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In this article we study a fractional-order mathematical model describing the spread of the new coronavirus (COVID-19) under the Caputo-Fabrizio sense. Exploiting the approach of fixed point theory, we compute existence as well as uniqueness of the related solution. To investigate the exact solution of our model, we use the Laplace Adomian decomposition method (LADM) and obtain results in terms of infinite series. We then present numerical results to illuminate the efficacy of the new derivative. Compared to the classical order derivatives, our obtained results under the new notion show better results concerning the novel coronavirus model. [ABSTRACT FROM AUTHOR]

• A compartmental epidemic model has been considered. • Vaccination, social distance, and testing of susceptible individuals have been included. • The effects of the uncertainty about these mitigation measures on the disease transmission have been quantified. • A spectral approach has been employed, in particular, a statistical moment-based polynomial chaos expansion. • A sensitivity analysis has also been conducted. In this paper, the uncertainty quantification and sensitivity analysis of a mathematical model of the SARS-CoV-2 virus transmission dynamics with mass vaccination strategy has been carried out. More specifically, a compartmental epidemic model has been considered, in which vaccination, social distance measures, and testing of susceptible individuals have been included. Since the application of these mitigation measures entails a degree of uncertainty, the effects of the uncertainty about the application of social distance actions and testing of susceptible individuals on the disease transmission have been quantified, under the assumption of a mass vaccination program deployment. A spectral approach has been employed, which allows the uncertainty propagation through the epidemic model to be represented by means of the polynomial chaos expansion of the output random variables. In particular, a statistical moment-based polynomial chaos expansion has been implemented, which provides a surrogate model for the compartments of the epidemic model, and allows the statistics, the probability distributions of the interesting output variables of the model at a given time instant to be estimated and the sensitivity analysis to be conducted. The purpose of the sensitivity analysis is to understand which uncertain parameters have most influence on a given output random variable of the model at a given time instant. Several numerical experiments have been conducted whose results show that the proposed spectral approach to uncertainty quantification and sensitivity analysis of epidemic models provides a useful tool to control and mitigate the effects of the COVID-19 pandemic, when it comes to healthcare resource planning. [ABSTRACT FROM AUTHOR]

• A new stochastic fractional Coronavirus (2019-nCov) mathematical model with modified parameters are presented. • Milstein's higher order method is constructed to study the model problem • Mean square stability of Milstein algorithm is proved. • Comparative studies and numerical simulations are implemented In this paper, a new stochastic fractional Coronavirus (2019-nCov) model with modified parameters is presented. The proposed stochastic COVID-19 model describes well the real data of daily confirmed cases in Wuhan. Moreover, a novel fractional order operator is introduced, it is a linear combination of Caputo's fractional derivative and Riemann-Liouville integral. Milstein's higher order method is constructed with the new fractional order operator to study the model problem. The mean square stability of Milstein algorithm is proved. Numerical results and comparative studies are introduced. [ABSTRACT FROM AUTHOR]

• We propose to study an optimal control approach with delay in state and control variables. • Numerical simulation of different strategies. • The cost of effectivness. As of June 02, 2020. The number of people infected with COVID-19 virus in Brazil was about 529,405, the number of death is 30046, the number of recovered is 211080, and the number is subject to increase. This is due to the delay by a number of countries in general, and Brazil in particular, in taking preventive and proactive measures to limit the spread of the COVID-19 pandemic. So, we propose to study an optimal control approach with delay in state and control variables in our mathematical model proposed by kouidere et al. which describes the dynamics of the transmission of the COVID-19. That the time with delay represent the delay to applying preventive precautions measures. Pontryagin's maximum principle is used to characterize the optimal controls and the optimality system is solved by an iterative method. Finally, some numerical simulations are performed to verify the theoretical analysis using MATLAB. [ABSTRACT FROM AUTHOR]

In this study, we propose a mathematical model about the spread of novel coronavirus. This model is a system of fractional order differential equations in Caputo's sense. The aim is to explain the virus transmission and to investigate the impact of quarantine on decreasing the prevalence rate of the virus in the environment. The unique solvability of the presented COVID-19 model is proved. Also, the equilibrium points and the reproduction number of the proposed model are discussed in two cases with and without considering the quarantine factor. Using the Adams-Bashforth-Moulton predictor-corrector method, some numerical simulations are implemented to survey the behavior of the considered model. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The COVID-19 pandemic has world-widely motivated numerous attempts to properly adjust classical epidemiological models, namely those of the SEIR-type, to the spreading characteristics of the novel Corona virus. In this context, the fundamental structure of the differential equations making up the SEIR models has remained largely unaltered—presuming that COVID-19 may be just "another epidemic". We here take an alternative approach, by investigating the relevance of one key ingredient of the SEIR models, namely the death kinetics law. The latter is compared to an alternative approach, which we call infection-to-death delay rule. For that purpose, we check how well these two mathematical formulations are able to represent the publicly available country-specific data on recorded fatalities, across a selection of 57 different nations. Thereby, we consider that the model-governing parameters—namely, the death transmission coefficient for the death kinetics model, as well as the apparent fatality-to-case fraction and the characteristic fatal illness period for the infection-to-death delay rule—are time-invariant. For 55 out of the 57 countries, the infection-to-death delay rule turns out to represent the actual situation significantly more precisely than the classical death kinetics rule. We regard this as an important step towards making SEIR-approaches more fit for the COVID-19 spreading prediction challenge. [ABSTRACT FROM AUTHOR]