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.

In December 2019, in Wuhan, China, a new disease was detected, and the virus easily spread throughout other nations. March 2, 2020, Morocco announced 1st infection of coronavirus. Morocco verified a total of 653,286 cases, 582,692 recovered, 60,579 active case, and 10,015 as confirmatory fatalities, as of 4 August 2021. The objective of this article is to study the mathematical modeling of undetected cases of the novel coronavirus in Morocco. The model is shown to have disease-free and an endemic equilibrium point. We have discussed the local and global stability of these equilibria. The parameters of the model and undiscovered instances of COVID-19 were assessed by the least squares approach in Morocco and have been eliminated. We utilized a Matlab tool to show developments in undiscovered instances in Morocco and to validate predicted outcomes. Like results, until August 4, 2021, the total number of infected cases of COVID-19 in Morocco is 24,663,240, including 653,286 confirmed cases, against 24,009,954 undetected. Further, our approach gives a good approximation of the actual COVID-19 data from Morocco and will be used to estimate the undetected cases of COVID-19 in other countries of the world and to study other pandemics that have the same nature of spread as COVID-19.

In this paper, existence and uniqueness of weak solutions for a linear parabolic problem with conformable derivative are proved, the existence of weak periodic solutions for conformable fractional parabolic nonlinear dierential equation is proved by using a more generalized monotone iterative method combined with the method of upper and lower solutions. We prove the convergence of monotone sequence to weak periodic minimal and maximal solutions. Moreover, the conformable version of the Lions-Magness and AubinLions lemmas are also proved.

In December 2019, a new virus belonging to the coronavirus strain has been discovered in Wuhan, China, this virus has attracted world-wide attention and it spread rapidly in the world, reaching nearly 216 countries in the world in November 2020. In this chapter, we study the fractional incommensurate SIQR (susceptible, infections, quarantined and removed) COVID-19 model with nonlinear saturated incidence rate using Atangana-Baleanu fractional derivatives. The existence and uniqueness of the solutions for the fractional model is proved using fixed point theorem, the model are shown to have two equilibrium point (disease free and an endemic equilibrium). Some numerical simulations using Euler method are also carried out to support our theoretical results. We estimated the value of the fractional orders and the parameters of the proposed model using the least squares method. Further, the sensitivity analysis of the parameter is performed as a result, our incommensurate model gives a good approximation to real data of COVID-19.

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