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A Lyapunov function and global properties for \(SIR\) and \(SEIR\) epidemiological models with nonlinear incidence. (English) Zbl 1062.92061
Summary: Explicit Lyapunov functions for SIR and SEIR compartmental epidemic models with nonlinear incidence of the form \(\beta I^pS^q\) for the case \(p\leq 1\) are constructed. Global stability of the models is thereby established.

MSC:
92D30 Epidemiology
34D20 Stability of solutions to ordinary differential equations
34D23 Global stability of solutions to ordinary differential equations
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