Mathematical Modelling of Tuberculosis and Hepatitis C Coinfection Dynamics with No Intervention

Abstract

In this study, a deterministic tuberculosis (TB)-hepatitis C (HCV) coinfection mathematical model with no intervention is analysed purposely to examine the dynamics of TB-HCV coinfection so as to find conditions for reducing the transmission of both TB and HCV. A unique solution to the model exists; it is positive and is bounded. The analytical and numerical analysis show that for basic reproduction number, R0=maxRT,RH<1, the TB and HCV disease-free equilibrium points are stable. Further analysis shows that when the TB-HCV coinfection basic reproduction number is greater than 1, the endemic equilibrium point is stable. Sensitivity analysis reveals that interventions to reduce TB or HCV infection need to aim and concentrate on minimizing the numbers of the effective contact rate with TB- or HCV-infected humans and the rate of progress from latent TB or acute HCV to infectious TB or chronic HCV stage. Numerical simulations reveal that over time, the number of TB latent humans, acute HCV humans, and the number of dually infected humans have a linear relationship with the effective contact and the progression rates for both TB- and HCV-infected humans. We recommend that health education campaigns to communities aimed at reducing the transmission rates of TB and HCV be conducted. These could include screening and isolation, wearing of face masks for TB cases and screening, sterilization of surgical instruments, and use of condoms for HCV-infected humans.