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 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 individual’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 susceptiblemore »
- Authors:
-
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Univ. of Michigan, Ann Arbor, MI (United States)
- Publication Date:
- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1321729
- Report Number(s):
- LA-UR-13-23019
Journal ID: ISSN 0973-5348
- Grant/Contract Number:
- AC52-06NA25396
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Mathematical Modelling of Natural Phenomena
- Additional Journal Information:
- Journal Volume: 9; Journal Issue: 2; Journal ID: ISSN 0973-5348
- Publisher:
- EDP Sciences
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 60 APPLIED LIFE SCIENCES; 59 BASIC BIOLOGICAL SCIENCES; HIV; transmission model; R0; generating functions; branching process
Citation Formats
Romero-Severson, Ethan O., Meadors, Grant D., and Volz, Erik M. A generating function approach to HIV transmission with dynamic contact rates. United States: N. p., 2014.
Web. doi:10.1051/mmnp/20149208.
Romero-Severson, Ethan O., Meadors, Grant D., & Volz, Erik M. A generating function approach to HIV transmission with dynamic contact rates. United States. https://doi.org/10.1051/mmnp/20149208
Romero-Severson, Ethan O., Meadors, Grant D., and Volz, Erik M. Thu .
"A generating function approach to HIV transmission with dynamic contact rates". United States. https://doi.org/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 = {Romero-Severson, 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 individual’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 = {Thu Apr 24 00:00:00 EDT 2014},
month = {Thu Apr 24 00:00:00 EDT 2014}
}
Web of Science