SEIR epidemiological model with varying infectivity and infinite delay

Abstract

A new SEIR model with distributed infinite delay is derived whenthe infectivity depends on the age of infection. The basic reproduction numberR0, which is a threshold quantity for the stability of equilibria, is calculated.If $R_0$ 1, then an endemicequilibrium appears which is locally asymptotically stable. Applying a perma-nence theorem for infinite dimensional systems, we obtain that the disease isalways present when $R_0$ > 1.

Keywords

• mathematical epidemiology
• permanence.
• stability
• seir model
• infinite delay