Wang, Zhenguo; Liu, Guirong Epidemic spreading of an SEIRS model based on homogeneous random mixing and heterogeneous networks. (Chinese. English summary) Zbl 1363.92061 Math. Pract. Theory 46, No. 6, 285-290 (2016). Summary: In this paper, we investigate an SEIRS epidemic model based on homogeneous and heterogeneous networks. The existence of endemic equilibrium is determined by the basic reproduction number \(R_0 =\frac{(1-\eta)A\lambda+\eta\beta}{\mu}\). The results show that if \(R_0 < 1\), then the disease free equilibrium \((1,0,0,0)\) is locally asymptotically stable. Otherwise, if \(R_0 > 1\), then the disease free equilibrium is unstable, and there exists a unique endemic equilibrium which is uniformly persistent in the time limit. Our simulation results verify the theory. MSC: 92D30 Epidemiology 34D20 Stability of solutions to ordinary differential equations Keywords:SEIRS epidemic model; heterogeneous networks; basic reproduction number; stability; uniform persistence PDFBibTeX XMLCite \textit{Z. Wang} and \textit{G. Liu}, Math. Pract. Theory 46, No. 6, 285--290 (2016; Zbl 1363.92061)