An SIS epidemic reaction–diffusion model with spontaneous infection in a spatially heterogeneous environment. (June 2018)

• Record Type: Journal Article
• Authors: Tong, Yachun; Lei, Chengxia
• Is Part Of: Nonlinear analysis. Volume 41(2018)
• Page Start: 443
• Page End: 460
• Publication Date: 2018-06
• Subjects: SIS epidemic reaction–diffusion model -- Spontaneous infection -- Spatially heterogeneous environment -- Endemic equilibria -- Small/large migration -- Disease persistence; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2017.11.002
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: This paper concerns an SIS epidemic reaction–diffusion model, which includes the possibility for spontaneous infection, in addition to disease transmission. We prove the global asymptotic stability of the unique endemic equilibrium when the spatial environment is homogeneous. When the spatial environment is heterogeneous, we show the existence of endemic equilibria and then analyze their asymptotic profile if the movement (migration) rate of the susceptible or infected population is small or large. Compared to the case that spontaneous infection is ignored, our theoretical study here suggests that spontaneous infection can enhance persistence of infectious disease and therefore gives new insight into disease control and prediction.