Globally, it is estimated that of the 36.7 million people infected with human immunodeficiency virus (HIV), 6.3% are coinfected with hepatitis C virus (HCV). Coinfection with HIV reduces the chance of HCV spontaneous clearance. In this work, we formulated and analysed a deterministic model to study the HIV and HCV coinfection dynamics in absence of therapy. Due to chronic stage of HCV infection being long, asymptomatic, and infectious, our model formulation was based on the splitting of the chronic stage into the following: before onset of cirrhosis and its complications and after onset of cirrhosis. We computed the basic reproduction numbers using the next generation matrix method. We performed numerical simulations to support the analytical results. We carried out sensitivity analysis to determine the relative importance of the different parameters influencing the HIV-HCV coinfection dynamics. The findings reveal that, in the long run, there is a substantial number of individuals coinfected with HIV and latent HCV. Therefore, HIV and latently HCV-infected individuals need to seek early treatment so as to slow down the progression of HIV to AIDS and latent HCV to advanced HCV.

In this work, we formulated and analysed a deterministic model to study the HIV-HCV co-infection dynamics in presence of HIV therapy. The HCV chronic stage was split into two periods: the period before and the period after onset of cirrhosis. This was done because the HCV chronic stage of infection is long, asymptomatic and infectious. The effective reproduction numbers, one of our outcome measures, were computed using the next generation matrix method. Numerical simulations were performed to support the analytical results from the model. The different parameters in the model were subjected to a sensitivity analysis to determine their relative importance on the HIV-HCV co-infection dynamics. The results indicated that both HIV and HCV infections enhance each other; and in the long run, increasing the rates at which people are put on HIV treatment reduces the prevalence of HCV in the community; however, it increases the prevalence of HIV. Therefore, there should be increased safer sexual behaviour campaigns among individuals on HIV treatment.