The effect of patterns of infectiousness on epidemic size
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Department of Mathematical Sciences, University of Puerto Rico-RUM
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2.
Department of Health Care and Epidemiology, University of British Columbia
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3.
Department of Mathematics and Statistics, Arizona State University
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Received:
01 January 2007
Accepted:
29 June 2018
Published:
01 June 2008
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MSC :
Primary: 92D30, Secondary: 93A30.
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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[J]. Mathematical Biosciences and Engineering, 2008, 5(3): 429-435. doi: 10.3934/mbe.2008.5.429
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Abstract
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.
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