Mathematical Model for Tuberculosis

Endogenous infection and exogenous reinfection are two mechanisms the cause of the reactivation or regeneration of active tuberculosis (TB) in people who have experienced prior active TB infections. Following primary TB infection, only approximately %10 of individuals develop active T.B. We are all assumed to mount a highly effective immune respond to the initial infection that limits proliferation from the bacilli and triggers long-lasting partial immunity both to advance infection and also to reactivation of latent bacilli remaining from the first infection. In this paper, we propose a new model of tuberculosis with endogenous reactivation and exogenous re-infection. Model formulations involve a variety of mathematical areas, such as ODEs (Ordinary Differential Equations) (both autonomous and non-autonomous systems), PDEs (Partial Differential Equations), system of difference equations.