On the dynamical modeling of COVID-19 involving Atangana–Baleanu fractional derivative and based on Daubechies framelet simulations

Abstract

In this paper, we present a novel fractional order COVID-19 mathematical model by involving fractional order with specific parameters. The new fractional model is based on the well-known Atangana–Baleanu fractional derivative with non-singular kernel. The proposed system is developed using eight fractional-order nonlinear differential equations. The Daubechies framelet system of the model is used to simulate the nonlinear differential equations presented in this paper. The framelet system is generated based on the quasi-affine setting. In order to validate the numerical scheme, we provide numerical simulations of all variables given in the model.

A Novel Numerical Method for Solving Fractional Diffusion-Wave and Nonlinear Fredholm and Volterra Integral Equations with Zero Absolute Error

“…, and F 1 (x), F 2 (x), F 3 (t), F 4 (t) are arbitrary functions that can be determined using the initial and boundary conditions given in Equation (3).…”

“…Fractional calculus is very useful and widely used in many applications in science, numerical computations and engineering, where the mathematical modeling of several real world problems is presented in terms of fractional differential equations, see, e.g., [1][2][3][4][5][6][7][8]. For example, the authors in [8] approximated the Caputo fractional derivative by quadratic segmentary interpolation.…”

Lessons drawn from China and South Korea for managing COVID-19 epidemic: Insights from a comparative modeling study

“…Several mathematical models have been devised to predict the epidemiologic trend of the COVID-19 outbreak, including stochastic/mathematical (integer derivative [15] , [16] or fractional-order [17] , [18] , [19] ) models, mass-action, (spatial) structured metapopulation, agent-based networked, and other compartmentalized models [20] , among others. According to a systematic survey of the literature, synthesizing 242 studies, 46.1% of studies used compartmental models, 31.8% statistical models (growth models and time series), 6.7%, 4.7%, 3.3%, 2.3% and 1.3% Artificial Intelligence-, Bayesian approach-, hybrid, network- and individual agent-based models, respectively [21] .…”

Threshold dynamics of difference equations for SEIR model with nonlinear incidence function and infinite delay

“…This projection was very helpful in predicting the newly discovered COVID-19 disease we cite for instance the paper [1,2], and other diseases as bovine Babesiosis disease [3], HIV [4], so on. Further, the application of fractional calculus in understanding and predicting the evolution of infectious diseases and evolution of species attract the attention of numerous scholars we cite for instance the papers [5][6][7][8][9][10][11][12]. For more information about different methods for mathematical modeling of some other natural problems, we invite the readers to check the following papers [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] In the literature, modeling the spread of infectious diseases using differential equations occupies a remarkable portion of the newly research achievements as example the researches [4,22,[31][32][33], where each population is considered that evolutes in terms of time only.…”