期刊
JOURNAL OF DIFFERENTIAL EQUATIONS
卷 262, 期 2, 页码 885-913出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2016.09.044
关键词
SIS epidemic reaction-diffusion mode with linear source; Endemic equilibria; Spatially heterogeneous environment; Persistence/extinction; Small/large diffusion; Asymptotic profile
类别
资金
- China Postdoctoral Science Foundation [2016M590335]
- NSF of China [11671144, 11671175, 11271167, 11571200]
- Natural Science Fund for Distinguished Young Scholars of Jiangsu Province [BK20130002]
- Priority Academic Program Development of Jiangsu Higher Education Institutions
- Qing Lan Project of Jiangsu Province
- Ministry of Science and Technology, Taiwan, Republic of China
This paper performs qualitative analysis on an SIS epidemic reaction-diffusion system with a linear source in spatially heterogeneous environment. The main feature of our model lies in that its total population number varies, compared to its counterpart proposed by Allen et al. [2]. The uniform bounds of solutions are derived, based on which, the threshold dynamics in terms of the basic reproduction number is established and the global stability of the unique endemic equilibrium is discussed when spatial environment is homogeneous. In particular, the asymptotic profile of endemic equilibria is determined if the diffusion rate of the susceptible or infected population is small or large. The theoretical results show that a varying total population can enhance persistence of infectious disease, and therefore the disease becomes more threatening and harder to control (C) 2016 Elsevier Inc. All rights reserved.
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