Analysis and optimal control problem for a fractional mathematical model of tuberculosis with smoking consideration
This article studies a mathematical model of the fractional order of tuberculosis (TB). It describes the dynamics of the spread of tuberculosis among smokers. The purpose of this research is to protect vulnerable people against the virus. According to the survey results, the required model has an equilibrium point: the disease-free equilibrium point $E_f$. We also analyze the local stability of this equilibrium point of the model, using the basic reproduction number $\mathcal{R}_{0}$ calculated according to the new generation method. In our model, we include three