Analysis of sexually transmitted disease spreading in heterosexual and homosexual populations

Sexually transmitted diseases can pose major health problems so scientists and health agencies are very concerned about the spread of these diseases. Sexually transmitted diseases spread through a network of contacts created by the formation of sexual partnerships. In the paper, the spreading of sexually transmitted diseases on bipartite scale-free graphs, representing heterosexual and homosexual contact networks, is considered. We propose an SIS model on sexual contact networks. We analytically derive the expression for the epidemic threshold and its dependence with the ratio of female and male in finite populations. It is shown that if the basic reproduction number R0R0 is less than 1 then the disease-free equilibrium is globally asymptotically stable; if R0>1R0>1 then the disease-free equilibrium is unstable and there is a unique endemic equilibrium, which asymptotically attracts all nontrivial solutions. These theoretical results are supported by numerical simulations. We also carry out some sensitivity analysis of the basic reproduction number R0R0 in terms of various model parameters.