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Bifurcation and stability of a diffusive SIRS epidemic model with time delay. (English) Zbl 1418.35159

Summary: In this article, we study a reaction-diffusion system for a SIRS epidemic model with time delay and nonlinear incidence rate. On the one hand, we study the existence and stability of the disease-free equilibrium, endemic equilibria and Hopf bifurcation, by analyzing the characteristic equations. On the other hand, we establish formulas determining the direction and stability of the bifurcating periodic solutions.

MSC:

35J60 Nonlinear elliptic equations
35K57 Reaction-diffusion equations
92D30 Epidemiology
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