title: A generating function approach to HIV transmission with dynamic contact rates.
abstract: The basic reproduction number,R0, is often defined as the average number of infections generated by a newly infected individual in a fully susceptible population. The interpretation, meaning, and derivation ofR0are controversial. However, in the context of mean field models,R0demarcates the epidemic threshold below which the infected population approaches zero in the limit of time. In this manner,R0has been proposed as a method for understanding the relative impact of public health interventions with respect to disease eliminations from a theoretical perspective. The use ofR0is made more complex by both the strong dependency ofR0on the model form and the stochastic nature of transmission. A common assumption in models of HIV transmission that have closed form expressions forR0is that a single individual's behavior is constant over time. In this paper we derive expressions for bothR0and probability of an epidemic in a finite population under the assumption that people periodically change their sexual behavior over time. We illustrate the use of generating functions as a general framework to model the effects of potentially complex assumptions on the number of transmissions generated by a newly infected person in a susceptible population. We find that the relationship between the probability of an epidemic andR0is not straightforward, but, that as the rate of change in sexual behavior increases bothR0and the probability of an epidemic also decrease.
authors.affiliation: Theoretical Biology and Biophysics, Los Alamos National Laboratory, Los Alamos, NM.
authors.forename: E O
authors.initials: EO
authors.lastname: Romero-Severson
authors.affiliation: Department of Physics, University of Michigan, Ann Arbor, MI.
authors.forename: G D
authors.initials: GD
authors.lastname: Meadors
authors.affiliation: Department of Epidemiology, University of Michigan, Ann Arbor, MI.
authors.forename: E M
authors.initials: EM
authors.lastname: Volz
keywords: HIV; R0; branching process; generating functions; transmission model