Zhang, Hui; Xu, Wenxiong; Li, Yingqi Global stability of an SEIR epidemic model with general nonlinear incidence rate. (Chinese. English summary) Zbl 1349.34185 Math. Pract. Theory 45, No. 4, 165-170 (2015). Summary: An SEIR epidemic model with general nonlinear incidence rate \(g(S)h(I)\) is studied. By using the Liapunov function method, it is proved that the disease-free equilibrium \(P_0\) is globally asymptotically stable in \(G\) if \(R_0 \leq 1\) and the disease always dies out eventually. By the Poincaré-Bendixson theory, it is proved that the endemic equilibrium \(P^*\) is globally asymptotically stable in the interior of \(G\) if \(R_0 > 1\), and the disease spreads to the endemic equilibrium. MSC: 34C60 Qualitative investigation and simulation of ordinary differential equation models 34D23 Global stability of solutions to ordinary differential equations 92D30 Epidemiology 34D05 Asymptotic properties of solutions to ordinary differential equations Keywords:nonlinear incidence rate; global asymptotic stability; liapunov function; orbital stability of periodic orbit PDFBibTeX XMLCite \textit{H. Zhang} et al., Math. Pract. Theory 45, No. 4, 165--170 (2015; Zbl 1349.34185)