Asymmetry and multiple endemic equilibria in a model for HIV transmission in a heterosexual population

The difference in transmissibility of HIV between heterosexual males and females in specific social contexts is known to play an important role in determining the form of HIV/AIDS epidemics across the globe. A fundamental constraint here is the conservation of the number of new partnerships formed between the sexes. We examine the impact of general asymmetry in sexual behaviour between the sexes, subject to this group contact constraint, on the transient and long term behaviour of a HIV epidemic. A homogeneously mixing heterosexual population is modelled in which males and females differ only in their infectivity rates (average sexual risk per infected partner) and sexual activity rates (the mean number of sexual partners per unit time for a typical individual). A dominance form of sexual activity rates yields conditions for the existence of multiple endemic equilibria for R0. the reproductive number, just less than unity. We interpret this as a resilience of the disease persistence for R0 > 1, which requires significant differences between the sexesʹ transmissibility. Model simulations in this region of the parameter space show that the time scale and shape of an epidemic curve can be considerably altered. Sexual activity rates modelling the proportions of sexually active groups are also used to address the role of asymmetry. We discuss the consequences of our results for management of the disease.