Mathematical Models for HIV-HCV Co-infection Dynamics under Various Control Strategies

Abstract

Both HIV and HCV have considerable contribution to the global morbidity and mortality. Since these two viruses have similar transmission routes, HIV-HCV co-infection is common. The existing HIV-HCV co-infection mathematical models have either ignored infection stages or considered HCV in acute and chronic infection. Nonetheless, the chronic stage of HCV is very long and consists of infected individuals that are asymptomatic yet infectious. This requires deep analysis that has not been fully elucidated. In this study, mathematical models for the dynamics of HIV-HCV co-infection were formulated. These mathematical models were used to investigate how HIV infection impacts the dynamics of HCV infection and vice versa in absence of therapy, the impact of ART on the co-infection of HIV and HCV, and the effect of joint therapies on the dynamics of HIV-HCV co-infection. The stability of the equilibrium points was investigated analytically using linearization theory and by construction of Lyapunov functions. Reproduction numbers were computed using the next generation matrix method and these indicated that in the presence of therapy for HIV only or therapies for both HIV and HCV, the dynamics of HIV-HCV co-infection were dominated by HIV. However, in absence of treatment, the dynamics of HIV-HCV co-infection were dominated by HCV. Numerical analysis revealed that increasing the rate of enrolment on HIV treatment reduces HCV prevalence and vice versa. Sensitivity analysis revealed that transmission probability per sexual contact and average number of sexual partners acquired per year were equally likely to result into increased HIV and HCV infections and these parameters were the most sensitive in increasing HIV(or HCV) infection. Thus, it is recommended that the community should be regularly sensitized to greatly reduce the rate of sexual partner acquisition and transmit-ability probabilities.