Tuberculosis (TB) is an infectious disease caused by the bacteria Mycobacterium Tuberculosis [2]. Until now, TB is one of the diseases that cannot be cured. The factors that make TB cases continue to increase is co-infection with Diabetes [1]. Diabetes is a chronic disease that occurs when the pancreas does not produce enough insulin or when the body cannot efficiently use the insulin it produces. Diabetes can be caused by hereditary factors or appear because of the individual's  lifestyle [4]. Several epidemiological studies have shown that Diabetes is positively associated with TB, where Diabetes makes a person's risk of getting TB three times bigger [3].

A new mathematical model for the transmission dynamics of Tuberculosis (TB) with the intervention of diabetes is designed and analyzed in this article. We introduce an SEIR-based model for tuberculosis (TB) with a deterministic approach. The model constructed as a system of eight-dimensional ordinary differential equation, where each population divided into two classes, i.e., susceptible population without and with diabetes, exposed population without and with diabetes, infectious population without and with diabetes, and recovered population without and with diabetes. The index 1 determines the population without diabetes, while 2 is the population with diabetes. The transmission and transition process of tuberculosis in this article is as follows:

 

EQUATION (1) (PLEASE SEE THE ABSTRACT FILE)

 

There is some of mathematical analysis that has been performed, including disease-free and endemic equilibrium points. The disease-free equilibrium is given by EQUATION (2) (PLEASE SEE THE ABSTRACT FILE), while the endemic equilibrium is not easy to be determine caused by the complexity of the model. So as basic reproduction number which obtained by constructing the next-generation matrix [5]. Although the existence of endemic equilibrium and basic reproduction number is difficult to be shown analytically, their existence still can be shown numerically. Using a specific set of parameters such that lead us into existence of endemic equilibrium given by EQUATION (3) (PLEASE SEE THE ABSTRACT FILE). Numerical simulations of the model for the sensitivity of parameters with different of R0 presented in level curve of R0 depending on \gamma_1 and \gamma_2. We find that as the value of  \gamma_1 and \gamma_2 increases, the value of R0 will decrease and the value of \gamma_2 is more influential than \gamma_1.

 

With numerical simulations, we also will see that each of the parameters will affect the value of R0. It will cause the value of R0 increase nor decrease. We expect by obtaining the value of each parameters that makes the value of R0 less than one, it can be used to reduce the spread of tuberculosis with diabetes.