Optimal control of a fractional order epidemic model with carriers

In this work, a fractional-order S–Ic\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$I_{c}$$\end{document}–I–R epidemic model with carriers has been proposed where we have also studied the dynamics of the carrier model in the presence of treatment and vaccination. We have studied the local and global stability of the model with different criteria. The existence and uniqueness criterion along with positivity and boundedness of the solutions have also been established. An optimal control problem has been formulated and studied by the help of Pontryagin principle. Finally, we have performed numerical simulation and studied the impacts of carriers in the transmission dynamics.