  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.
