Dynamic Analysis of a Mathematical Model for HIV and Hepatitis C Virus Co-Infection

Hepatitis C is the leading cause of death among individuals infected with human. Here, we present a deterministic model for HCV and HIV infections transmission and use the model to assess the potential impact of antiviral therapy. The model is based on the Susceptible-Infective-Removed-Susceptible (SIRS) compartmental structure with chronic primary infection and possibility of reinfection. Important epidemiologic thresholds such as the basic and control reproduction numbers and a measure of treatment impact are derived. We find that if the control reproduction number is greater than unity, there is a locally unstable infection-free equilibrium and a unique, globally asymptotically stable endemic equilibrium. If the control reproduction number is less than unity, the infection-free equilibrium is globally asymptotically stable