Author(s)

Sr Mary Nyambura Mwangi^*, Virginia M. Kitetu, Isaac O. Okwany

Department of Mathematics and Actuarial Science, Catholic University of Eastern Africa, Nairobi, Kenya.

A non-linear HIV-TB co-infection has been formulated and analyzed. The positivity and invariant region has been established. The disease free equilibrium and its stability has been determined. The local stability was determined and found to be stable under given conditions. The basic reproduction number was obtained and according to findings, co-infection diminishes when this number is less than unity, and persists when the number is greater than unity. The global stability of the endemic equilibrium was calculated. The impact of HIV on TB was established as well as the impact of TB on HIV. Numerical solution was also done and the findings indicate that when the rate of HIV treatment increases the latent TB increases while the co-infected population decreases. When the rate of HIV treatment decreases the latent TB population decreases and the co-infected population increases. Encouraging communities to prioritize the consistent treatment of HIV infected individuals must be emphasized in order to reduce the scourge of HIV-TB co-infection.

Co-Infection Modeling, HIV-TB Co-Infection, Mathematical Modeling, Reproduction Number, Inconsistent Treatment

Mwangi, S. , Kitetu, V. and Okwany, I. (2024) Mathematical Modeling of the Co-Infection Dynamics of HIV and Tuberculosis Incorporating Inconsistency in HIV Treatment. Journal of Applied Mathematics and Physics, 12, 1744-1768. doi: 10.4236/jamp.2024.125109.