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A Generating Function Approach to HIV Transmission with DynamicContact Rates

Published online by Cambridge University Press:  24 April 2014

E.O. Romero-Severson ,
G.D. Meadors  and
E.M. Volz
E.O. Romero-Severson*
Affiliation:
Theoretical Biology and Biophysics, Los Alamos National Laboratory, Los Alamos, NM
G.D. Meadors
Affiliation:
Department of Physics, University of Michigan, Ann Arbor, MI
E.M. Volz
Affiliation:
Department of Epidemiology, University of Michigan, Ann Arbor, MI
*
⋆Corresponding author. E-mail: [email protected]
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Abstract

The basic reproduction number, R0, is often defined as the averagenumber of infections generated by a newly infected individual in a fully susceptiblepopulation. The interpretation, meaning, and derivation of R0 arecontroversial. However, in the context of mean field models, R0 demarcatesthe epidemic threshold below which the infected population approaches zero in the limit oftime. In this manner, R0 has been proposed as a method forunderstanding the relative impact of public health interventions with respect to diseaseeliminations from a theoretical perspective. The use of R0 is made morecomplex by both the strong dependency of R0 on the model form and the stochasticnature of transmission. A common assumption in models of HIV transmission that have closedform expressions for R0 is that a single individual’sbehavior is constant over time. In this paper we derive expressions for bothR0 and probability of an epidemic in afinite population under the assumption that people periodically change their sexualbehavior over time. We illustrate the use of generating functions as a general frameworkto model the effects of potentially complex assumptions on the number of transmissionsgenerated by a newly infected person in a susceptible population. We find that therelationship between the probability of an epidemic and R0 is notstraightforward, but, that as the rate of change in sexual behavior increases bothR0 and the probability of an epidemic alsodecrease.

Keywords

HIVtransmission modelR0generating functionsbranching process
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 9 , Issue 2: Epidemics models on networks , 2014 , pp. 121 - 135
Copyright
© EDP Sciences, 2014

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