Sexually Transmitted Diseases on Bipartite Graph

We study the susceptible--infected--susceptible (SIS) epidemic model on bipartite graph. According to the difference of sex conception in western and oriental nations, we construct the Barabási Albert--Barabási Albert (BA-BA) model and Barabási-Albert Homogeneity (BA-HO) model for sexually transmitted diseases (STDs). Applying the rate equation approach, the positive equilibria of both models are given analytically. We find that the ratio between infected females and infected males is distinctly different in both models and the infected density in the BA-HO model is much less than that in the BA-BA model. These results explain that the countries with small ratio have less infected density than those with large ratio. Our numerical simulations verify these theoretical results.