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, cilt.59, sa.5, ss.3187-3196, 2020 (SCI İndekslerine Giren Dergi) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 59 Konu: 5
  • Basım Tarihi: 2020
  • Doi Numarası: 10.1016/j.aej.2020.07.040
  • Dergi Adı: ALEXANDRIA ENGINEERING JOURNAL
  • Sayfa Sayıları: ss.3187-3196

Özet

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.