The SEIR Covid-19 model described by fractional-order difference equations: analysis and application with real data in Brazil

Abstract

Several efforts have been recently devoted to the studies on epidemic mathematical models based on fractional-order operators, by virtue of their capability to take into account memory effects and nonlocal features. The aim of this paper is to make a contribution to the topic by introducing a novel Covid-19 model described by non-integer-order difference equations. By conducting a stability analysis, the paper shows that the conceived system has two fixed points at most, i.e. a disease-free fixed point and an endemic fixed point. In particular, a theorem is proved, which assures the global stability of the disease-free fixed point, indicating that the pandemic will disappear when a simple condition on the system parameters is satisfied. Finally, simulation results are carried out with the aim to highlight the capability of the conceived approach.

Keywords:

• Covid-19 pandemic model
• commensurate and incommensurate fractional-order difference operators
• stability
• basic reproduction number

Mathematics Subject Classifications:

• 37D05
• 39A13
• 39A05
• 39A30
• 39A70

Disclosure statement

No potential conflict of interest was reported by the author.