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2008, 5(3): 429-435. doi: 10.3934/mbe.2008.5.429

The effect of patterns of infectiousness on epidemic size

1. 

Department of Mathematical Sciences, University of Puerto Rico-RUM, Puerto Rico

2. 

Department of Health Care and Epidemiology, University of British Columbia, Canada

3. 

Department of Mathematics and Statistics, Arizona State University, United States

Received  January 2007 Revised  May 2008 Published  June 2008

In the course of an infectious disease in a population, each in fected 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.
Citation: Luis F. Gordillo, Stephen A. Marion, Priscilla E. Greenwood. The effect of patterns of infectiousness on epidemic size. Mathematical Biosciences & Engineering, 2008, 5 (3) : 429-435. doi: 10.3934/mbe.2008.5.429
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