Journal
SIAM JOURNAL ON APPLIED MATHEMATICS
Volume 78, Issue 4, Pages 2129-2153Publisher
SIAM PUBLICATIONS
DOI: 10.1137/18M1167863
Keywords
SIS epidemic reaction-diffusion model; mass action infection mechanism; basic reproduction number; endemic equilibria; small diffusion; asymptotic profile; persistence/extinction
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Funding
- NSF of China [11601170, 11671143, 11671144, 11671175, 11571200]
- Priority Academic Program Development of Jiangsu Higher Education Institutions
- Top-notch Academic Programs Project of Jiangsu Higher Education Institutions [PPZY2015A013]
- Qing Lan Project of Jiangsu Province
- Hong Kong RGC GRF grant [PolyU 153298/16P]
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In the present paper, we are concerned with a susceptible-infected-susceptible epidemic reaction-diffusion model governed by a mass action infection mechanism and linear birth-death growth with no flux boundary condition. By performing qualitative analysis, we study the stability of the disease-free equilibrium, uniform persistence property in terms of the basic reproduction number and the global stability of the endemic equilibrium in a homogeneous environment, and investigate the asymptotic profile of endemic equilibria (when they exist) in a heterogeneous environment when the movement rate of the susceptible and infected populations is small. Our results, together with those in previous works on three other closely related modeling systems, suggest that factors such as infection mechanism, variation of total population, and population movement play vital but subtle roles in the transmission dynamics of diseases and hence provide useful insights into the strategies designed for disease control and prevention.
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