Interplay between HIV/AIDS Epidemics and Demographic Structures Based on   Sexual Contact Networks
  In this article, we propose a network spread model for HIV epidemics, wherein each individual is represented by a node of the transmission network and the edges are the connections between individuals along which the infection may spread. The sexual activity of each individual, measured by its degree, is not homogeneous but obeys a power-law distribution. Due to the heterogeneity of activity, the infection can persistently exist at a very low prevalence, which has been observed in real data but can not be illuminated by previous models with homogeneous mixing hypothesis. Furthermore, the model displays a clear picture of hierarchical spread: In the early stage the infection is adhered to these high-risk persons, and then, diffuses toward low-risk population. The prediction results show that the development of epidemics can be roughly categorized into three patterns for different countries, and the pattern of a given country is mainly determined by the average sex-activity and transmission probability per sexual partner. In most cases, the effect of HIV epidemics on demographic structure is very small. However, for some extremely countries, like Botswana, the number of sex-active people can be depressed to nearly a half by AIDS. 
Wen-Jie Bai, Tao Zhou, and Bing-Hong Wang