Modeling Perspective of Diabetes Mellitus with Tuberculosis

The main focus of this paper is to study the dynamics of diabetes mellitus (DM) and tuberculosis (TB) infectious disease. Numerous studies have manifested that the pandemic of DM and TB is going to be regarded as a significant challenge for the healthcare sector in the future [5, 7, 8, 9, 12, 13]. DM increases the risk of developing TB infection by three times, including treatment failure. Hence, there is an urgent requirement to study the dynamics of these two diseases. We build the mathematical model and study the existence and uniqueness results. The equilibria are analyzed for their stability properties. We estimate the infection rate parameter using dynamic programming approach. Finally, we apply a discretization scheme named dynamics preserving discretization (DPD) scheme, which is also known as nonstandard finite difference (NSFD) scheme, for the study of DM-TB model and check whether all the properties of the continuous system is preserved in the discrete counterpart or not. We also compare the numerical results between the DPD scheme and the traditional numerical schemes like Euler and Runge-Kutta schemes. This study highlights that with controlled infection rate, the TB infected diabetic population can be made stable in the long run hence helping the public health policy makers with decision making at various levels.