Modelling and stability analysis for a tuberculosis model with healthy education and treatment

• DOI: 10.1007/s40314-013-0008-8
• Publication Date: 2013-08-28T16:46:41Z
• Authors: Xueyong Zhou; Xiangyun Shi; Huidong Cheng
• Keywords: 0301 basic medicine; 03 medical and health sciences; 3. Good health

In this paper, we study a tuberculosis model with healthy education and treatment. The analysis of the model is presented in terms of the TB epidemic threshold $$\mathcal{R }_0$$ . It is shown that the model has multiple equilibria and using the center manifold theory, the model exhibits the phenomenon of backward bifurcation where a stable disease-free equilibrium co-exists with a stable endemic equilibrium for a certain defined range of $$\mathcal{R }_0$$ . We perform sensitivity analysis of $$\mathcal{R }_0$$ on the parameters to determine their relative importance to TB transmission and prxevalence. Numerical simulations are presented to illustrate the results.