On analysis generalization of TB-HIV dynamics by a two-scale reduction process
Emile Franc Doungmo Goufo, Abdon Atangana
Abstract
It is widely known that Tuberculosis (TB) and Human Immunodeficiency Virus (HIV) diseases are closely linked to each other, but the dynamic of TB epidemic in our communities is usually faster than the dynamic of HIV epidemic. In this work, we use the geometric singular perturbation method to sub-divide, investigate and analyze a model of TB-HIV co-infection. The full model is divided into two sub-models: one characterized by a slower dynamic of an HIV transmission and the other by the fast dynamic of the TB infection. The focus here is on the slow dynamic on which non local operators are applied to assess their effects and where a comprehensive stability analysis is performed. We show that it is possible to establish and analyze the dynamic of the original model by only studying the reduced one. This result is corroborated by numerical simulations. Furthermore, non-local operators applied to the slow model show similar results with even a better approximation. However, such approximation is a bit inaccurate when the basic reproduction number of the slow model is greater than one and associated with its endemic equilibrium.