Complex dynamics of a Caputo derivative-based fractional-order SIR model incorporating saturated incidence and recovery

In the current study, we develop and analyze a Caputo derivative-based fractional-order SIR-type epidemic model. The exact value of the basic reproduction number and its importance in the model system has also been discussed. Then, we provide a mathematical analysis of this model focused on endemic and infection-free states. Next, the global behavior of the model, along with the existence of the Backward and Hopf bifurcations, has been extensively studied. The impacts of the model parameters on the system are analyzed. Also, we have formulated an optimum control problem incorporating a time-dependent treatment control variable and studied the effects of the control parameter on the disease dynamics. To confirm the obtained analytical results, the model is also numerically simulated using the predictor-corrector approach.