On a Novel Dynamics of SEIR Epidemic Models with a Potential Application to COVID-19

Maheswari Rangasamy, Christophe Chesneau, Carlos Martin-Barreiro, Víctor Leiva

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we study a type of disease that unknowingly spreads for a long time, but by default, spreads only to a minimal population. This disease is not usually fatal and often goes unnoticed. We propose and derive a novel epidemic mathematical model to describe such a disease, utilizing a fractional differential system under the Atangana–Baleanu–Caputo derivative. This model deals with the transmission between susceptible, exposed, infected, and recovered classes. After formulating the model, equilibrium points as well as stability and feasibility analyses are stated. Then, we present results concerning the existence of positivity in the solutions and a sensitivity analysis. Consequently, computational experiments are conducted and discussed via proper criteria. From our experimental results, we find that the loss and regain of immunity result in the gain and loss of infections. Epidemic models can be linked to symmetry and asymmetry from distinct points of view. By using our novel approach, much research may be expected in epidemiology and other areas, particularly concerning COVID-19, to state how immunity develops after being infected by this virus.

Original languageEnglish
Article number1436
JournalSymmetry
Volume14
Issue number7
DOIs
StatePublished - Jul 2022
Externally publishedYes

Keywords

  • ABC derivatives
  • basic reproduction number
  • equilibrium points
  • fractional derivatives
  • Laplace transform
  • numerical methods
  • SARS-CoV-2
  • sensitivity and stability analyses

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