title: The effect of patterns of infectiousness on epidemic size.
abstract: 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 stochastic infectiousness process for each individual with an almost surely finite integral, or total infectiousness. Individuals also have different contact rates. We show that the distribution of the final epidemic size depends only on the contact rates and the integrated infectiousness. As a particular case, zero infectiousness on an initial time interval corresponds to a period of latency, which does not affect the final epidemic size in general stochastic and deterministic epidemic models, as is well known from the literature.
authors.affiliation: Department of Mathematical Sciences, University of Puerto Rico-RUM. gordillo@math.uprm.edu
authors.forename: Luis F
authors.initials: LF
authors.lastname: Gordillo
authors.forename: Stephen A
authors.initials: SA
authors.lastname: Marion
authors.forename: Priscilla E
authors.initials: PE
authors.lastname: Greenwood
mesh_terms: D000465:Algorithms; D003141:Communicable Diseases / Q000453:epidemiology* / Q000635:transmission; D003198:Computer Simulation; D016358:Contact Tracing; D004196:Disease Outbreaks; D018562:Disease Transmission, Infectious; D015658:HIV Infections / Q000453:epidemiology; D006801:Humans; D015233:Models, Statistical; D009716:Numerical Analysis, Computer-Assisted; D013269:Stochastic Processes