The dynamics of COVID-19 in the UAE based on fractional derivative modeling using Riesz wavelets simulation

Abstract

The well-known novel virus (COVID-19) is a new strain of coronavirus family, declared by the World Health Organization (WHO) as a dangerous epidemic. More than 3.5 million positive cases and 250 thousand deaths (up to May 5, 2020) caused by COVID-19 and has affected more than 280 countries over the world. Therefore studying the prediction of this virus spreading in further attracts a major public attention. In the Arab Emirates (UAE), up to the same date, there are 14,730 positive cases and 137 deaths according to national authorities. In this work, we study a dynamical model based on the fractional derivatives of nonlinear equations that describe the outbreak of COVID-19 according to the available infection data announced and approved by the national committee in the press. We simulate the available total cases reported based on Riesz wavelets generated by some refinable functions, namely the smoothed pseudosplines of types I and II with high vanishing moments. Based on these data, we also consider the formulation of the pandemic model using the Caputo fractional derivative. Then we numerically solve the nonlinear system that describes the dynamics of COVID-19 with given resources based on the collocation Riesz wavelet system constructed. We present graphical illustrations of the numerical solutions with parameters of the model handled under different situations. We anticipate that these results will contribute to the ongoing research to reduce the spreading of the virus and infection cases.

A particle swarm optimization approach for predicting the number of COVID-19 deaths

“…In 6 , a conceptual mathematical model on the transmission dynamics of COVID-19 between the frontliners and the general public was formulated by considering an SEIR (susceptible–exposed–infected–recovered) compartment model where a huge number of parameters is required (up to 23 parameters). According to the available infection data, authors in 7 elaborate a dynamical model based on the fractional derivatives of nonlinear equations that describe the outbreak of COVID-19. Such a model necessitates a very large number of parameters.…”

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

“…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.…”

Numerical Solutions for Systems of Fractional and Classical Integro-Differential Equations via Finite Integration Method Based on Shifted Chebyshev Polynomials

“…Some interesting applications of fractional calculus can be found in various fields of sciences and engineering, for examples, viscoelasticity [1], nonlinear dynamical system [2], chaotic system [3], electromagnetic wave [4], heat transfer modeling [5], etc. In addition, the fractional calculus has grown in popularity as a tool for describing the physical features of real-world situations, particularly COVID-19, SIR model and health problems, as evidenced in [6,7] and references therein. One interesting issue regarding the fractional calculus is a fractional integro-differential equation (FIDE).…”