Analysis of the Epidemic Biological Model of Tuberculosis (TB) via Numerical Schemes

Abstract

Tuberculosis (TB) is caused by bacillus Mycobacterium tuberculosis (MTB). In this study, a mathematical model of tuberculosis (TB) is analyzed. The numerical behaviour of the considered model is analyzed including basic reproduction number and stability. We applied three numerical techniques to this model, i.e., nonstandard finite difference (NSFD) scheme, Runge–Kutta method of order 4(RK-4), and forward Euler (FD) scheme. NSFD scheme preserves all the essential properties of the model. Acquired results corroborate that NSFD scheme converges for each step size. While the other two schemes failed to preserve some properties of the model such as positivity and convergence. A graphical comparison presented in this study confirms the numerical stability of the NSFD technique shown here is maintained over a large area.