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Global properties of SIR and SEIR epidemic models with multiple parallel infectious stages. (English) Zbl 1169.92041
Summary: We consider global properties of compartment SIR and SEIR models of infectious diseases, where there are several parallel infective stages. For instance, such a situation may arise if a fraction of the infected are detected and treated, while the rest of the infected remains undetected and untreated. We assume that the horizontal transmission is governed by the standard bilinear incidence rate. The direct Lyapunov method enables us to prove that the considered models are globally stable: There is always a globally asymptotically stable equilibrium state. Depending on the value of the basic reproduction number R 0 , this state can be either endemic (R 0 >1), or infection-free (R 0 1).
MSC:
92D30Epidemiology
34D23Global stability of ODE
34D20Stability of ODE
37N25Dynamical systems in biology
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