Document Type : Research Paper

Author

• Saeid Shagholi

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

Abstract

In this paper, we study the spread of COVID-19 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-19 pandemic. The proposed nonlinear fractional model is an extension of a formulated integer-order COVID-19 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, $R_{0}$ 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.

Keywords

• Time-fractional model
• SEIR epidemic model
• Covid-19
• Banach fixed-point
• Stability Analysis