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This paper studies the distribution function of the time of extinction of asubcritical epidemic, when a large enough proportion of the population has beenimmunized and/or the infectivity of the infectious individuals has beenreduced, so that the effective reproduction number is less than one. We do thatfor a SIR/SEIR model, where infectious individuals have an infection agedependent infectivity, as in the model introduced in the 1927 seminal paper ofKermack and McKendrick. Our main conclusion is that simplifying the model as anODE SIR model, as it is largely done in the epidemics literature, introduces abiais toward shorter extinction time.

Extinction time of an epidemic with infection age dependent infectivity