Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

On the basic reproduction number $R_0$ in sexual activity models for HIV/AIDS epidemics: Example from Yunnan, China

1. Institut de Recherche pour le Développement (I.R.D.), 32 avenue Henri Varagnat, 93143 Bondy cedex
2. College of Mathematics and System Sciences, Xinjiang University, 14 Shengli Road, Urumqi, 830046
3. National Center for Women and Children's Health, Department of Information Management, 13 Dong Tu Cheng Street, Chang Yang District, Beijing, 100013

Heterogeneity in sexual behavior is known to play an important role in the spread of HIV. In 1986, a mathematical model based on ordinary differential equations was introduced to take into account the distribution of sexual activity. Assuming proportionate mixing, it was shown that the basic reproduction number $R_0$ determining the epidemic threshold was proportional to $M+V/M$, where $M$ is the mean and $V$ the variance of the distribution. In the present paper, we notice that this theoretical distribution is different from the one obtained in behavioral surveys for the number of sexual partnerships over a period of length $\tau$. The latter is a ''mixed Poisson distribution'' whose mean $m$ and variance $v$ are such that $M=m/\tau$ and $V=(v-m)/\tau^2$. So $M+V/M=(m+v/m-1)/\tau$. This way, we improve the link between theory and data for sexual activity models of HIV/AIDS epidemics. As an example, we consider data concerning sex workers and their clients in Yunnan, China, and find an upper bound for the geometric mean of the transmission probabilities per partnership in this context.
  Article Metrics

Keywords basic reproduction number; HIV; mixed Poisson distribution.

Citation: Nicolas Bacaër, Xamxinur Abdurahman, Jianli Ye, Pierre Auger. On the basic reproduction number $R_0$ in sexual activity models for HIV/AIDS epidemics: Example from Yunnan, China. Mathematical Biosciences and Engineering, 2007, 4(4): 595-607. doi: 10.3934/mbe.2007.4.595


This article has been cited by

  • 1. Mustafa Al-Zoughool, David Cottrell, Susie Elsaadany, Noel Murray, Tamer Oraby, Robert Smith, Daniel Krewski, Mathematical Models for Estimating the Risks of Bovine Spongiform Encephalopathy (BSE), Journal of Toxicology and Environmental Health, Part B, 2015, 18, 2, 71, 10.1080/10937404.2015.1036963
  • 2. José L. Herrera-Diestra, Lauren Ancel Meyers, Yang Yang, Local risk perception enhances epidemic control, PLOS ONE, 2019, 14, 12, e0225576, 10.1371/journal.pone.0225576

Reader Comments

your name: *   your email: *  

Copyright Info: 2007, , licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved