Fractional Model and Numerical Algorithms for Predicting COVID-19 with Isolation and Quarantine Strategies

Abstract

In December 2019, a new outbreak in Wuhan, China has attracted world-wide attention, the virus then spread rapidly in most countries of the world, the objective of this paper is to investigate the mathematical modelling and dynamics of a novel coronavirus (COVID-19) with Caputo-Fabrizio fractional derivative in the presence of quarantine and isolation strategies. The existence and uniqueness of the solutions for the fractional model is proved using fixed point iterations, the fractional model are shown to have disease-free and an endemic equilibrium point.We construct a fractional version of the four-steps Adams-Bashforth method as well as the error estimate of this method. We have used this method to determine the numerical scheme of this model and Matlab program to illustrate the evolution of the virus in some countries (Morocco, Qatar, Brazil and Mexico) as well as to support theoretical results. The Least squares fitting is a way to find the best fit curve or line for a set of points, so we apply this method in this paper to construct an algorithm to estimate the parameters of fractional model as well as the fractional order, this model gives an estimate better than that of classical model.

RETRACTED: SIR model for the spread of COVID-19: A case study

“…D. P. Mahapatra and S. Triambak [9] applied random 2D Monte Carlo computations to sufficiently understand the spread of COVID-19 through contact interactions. Abdelouahed Alla Hamou et al [10] built a fractional version of the Adams-Bashforth four-step method and the estimation of the error of that method. Ç Oğuz, M Yağanoğlu [11] designed a model to reduce the duration and number of disease transmissions by shortening the diagnostic time for COVID-19 patients using Computed Tomography (CT).…”

Implementation of computationally efficient numerical approach to analyze a Covid-19 pandemic model

“…Their goal was to gather understanding of the disease spread, virus mode of transformation, effects after the spread, and then prevention or control. These models are extremely important in the study of epidemiology to perform a reliable and competitive mathematical analysis of several disease control measures [29] . As a result of this process, the pattern of many infectious diseases is better understood.…”

Global stability and analysing the sensitivity of parameters of a multiple-susceptible population model of SARS-CoV-2 emphasising vaccination drive

“…Using mathematical formulations to model the transmission of infectious diseases like COVID-19 is a well-established approach to analysing individuals and their infections in communities. Several studies have been published examining the dynamics of the COVID-19 epidemic worldwide [14] , [15] , [16] , [17] , [18] , [19] , [20] , [21] , [22] , [23] , [24] , [25] , [26] , [27] , [28] , [30] , [32] , [35] , [36] , [37] , [38] , [39] , [41] , [42] , [43] , [44] , [45] , [46] , [47] , [48] , [49] , [50] , [52] , [53] , [54] , [55] , [57] , [58] , [59] , [60] , [61] , [62] , [63] , [64] , [65] , [66] , [67] , [68] , [69] , [70] , [71] , [72] , [73] , [74] , [75] , [76] , [77] , [78] , [79] , [80] , [81] , [82] , [83] . Vaccination’s impact on the spread of COVID-19 has been the subject of several articles [40] , [51] .…”