Realized generation times: contraction and impact of infectious period, reproduction number and population size release_6o5kzoadnnh3bp475mu3wemrhy

Abstract

One of the key characteristics of the transmission dynamics of infectious diseases is the generation time which refers to the time interval between the infection of a secondary case and the infection of its infector. The generation time distribution together with the reproduction number determines the rate at which an infection spreads in a population. When defining the generation time distribution at a calendar time t two definitions are plausible according whether we regard t as the infection time of the infector or the infection time of the infectee. The resulting measurements are respectively called forward generation time and backward generation time. It has been observed that the average forward generation time contracts around the peak of an epidemic. This contraction effect has previously been attributed to either competition among potential infectors or depletion of susceptibles in the population. The first explanation requires many infectives for contraction to occur whereas the latter explanation suggests that contraction occurs even when there are few infectives. With a simulation study we show that both competition and depletion cause the mean forward generation time to contract. Our results also reveal that the distribution of the infectious period and the reproduction number have a strong effect on the size and timing of the contraction, as well as on the mean value of the generation time in both forward and backward scheme.
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