A new fractional-order compartmental disease model


Luu Vu Cam Hoan L. V. C. H. , AKINLAR M. A. , İNÇ M., Gomez-Aguilar J. F. , Chu Y., Almohsen B.

ALEXANDRIA ENGINEERING JOURNAL, vol.59, no.5, pp.3187-3196, 2020 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 59 Issue: 5
  • Publication Date: 2020
  • Doi Number: 10.1016/j.aej.2020.07.040
  • Title of Journal : ALEXANDRIA ENGINEERING JOURNAL
  • Page Numbers: pp.3187-3196

Abstract

In this paper, we propose a new SEIRS model and are concerned with stability and numerical solutions of the model. The model is generated under certain assumptions such as individuals are vaccinated or have a special treatment but do not carry lifelong immunity. After generating a new SEIRS model, we perturb the model into fractional time derivative form where Caputo type fractional-order derivative operators are employed. After showing existence and uniqueness of the non-negative solutions, we determine disease free steady-state point and basic reproduction number. We also determine endemic steady state points and study on stability of the fractional system in these equilibrium points. We solve fractional-order system approximately with an efficient Euler type numerical method. We conclude that the proposed system may serve as a kernel for understanding, analysis and computational solutions of a wide range of disease models in epidemiology. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University.