Transmission Probabilities and Reproduction Numbers for Sexually Transmitted Infections with Variable Infectivity: Application to the Spread of HIV Between Low- and High-Activity Populations

Probabilities of transmission and numbers of secondary cases are given for an infection which is transmitted sexually by individuals engaged in multiple partnerships with specified durations and timings. The results applied to the human immunodeficiency virus (HIV) hinge on a function which captures the dependence of the per coital act probability of transmission on the time since disease onset and on the duration of infection at death. Reproduction numbers are derived in a heterogeneous population consisting of low- and high-activity men and women. An expression for the basic reproduction number R-0 of this system sheds light on the role of concurrency, on the timing of the partnerships, and on bridging effects. A high-activity group can cause a significant epidemic outbreak no matter how small the bridging effect, as long as it is not 0. Only if the bridging effect is eliminated altogether can the growth factor in the low- activity group be reduced independently of what happens in the high-activity group. The role of the relationship between client and sex worker and the role of bridging populations in sub-Saharan Africa are assessed.