A SIS reaction-diffusion model with a free boundary condition and nonhomogeneous coefficients

Yizhuo Wang; Shangjiang Guo

doi:10.3934/dcdsb.2018223

Article Contents

2019, Volume 24, Issue 4: 1627-1652. Doi: 10.3934/dcdsb.2018223

This issue Previous Article Nonconstant periodic solutions with any fixed energy for singular Hamiltonian systems Next Article On the finite-time Bhat-Bernstein feedbacks for the strings connected by point mass

A SIS reaction-diffusion model with a free boundary condition and nonhomogeneous coefficients

Yizhuo Wang and
Shangjiang Guo^,

College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, China

^* Corresponding author: S. Guo
^* Corresponding author: S. Guo

Received: January 31, 2018

Early access: June 2018

Published: January 2019

The second author is supported by NSF of China (Grants No. 11671123).

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Abstract

This paper is devoted to a spatial heterogeneous SIS model with the infected group equipped with a free boundary. Our main aim is to determine whether the disease is spreading forever or extinct eventually, and to illustrate, under the nonhomogeneous spatial environment, free boundaries can have a large influence on the infected behavior at the large time. For this purpose, we first introduce a basic reproduction number and then establish a spreading-vanishing dichotomy. Then by investigating the effect of the diffusion rate, initial domain and spreading speed on the asymptotic behavior of the infected group, we establish some sufficient conditions and even necessary and sufficient conditions for disease spreading or vanishing.

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Mathematics Subject Classification: Primary: 35K57, 92D30; Secondary: 35R35, 35J47.

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