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Global properties of a delayed SIR epidemic model with multiple parallel infectious stages. (English) Zbl 1260.92109
Summary: We study the global properties of an SIR epidemic model with distributed delays, when there are several parallel infective stages, and some of the infected cells are detected and treated, while others remain undetected and untreated. The model is analyzed by determining a basic reproduction number $$R_0$$, and by using Lyapunov functionals. We prove that the infection-free equilibrium $$E^0$$ of our system is globally asymptotically attractive when $$R_0 \leq 1$$, and that the unique infected equilibrium $$E^\ast$$ of the system exists and it is globally asymptotically attractive when $$R_0 > 1$$.

MSC:
 92D30 Epidemiology 37N25 Dynamical systems in biology 34C60 Qualitative investigation and simulation of ordinary differential equation models
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