Dynamic Study of a Delayed Fractional-Order SEIR Epidemic Model with General Incidence and Treatment Functions

This study examines the global features of the SEIR epidemic model in its fractional-order version with time delay. General functions are considered to govern the infection transmission rate, and the rate at which diseased individuals are removed from the infected class. First, we form the proposed model in the Caputo case and perform fundamental mathematical analysis of the model solutions, such as checking for non-negativity and boundedness. The basic reproduction number R0 is then provided after computing the equilibrium points. Following that, sufficient criteria for the global stability of each equilibrium are checked using the relevant Lyapunov functions. It is shown that the characteristics of these general functions, along with the basic reproduction number R0, impact the model’s global features. Finally, a numerical simulation is presented to show the viability and effectiveness of the derived analytical conclusions. According to the results, the system’s enhanced dynamic behavior and larger stability regions in equilibria demonstrate the influence of incorporating the time delay and fractional-order