An edge-based SIR model for sexually transmitted diseases on the contact network.

Sexually transmitted diseases, which are infections through sexual contact, pose severe public health threat nowadays. In this paper, we develop a novel model for such diseases on a bipartite random contact network. Our model is precise with arbitrary initial conditions, which makes it suitable to study preventative vaccination strategies. We derive the reproduction number and show that R0 =1 is the disease threshold. An implicit formula for the final epidemic size is also derived, and we show that the formula gives a unique positive final epidemic size when the reproduction number is larger than unity. We find that the final size in either sex is heavily influenced by the degree distribution of the opposite sex.