SEIR epidemiological model with varying infectivity and infinite delay

Röst, Gergely (2008) SEIR epidemiological model with varying infectivity and infinite delay. Mathematical Biosciences and Engineering, 5 (2). pp. 389-402. ISSN 1547-1063 (print), 1551-0018 (online)

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Abstract

A new SEIR model with distributed infinite delay is derived when the infectivity depends on the age of infection. The basic reproduction number R-0, which is a threshold quantity for the stability of equilibria, is calculated. If R-0 < 1, then the disease-free equilibrium is globally asymptotically stable and this is the only equilibrium. On the contrary, if R-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 R-0 > 1.

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