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Stability analysis of a delayed SIR epidemic model with stage structure and nonlinear incidence. (English) Zbl 1183.34130
Summary: We investigate the stability of an SIR epidemic model with stage structure and time delay. By analyzing the eigenvalues of the corresponding characteristic equation, the local stability of each feasible equilibrium of the model is established. By using comparison arguments, we prove that if the basic reproduction number is less than 1, the disease free equilibrium is globally asymptotically stable. When the basic reproduction number is greater than 1, sufficient conditions are derived for the global stability of an endemic equilibrium of the model. Numerical simulations are carried out to illustrate the theoretical results.
MSC:
34K60Qualitative investigation and simulation of models
34K20Stability theory of functional-differential equations
34K21Stationary solutions of functional-differential equations
92D30Epidemiology