Mathematical Modelling of the Epidemiology of Tuberculosis with Silicosis Coinfection

The study presents an innovative mathematical model analysing the epidemiology of Tuberculosis with silicosis coinfection. It effectively integrates epidemiological factors and historical theoretical research with well-structured model formulation and numerical verification through MATLAB. The use of partial differential equation, Jacobian matrix, deterministic techniques as well as Routh Hurwitz algebraic criteria plays significant role in the stability of disease-free equilibrium point and stability of the endemic equilibrium point analytically which indicates locally stable system asymptotically which indicates locally stable system asymptotically as equally demonstrated by the reproduction number. The solutions of the model equations are integrated using the Range Kutta Fourth order method in MATLAB and observed the impact of β_2 which proves that the endemic equilibrium point increased for the recorded population meanwhile, decreased for the coinfected population as β_2 increases. Since the Ro < 1, it shows that the disease-free equilibrium point is stable beyond 2500 days and no endemic equilibrium point exists. It is equally observed that the solution trajectories of the silicosis only sub-model converge to a single point believe to be disease free equilibrium point also known as silica free movement