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Global analysis on delay epidemiological dynamic models with nonlinear incidence. (English) Zbl 1230.92048
Summary: We derive and study the classical SIR, SIS, SEIR and SEI models of epidemiological dynamics with time delays and a general incidence rate. By constructing Lyapunov functionals, the global asymptotic stability of the disease-free equilibrium and the endemic equilibrium is shown. This analysis extends and develops further our previous results and can be applied to the other biological dynamics, including such as single species population delay models and chemostat models with delay response.

MSC:
92D30Epidemiology
34K20Stability theory of functional-differential equations
34D23Global stability of ODE
34K60Qualitative investigation and simulation of models
References:
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