A stochastic model for the spread of a sexually transmitted disease which results in a scale-free network

A stochastic model for the spread of a sexually transmitted disease (STD) is presented. To reflect varying degrees of promiscuity among individuals it is assumed that the infectivity of any infected individual is proportional to the number of previous contacts the individual has had with other infected individuals. In both the simple single-sex model and in the more complex two-sex model, the tree graphs of the infection exhibit scale-free network behaviour (i.e. power-law behaviour in the upper tail of the degree distribution). The distributions of the size of the infection and of the ring number (distance from the original source of the infection) are determined.