Analysis and simulation of a stochastic, discrete-individual model of STD transmission with partnership concurrency

Deterministic differential equation models indicate that partnership concur rency and non-homogeneous mixing patterns play an important role in the spr ead of sexually transmitted infections. Stochastic discrete-individual simu lation studies arrive at similar conclusions, but from a very different mod eling perspective. This paper presents a stochastic discrete-individual inf ection model that helps to unify these two approaches to infection modeling . The model allows for both partnership concurrency, as well as the infecti on, recovery, and reinfection of an individual from repeated contact with a partner, as occurs with many mucosal infections. The simplest form of the model is a network-valued Markov chain, where the network's nodes are indiv iduals and arcs represent partnerships. Connections between the differentia l equation and discrete-individual approaches are constructed with large-po pulation limits that approximate endemic levels and equilibrium probability distributions that describe partnership concurrency. A more general form o f the discrete-individual model that allows for semi-Markovian dynamics and heterogeneous contact patterns is implemented in simulation software. Anal ytical and simulation results indicate that the basic reproduction number R o increases when reinfection is possible, and the epidemic rate of rise and endemic levels are not related by 1 - 1/R-0, when partnerships are not poi nt-time processes. (C) 2000 Elsevier Science Inc. All rights reserved.