A generating function approach to HIV transmission with dynamic contact rates
The basic reproduction number, R _{0}, 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 of R _{0} are controversial. However, in the context of mean field models, R _{0} demarcates the epidemic threshold below which the infected population approaches zero in the limit of time. In this manner, R _{0} has 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 of R _{0} is made more complex by both the strong dependency of R _{0} on the model form and the stochastic nature of transmission. A common assumption in models of HIV transmission that have closed form expressions for R _{0} is that a single individualâ€™s behavior is constant over time. For this research, we derive expressions for both R _{0} and 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 generatedmore »
 Authors:

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 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Univ. of Michigan, Ann Arbor, MI (United States)
 Publication Date:
 Report Number(s):
 LAUR1323019
Journal ID: ISSN 09735348
 Grant/Contract Number:
 AC5206NA25396
 Type:
 Accepted Manuscript
 Journal Name:
 Mathematical Modelling of Natural Phenomena
 Additional Journal Information:
 Journal Volume: 9; Journal Issue: 2; Journal ID: ISSN 09735348
 Publisher:
 EDP Sciences
 Research Org:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 60 APPLIED LIFE SCIENCES; 59 BASIC BIOLOGICAL SCIENCES; HIV; transmission model; R0; generating functions; branching process
 OSTI Identifier:
 1321729
RomeroSeverson, Ethan O., Meadors, Grant D., and Volz, Erik M.. A generating function approach to HIV transmission with dynamic contact rates. United States: N. p.,
Web. doi:10.1051/mmnp/20149208.
RomeroSeverson, Ethan O., Meadors, Grant D., & Volz, Erik M.. A generating function approach to HIV transmission with dynamic contact rates. United States. doi:10.1051/mmnp/20149208.
RomeroSeverson, Ethan O., Meadors, Grant D., and Volz, Erik M.. 2014.
"A generating function approach to HIV transmission with dynamic contact rates". United States.
doi:10.1051/mmnp/20149208. https://www.osti.gov/servlets/purl/1321729.
@article{osti_1321729,
title = {A generating function approach to HIV transmission with dynamic contact rates},
author = {RomeroSeverson, Ethan O. and Meadors, Grant D. and Volz, Erik M.},
abstractNote = {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 of R0 are controversial. However, in the context of mean field models, R0 demarcates the epidemic threshold below which the infected population approaches zero in the limit of time. In this manner, R0 has 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 of R0 is made more complex by both the strong dependency of R0 on the model form and the stochastic nature of transmission. A common assumption in models of HIV transmission that have closed form expressions for R0 is that a single individualâ€™s behavior is constant over time. For this research, we derive expressions for both R0 and 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. In conclusion, we find that the relationship between the probability of an epidemic and R0 is not straightforward, but, that as the rate of change in sexual behavior increases both R0 and the probability of an epidemic also decrease.},
doi = {10.1051/mmnp/20149208},
journal = {Mathematical Modelling of Natural Phenomena},
number = 2,
volume = 9,
place = {United States},
year = {2014},
month = {4}
}