A MATHEMATICAL MODEL WITH OPTIMAL CONTROLS FOR CELLULAR IMMUNOLOGY OF TUBERCULOSIS

Abstract

In this paper we propose a system of ordinary differential equations to model the interaction among non-infected macrophages, infected macrophages, T cells and Mtb bacilli. Model analysis reveals the existence of infection-free equilibrium and the endemically infected equilibrium. And we analyze the dynamics of this model, characterize the optimal controls related to drug therapy, and discuss a quadratic control and a linear control. The quadratic control allows for a weaker treatment that more effectively than the linear control.