Fractional-order coronavirus models with vaccination strategies impacted on Saudi Arabia’s infections

Several newly nonlinear models for describing dynamics of COVID-19 pandemic have been proposed and investigated in literature recently. In light of these models, we attempt to reveal the role of fractional calculus in describing the growth of COVID-19 dynamics implemented on Saudi Arabia’s society over 107 days;from 17 Dec 2020 to 31 March 2021. Above is achieved by operating two fractional-order differential operators, Caputo and the Caputo-Fabrizio operators, instead of the classical one. One of expanded SEIR models is utilized for achieving our purpose. With the help of using the Generalized Euler Method (GEM) and Adams-Bashforth Method (ABM), the numerical simulations are performed respectively in view of the Caputo and Caputo-Fabrizio operators. Accordance with said, the stability analysis of the two proposed fractional-order models is discussed and explored in view of obtaining the equilibrium points, determining the reproductive number (R0) and computing the elasticity indices of R0. Several numerical comparisons reveal that the fractional-order COVID-19 models proposed in this work are better than that of classical one when such comparisons are performed between them and some real data collected from Saudi Arabia’s society. This inference together with the cases predictions that could easily deduced from the proposed fractional-order models can allow primary decision makers and influencers to set the right plans and logic strategies that should be followed to face this pandemic. © 2022 the Author(s), licensee AIMS Press.

Chaotic dynamics in a novel COVID-19 pandemic model described by commensurate and incommensurate fractional-order derivatives.

Mathematical models based on fractional-order differential equations have recently gained interesting insights into epidemiological phenomena, by virtue of their memory effect and nonlocal nature. This paper investigates the nonlinear dynamic behavior of a novel COVID-19 pandemic model described by commensurate and incommensurate fractional-order derivatives. The model is based on the Caputo operator and takes into account the daily new cases, the daily additional severe cases, and the daily deaths. By analyzing the stability of the equilibrium points and by continuously varying the values of the fractional order, the paper shows that the conceived COVID-19 pandemic model exhibits chaotic behaviors. The system dynamics are investigated via bifurcation diagrams, Lyapunov exponents, time series, and phase portraits. A comparison between integer-order and fractional-order COVID-19 pandemic models highlights that the latter is more accurate in predicting the daily new cases. Simulation results, besides to confirming that the novel fractional model well fit the real pandemic data, also indicate that the numbers of new cases, severe cases, and deaths undertake chaotic behaviors without any useful attempt to control the disease. Supplementary Information: The online version contains supplementary material available at 10.1007/s11071-021-06867-5.