Modelling HIV superinfection among men who have sex with men

Superinfection, a phenomenon that an individual infected by one HIV strain is re-infected by the second heterologous HIV strain, occurs in HIV infection. A mathematical model is formulated to examine how superinfection affects transmission dynamics of drug sensitive/resistant strains. Three reproduction numbers are defined: reproduction numbers Rr and Rs for drug-resistant and drug-sensitive strains, respectively, and the invasion reproduction number R (r)s. The disease-free equilibrium always exists and is locally stable when the larger of Rs and Rr is less than one. The drug resistant strain-only equilibrium is locally stable when Rr > 1 and R (r)s < 1. Numerical studies show that as the superinfection coefficient of the sensitive strain increases the system may (1) change to bistable states of disease-free equilibrium and the coexistence state from the stable disease-free equilibrium under no superinfection; (2) experience the stable resistant-strain only equilibrium, the bistable states of resistant-strain only equilibrium and the coexistence state, and the stable coexistence state in turn. This implies that superinfection of the sensitive strain is beneficial for two strains to coexist. While superinfection of the resistant strain makes resistant strain more likely to be sustained. The findings suggest that superinfection induces the complicated dynamics, and brings more difficulties in antiretroviral therapy.