A MATHEMATICAL MODEL FOR TB/HIV CO-INFECTION TREATMENT AND TRANSMISSION MECHANISM

A Mathematical model that focuses on the underlying transmission mechanism of TB and HIV co-infection is developed and analysed to help understand and predict the spread and progression of two infectious diseases in different population. The models exhibit two equilibriums: the equilibrium for a free disease and the endemic. To establish that if the disease free equilibrium is locally asymptotically stable, the fundamental reproductive number (R0) is less than 1. If R0 > 1, the endemic equilibrium exists which is locally asymptotically stable under certain conditions. Numerical simulations suggest that the individual experiencing incident of HIV infections are at a risk of TB co-infection, compared with individuals without HIV infection. This R0<1 (i.e.RT<1 and RH<1) condition is considered to ascertain the stability of the disease free equilibrium E0. It is indicated numerically that the susceptible individuals (yS) converges to the population (N) as t→∞, while the rest of the remaining disease dies out in the population. This R0>1 (RT>1 and RH>1) condition is considerably ascertained the endemic equilibrium stability (E0*).