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

Kousuke Kuto, Hiroshi Matsuzawa, Rui Peng*

*この研究の対応する著者

研究成果: Article査読

51 被引用数 (Scopus)

抄録

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.

本文言語English
論文番号112
ジャーナルCalculus of Variations and Partial Differential Equations
56
4
DOI
出版ステータスPublished - 2017 8月 1
外部発表はい

ASJC Scopus subject areas

  • 分析
  • 応用数学

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