(untitled) (European Journal of Pure and Applied Mathematics, 2025)
In this paper, a deterministic mathematical model for the transmission dynamics of COVID-19 and tuberculosis co-infection, using a system of nonlinear ordinary differential equations, is proposed and analyzed. We begin our mathematical analysis of the COVID-19 and tuberculosis sub-models by establishing the existence, uniqueness, non-negativity, and boundedness of the solutions. Subsequently, we determine the equilibrium points and the reproduction numbers of the sub-models as well as the co-infection model. We then proceed to prove that the disease-free equilibrium point of each sub-model and the co-infection model is locally and globally asymptotically stable if its corresponding reproduction number is less than 1 and unstable otherwise. Moreover, if the reproduction number is greater than 1, then the corresponding sub-model is locally asymptotically stable at the endemic equilibrium point. Numerical simulations are conducted to validate the theoretical findings. This study demonstrates that effective quarantine measures are crucial for controlling and potentially eradicating COVID-19 and tuberculosis co-infections.