## Stability analysis of a disease resistance SEIRS model with nonlinear incidence rate.(English)Zbl 1445.92273

Summary: In this paper, we study a new SEIRS epidemic model describing nonlinear incidence with a more general form and the transmission of influenza virus with disease resistance. The basic reproductive number $$\operatorname{Re}_{0}$$ is obtained by using the method of next generating matrix. If $$\operatorname{Re}_{0}<1$$, the disease-free equilibrium is globally asymptotically stable, and if $$\operatorname{Re}_{0}>1$$, by using the geometric method, we obtain some sufficient conditions for global stability of the unique endemic equilibrium. Finally, numerical simulations are provided to support our theoretical results.

### MSC:

 92D30 Epidemiology 34D20 Stability of solutions to ordinary differential equations 34C60 Qualitative investigation and simulation of ordinary differential equation models 92D25 Population dynamics (general) 34D23 Global stability of solutions to ordinary differential equations
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