Saeid Shagholi - Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, Semnan University, Iran

In this paper, we study the spread of COVID-۱۹ and its effect on a population through mathematical models. We propose a Caputo time-fractional compartmental model (SEIR) comprising the susceptible, exposed, infected and recovered population for the dynamics of the COVID-۱۹ pandemic. The proposed nonlinear fractional model is an extension of a formulated integer-order COVID-۱۹ mathematical model. The existence of a unique solution for the proposed model was shown by using basic concepts such as continuity and Banach's fixed-point theorem. The uniqueness and boundedness of the solutions of the proposed model are investigated. We calculate a central quantity in epidemiology called the basic reproduction number, R_{۰} by the concept of the next-generation matrices approach. The equilibrium points of the model are calculated and the local asymptotic stability for the derived disease-free equilibrium point is discussed.

Time-fractional model, SEIR epidemic model, COVID-۱۹, Banach fixed-point, Stability analysis