Mathematical model of tuberculosis with saturated treatment function

Mathematical model of tuberculosis with saturated treatment function. In this thesis SIR and SEIR tuberculosis models which include a saturated treatment function are studied. It is beneficial to include a saturated treatment in developing countries because medical conditions can be poor. The local and global stability of the equilibrium points determine the dynamics of the proposed models. Conditions for the global stability of the disease free equilibrium are given. It plays an important role in determining if an infection can be eradicated. The basic reproduction number $R_0$ is the average number of new infections generated by one infectious individual. While in most epidemiological models it is sufficient to decrease $R_0$ to below unity, in the SEIR model bistability may occur and different kinds of stable equilibria coexist. It is shown that improving medical conditions is an effective way of decreasing $R_0$ below a new threshold value $R_0^c$. An optimal control problem is then formulated to reduce the number of infected individuals. We illustrate the theoretical findings by using numerical simulations