Concentration profile of endemic equilibrium of a reaction–diffusion–advection SIS epidemic model

Kousuke Kuto, Hiroshi Matsuzawa, Rui Peng

Research output: Contribution to journalArticlepeer-review

26 Citations (Scopus)

Abstract

Cui and Lou (J Differ Equ 261:3305–3343, 2016) proposed a reaction–diffusion–advection SIS epidemic model in heterogeneous environments, and derived interesting results on the stability of the DFE (disease-free equilibrium) and the existence of EE (endemic equilibrium) under various conditions. In this paper, we are interested in the asymptotic profile of the EE (when it exists) in the three cases: (i) large advection; (ii) small diffusion of the susceptible population; (iii) small diffusion of the infected population. We prove that in case (i), the density of both the susceptible and infected populations concentrates only at the downstream behaving like a delta function; in case (ii), the density of the susceptible concentrates only at the downstream behaving like a delta function and the density of the infected vanishes on the entire habitat, and in case (iii), the density of the susceptible is positive while the density of the infected vanishes on the entire habitat. Our results show that in case (ii) and case (iii), the asymptotic profile is essentially different from that in the situation where no advection is present. As a consequence, we can conclude that the impact of advection on the spatial distribution of population densities is significant.

Original languageEnglish
Article number112
JournalCalculus of Variations and Partial Differential Equations
Volume56
Issue number4
DOIs
Publication statusPublished - 2017 Aug 1
Externally publishedYes

Keywords

  • 35B32
  • 35J55
  • 35K57
  • 92D25

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Concentration profile of endemic equilibrium of a reaction–diffusion–advection SIS epidemic model'. Together they form a unique fingerprint.

Cite this