Our primary focus is to determine the asymptotic profile of endemic equilibria (when exist) if the diffusion (migration) rate of the susceptible or infected population is small or large. Combined with the results of Li et al. (J Differ Equ 262:885–913, 2017) where the case of linear source is studied, our analysis suggests that varying total population enhances persistence of infectious disease.

Journal

Zeitschrift für angewandte Mathematik und PhysikSpringer Journals

Published: Aug 6, 2017

References

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