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SEIR epidemiological model with varying infectivity and infinite delay. (English) Zbl 1165.34421
Summary: A new SEIR model with distributed infinite delay is derived when the infectivity depends on the age of infection. The basic reproduction number 0 , which is a threshold quantity for the stability of equilibria, is calculated. If 0 <1, then the disease-free equilibrium is globally asymptotically stable and this is the only equilibrium. On the contrary, if 0 >1, then an endemic equilibrium appears which is locally asymptotically stable. Applying a permanence theorem for infinite dimensional systems, we obtain that the disease is always present when 0 >1.

MSC:
34K60Qualitative investigation and simulation of models
92D30Epidemiology
34K20Stability theory of functional-differential equations
34K25Asymptotic theory of functional-differential equations