Stability Analysis of the Transmission Model of TB-HIV Co-Dynamics with Vaccination and Treatment

Abstract

This study aims to analyse and determine the stability of the equilibrium point of the spread model consists of TB infection, HIV infection, and TB-HIV co-infection disease. This model considers eight compartments, namely unvaccinated susceptible, vaccinated susceptible, exposed, infected with TB, infected with HIV, infected with TB and HIV, treatment, and recovered by considering vaccination and treatment in the compartments as the strategies to manage spread of the diseases. The stability of non-endemic equilibrium point is carried out by determining the basic reproduction number and eigenvalues. Simulation is conducted to investigate effect of vaccination and treatment. By giving appropriate values of parameters and varying values of vaccination rate we found that increasing value of vaccination rate will reduce and eliminate TB infection, HIV infection, and TB-HIV co-infection disease from the population. The curve solutions of the dynamics of each compartment are given to confirm the analytical results.