Sounvoravong, Bounsanong; Guo, Shangjiang; Bai, Yuzhen Bifurcation and stability of a diffusive SIRS epidemic model with time delay. (English) Zbl 1418.35159 Electron. J. Differ. Equ. 2019, Paper No. 45, 16 p. (2019). 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. Cited in 5 Documents MSC: 35J60 Nonlinear elliptic equations 35K57 Reaction-diffusion equations 92D30 Epidemiology Keywords:reaction-diffusion system; SIRS epidemic model PDFBibTeX XMLCite \textit{B. Sounvoravong} et al., Electron. J. Differ. Equ. 2019, Paper No. 45, 16 p. (2019; Zbl 1418.35159) Full Text: Link