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Title: 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 individual’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 » by a newly infected person in a susceptible population. In conclusion, we find that the relationship between the probability of an epidemic and R 0 is not straightforward, but, that as the rate of change in sexual behavior increases both R 0 and the probability of an epidemic also decrease.« less
 [1] ;  [2] ;  [2]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  2. Univ. of Michigan, Ann Arbor, MI (United States)
Publication Date:
OSTI Identifier:
Report Number(s):
Journal ID: ISSN 0973-5348
Grant/Contract Number:
Accepted Manuscript
Journal Name:
Mathematical Modelling of Natural Phenomena
Additional Journal Information:
Journal Volume: 9; Journal Issue: 2; Journal ID: ISSN 0973-5348
EDP Sciences
Research Org:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org:
Country of Publication:
United States
60 APPLIED LIFE SCIENCES; 59 BASIC BIOLOGICAL SCIENCES; HIV; transmission model; R0; generating functions; branching process