A new design of stochastic partnership models for epidemics of sexually transmitted diseases with stages

A problem of importance in modelling epidemics of sexually transmitted diseases is the development of mathematical structures accommodating sexual and other contacts among members of a population. Because these models may be complex, it is often necessary to use computer intensive methods in their analysis, which raises questions on the design of computer models. In this paper a new approach to designing models sexual contacts is presented within the context of a stochastic model accommodating the formation and dissolution of partnerships in heterosexual populations. Emphasis will be placed on the development of algorithms with a view towards developing software to implement computer intensive methods. Unlike previous formulations, rather than using rejection methods in Monte Carlo simulations to impose necessary constraints on random functions describing partnership formation, in the new formulation all constraints are satisfied with probability one.