Mathematical Modeling of Tuberculosis Dynamics with Vaccination, Public Awareness and Treatment

Abstract

Tuberculosis (TB) is a bacterial infection caused by Mycobacterium tuberculosis that typically affects the lungs, but can also impact other organs. Globally, tuberculosis (TB) remains a significant cause of mortality from infectious diseases. In this paper, we developed a nonlinear deterministic model which incorporates vaccination, treatment and public awareness to study the dynamics of tuberculosis. The analysis of the model establishes the boundedness and positivity of the solutions, TB free equilibrium is shown to be both locally and asymptotically stable when and unstable when. Conversely, the endemic globally equilibrium is globally asymptotically stable when and unstable when. The most sensitive parameters for controlling TB transmission are identified using the forward normalized sensitivity index method and found that vaccination and treatment are the most sensitive parameters for decreasing TB transmission. Numerical simulations that shows vaccination, public awareness and treatment of infected individuals are crucial strategies for the effective control of tuberculosis in the population.