The effect of patterns of infectiousness on epidemic size - Luis F. Gordillo; Stephen A. Marion; Priscilla E. Greenwood (Mathematical Biosciences and Engineering)
In the course of an infectious disease in a population, each infected individual presents a different pattern of progress through the disease,producing a corresponding pattern of infectiousness. We postulate a stochasticinfectiousness process for each individual with an almost surely finite integral,or total infectiousness. Individuals also have different contact rates. We showthat the distribution of the final epidemic size depends only on the contact ratesand the integrated infectiousness. As a particular case, zero infectiousness onan initial time interval corresponds to a period of latency, which does not affectthe final epidemic size in general stochastic and deterministic epidemic models,as is well known from the literature.