International Journal of Nonlinear Analysis and Applications

Analysis of Caputo fractional SEIR model for Covid-19 pandemic

Document Type : Research Paper

Author

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

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International Journal of Nonlinear Analysis and Applications
Volume 14, Issue 12
December 2023
Pages 305-314
  • Receive Date: 22 March 2022
  • Revise Date: 28 April 2022
  • Accept Date: 31 May 2022