Mathematical model for dynamics of Tuberculosis epidemiology with optimal control strategies

Abstract

Tuberculosis (TB) is caused by bacteria (Mycobacterium tuberculosis) and it most often affects the lungs. TB is spread through the air when people with lung TB cough, sneeze or spit. A person needs to inhale only a few germs to become infected. To curtail the disease a mathematical model strictly on the Susceptible - Vaccinated - Latent - Active - Chronic - Treatment-Recovery (SVLACTR) compartments for tuberculosis is formulated. We assume the recruitment factor to be Vertical. Already existing tuberculosis data was used in verifying the model to comprehend the transmission of TB dynamics as it will help in warding off, regulating, eliminating the disease, and enhance the well being of lives. We show that the Global Dynamics are completely figured out
by basic infection rate RT B0 , that if RT B0 < 1 the disease free equilibrium is locally and globally stable. But if RT B0 > 1, and endemic equilibrium exist and is uncertain. Sensitivity analysis was performed on the model parameters in RT B0 to determine the effect of each of the parameter value on the TB propagation. Four control strategies, vaccination, reduce contact rate, treatment and sensitization are introduced. By combining these strategies, we can effectively control the spread of TB, improve lives, and ultimately work towards eradicating the disease from the population. This study contributes to the existing literature by highlighting the importance of a multi-faceted approach to TB control and eradication. The model system was solved using the classical Runge-Kutta of order four, forward in 60 years and the algorithm were implemented using MATLAB and MAPLE.