Mathematical Models For Tuberculosis Spread In Humans

ABSTRACT

We studied two models describing transmission dynamics of tuberculosis (TB) and discussed their implications to human health. The first model is analyzed in the presence of treatment of active TB persons and the screened asymptomatic TB infectives. The second model is analyzed by looking at treatment of drug sensitive TB as well as drug resistant TB individuals. The models are built with a motive to study the dynamical behaviors of the trajectories which has the potential to guide TB control and also to influence policies for decision making. The basic reproduction number for each model is calculated by using the next generation method and conditions for disease elimination/persistence are determined. Numerical simulation results show that for the first model, R0 > 1, implying that the disease-free equilibrium is unstable. For the second model, however, R0 < 1, indicating that the disease-free equilibrium is a stable steady state and that in case of an outbreak, the disease will not spread. Simulation results also shows that increasing the rate of treatment significantly reduces the value of the reproductive number. Hence, we concluded through this study that proper screening, early detection and a high treatment rate, leading to a high successful treatment rate can reduce TB spread.