Modelling HIV superinfection among men who have sex with men

Superinfection, a phenomenon that an individual infected by one HIVstrain is re-infected by the second heterologous HIV strain, occursin HIV infection. A mathematical model is formulated to examine howsuperinfection affects transmission dynamics of drugsensitive/resistant strains. Three reproduction numbers are defined:reproduction numbers $R_r$ and $R_s$ for drug-resistant anddrug-sensitive strains, respectively, and the invasion reproductionnumber $R_s^r$. The disease-free equilibrium always exists and islocally stable when the larger of $R_s$ and $R_r$ is less thanone. The drug resistant strain-only equilibrium is locally stable when$R_r>1$ and $R_s^r<1$. Numerical studies show that as thesuperinfection coefficient of the sensitive strain increases thesystem may (1) change to bistable states of disease-free equilibriumand the coexistence state from the stable disease-freeequilibrium under no superinfection; (2) experience the stable resistant-strain onlyequilibrium, the bistable states of resistant-strain onlyequilibrium and the coexistence state, and the stable coexistencestate in turn. This implies that superinfection of the sensitive strain isbeneficial for two strains to coexist. While superinfection ofthe resistant strain makes resistant strain more likely to be sustained.The findings suggest that superinfection induces the complicateddynamics, and brings more difficulties in antiretroviral therapy.