×

Epidemic spreading of an SEIRS model based on homogeneous random mixing and heterogeneous networks. (Chinese. English summary) Zbl 1363.92061

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
PDFBibTeX XMLCite