Stationary patterns of a cross-diffusion epidemic model. (English) Zbl 1470.92284

Cai, Yongli; Chi, Dongxuan; Liu, Wenbin; Wang, Weiming

Abstr. Appl. Anal. 2013, Article ID 852698, 10 p. (2013).

Summary: We investigate the complex dynamics of cross-diffusion \(S I\) epidemic model. We first give the conditions of the local and global stability of the nonnegative constant steady states, which indicates that the basic reproduction number determines whether there is an endemic outbreak or not. Furthermore, we prove the existence and nonexistence of the positive nonconstant steady states, which guarantees the existence of the stationary patterns.

MSC:

92D30	Epidemiology
35B35	Stability in context of PDEs
35K51	Initial-boundary value problems for second-order parabolic systems
35K57	Reaction-diffusion equations

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