A case study of Covid-19 epidemic in India via new generalised Caputo type fractional derivatives.

The first symptomatic infected individuals of coronavirus (Covid-19) was confirmed in December 2020 in the city of Wuhan, China. In India, the first reported case of Covid-19 was confirmed on 30 January 2020. Today, coronavirus has been spread out all over the world. In this manuscript, we studied the coronavirus epidemic model with a true data of India by using Predictor-Corrector scheme. For the proposed model of Covid-19, the numerical and graphical simulations are performed in a framework of the new generalised Caputo sense non-integer order derivative. We analysed the existence and uniqueness of solution of the given fractional model by the definition of Chebyshev norm, Banach space, Schauder's second fixed point theorem, Arzel's-Ascoli theorem, uniform boundedness, equicontinuity and Weissinger's fixed point theorem. A new analysis of the given model with the true data is given to analyse the dynamics of the model in fractional sense. Graphical simulations show the structure of the given classes of the non-linear model with respect to the time variable. We investigated that the mentioned method is copiously strong and smooth to implement on the systems of non-linear fractional differential equation systems. The stability results for the projected algorithm is also performed with the applications of some important lemmas. The present study gives the applicability of this new generalised version of Caputo type non-integer operator in mathematical epidemiology. We compared that the fractional order results are more credible to the integer order results.

The analysis of a time delay fractional COVID-19 model via Caputo type fractional derivative.

Novel coronavirus (COVID-19), a global threat whose source is not correctly yet known, was firstly recognised in the city of Wuhan, China, in December 2019. Now, this disease has been spread out to many countries in all over the world. In this paper, we solved a time delay fractional COVID-19 SEIR epidemic model via Caputo fractional derivatives using a predictor-corrector method. We provided numerical simulations to show the nature of the diseases for different classes. We derived existence of unique global solutions to the given time delay fractional differential equations (DFDEs) under a mild Lipschitz condition using properties of a weighted norm, Mittag-Leffler functions and the Banach fixed point theorem. For the graphical simulations, we used real numerical data based on a case study of Wuhan, China, to show the nature of the projected model with respect to time variable. We performed various plots for different values of time delay and fractional order. We observed that the proposed scheme is highly emphatic and easy to implementation for the system of DFDEs.

Fractional order mathematical model for B.1.1.529 SARS-Cov-2 Omicron variant with quarantine and vaccination.

In this paper, a fractional order nonlinear model for Omicron, known as B.1.1.529 SARS-Cov-2 variant, is proposed. The COVID-19 vaccine and quarantine are inserted to ensure the safety of host population in the model. The fundamentals of positivity and boundedness of the model solution are simulated. The reproduction number is estimated to determine whether or not the epidemic will spread further in Tamilnadu, India. Real Omicron variant pandemic data from Tamilnadu, India, are validated. The fractional-order generalization of the proposed model, along with real data-based numerical simulations, is the novelty of this study.

Some novel mathematical analysis on the fractional-order 2019-nCoV dynamical model.

Since December 2019, the whole world has been facing the big challenge of Covid-19 or 2019-nCoV. Some nations have controlled or are controlling the spread of this virus strongly, but some countries are in big trouble because of their poor control strategies. Nowadays, mathematical models are very effective tools to simulate outbreaks of this virus. In this research, we analyze a fractional-order model of Covid-19 in terms of the Caputo fractional derivative. First, we generalize an integer-order model to a fractional sense, and then, we check the stability of equilibrium points. To check the dynamics of Covid-19, we plot several graphs on the time scale of daily and monthly cases. The main goal of this content is to show the effectiveness of fractional-order models as compared to integer-order dynamics.

Dynamics of COVID-19 epidemic via two different fractional derivatives

In December 2019, the novel Coronavirus, also known as 2019-nCoV or SARS-CoV-2 or COVID-19, was first recognized as a deadly disease in Wuhan, China. In this paper, we analyze two different nonclassical Coronavirus models to observe the outbreaks of this disease. Caputo and Caputo-Fabrizio (C-F) fractional derivatives are considered to simulate the given epidemic models by using two separate methods. We perform all required graphical simulations with the help of real data to demonstrate the behavior of the proposed systems. We observe that the given schemes are highly effective and suitable to analyze the dynamics of Coronavirus. We find different natures of the given model classes for both Caputo and C-F derivative sense. The main contribution of this study is to propose a novel framework of modeling to show how the fractional-order solutions can describe disease dynamics much more clearly as compared to integer-order operators. The motivation to use two different fractional derivatives, Caputo (singular-type kernel) and Caputo-Fabrizio (exponential decay-type kernel) is to explore the model dynamics under different kernels. The applications of two various kernel properties on the same model make this study more effective for scientific observations.

A new study on two different vaccinated fractional-order COVID-19 models via numerical algorithms.

The main purpose of this paper is to provide new vaccinated models of COVID-19 in the sense of Caputo-Fabrizio and new generalized Caputo-type fractional derivatives. The formulation of the given models is presented including an exhaustive study of the model dynamics such as positivity, boundedness of the solutions and local stability analysis. Furthermore, the unique solution existence for the proposed fractional order models is discussed via fixed point theory. Numerical solutions are also derived by using two-steps Adams-Bashforth algorithm for Caputo-Fabrizio operator, and modified Predictor-Corrector method for generalised Caputo fractional derivative. Our analysis allow to show that the given fractional-order models exemplify the dynamics of COVID-19 much better than the classical ones. Also, the analysis on the convergence and stability for the proposed methods are performed. By this study, we see that how the vaccine availability plays an important role in the control of COVID-19 infection.

Fractional dynamics of 2019-nCOV in Spain at different transmission rate with an idea of optimal control problem formulation

In this article, we studied the fractional dynamics of the most dangerous deathly disease which outbreaks have been recorded all over the world, called 2019-nCOV or COVID-19. We used the numerical values of the given parameters based on the real data of the 2019-nCOV cases in Spain for the time duration of 25 February to 9 October 2020. We performed our observations with the help of the Atangana-Baleanu (AB) non-integer order derivative. We analysed the optimal control problem in a fractional sense for giving the information on all necessary health care issues. We applied the Predictor-Corrector method to do the important graphical simulations. Also, we provided the analysis related to the existence of a unique solution and the stability of the proposed scheme. The aim and the main contribution of this research is to analyse the structure of novel coronavirus in Spain at different transmission rate and to indicate the danger of this deathly disease for future with the introduction of some optimal controls and health care measures.

A case study of 2019-nCOV cases in Argentina with the real data based on daily cases from March 03, 2020 to March 29, 2021 using classical and fractional derivatives.

In this study, our aim is to explore the dynamics of COVID-19 or 2019-nCOV in Argentina considering the parameter values based on the real data of this virus from March 03, 2020 to March 29, 2021 which is a data range of more than one complete year. We propose a Atangana-Baleanu type fractional-order model and simulate it by using predictor-corrector (P-C) method. First we introduce the biological nature of this virus in theoretical way and then formulate a mathematical model to define its dynamics. We use a well-known effective optimization scheme based on the renowned trust-region-reflective (TRR) method to perform the model calibration. We have plotted the real cases of COVID-19 and compared our integer-order model with the simulated data along with the calculation of basic reproductive number. Concerning fractional-order simulations, first we prove the existence and uniqueness of solution and then write the solution along with the stability of the given P-C method. A number of graphs at various fractional-order values are simulated to predict the future dynamics of the virus in Argentina which is the main contribution of this paper.

A new fractional mathematical modelling of COVID-19 with the availability of vaccine.

The most dangerous disease of this decade novel coronavirus or COVID-19 is yet not over. The whole world is facing this threat and trying to stand together to defeat this pandemic. Many countries have defeated this virus by their strong control strategies and many are still trying to do so. To date, some countries have prepared a vaccine against this virus but not in an enough amount. In this research article, we proposed a new SEIRS dynamical model by including the vaccine rate. First we formulate the model with integer order and after that we generalize it in Atangana-Baleanu derivative sense. The high motivation to apply Atangana-Baleanu fractional derivative on our model is to explore the dynamics of the model more clearly. We provide the analysis of the existence of solution for the given fractional SEIRS model. We use the famous Predictor-Corrector algorithm to derive the solution of the model. Also, the analysis for the stability of the given algorithm is established. We simulate number of graphs to see the role of vaccine on the dynamics of the population. For practical simulations, we use the parameter values which are based on real data of Spain. The main motivation or aim of this research study is to justify the role of vaccine in this tough time of COVID-19. A clear role of vaccine at this crucial time can be realized by this study.

Prediction studies of the epidemic peak of coronavirus disease in Brazil via new generalised Caputo type fractional derivatives

The first reported case of coronavirus disease (COVID-19) in Brazil was confirmed on 25 February 2020 and then the number of symptomatic cases produced day by day. In this manuscript, we studied the epidemic peaks of the novel coronavirus (COVID-19) in Brazil by the successful application of Predictor-Corrector (P-C) scheme. For the proposed model of COVID-19, the numerical solutions are performed by a model framework of the recent generalized Caputo type non-classical derivative. Existence of unique solution of the given non-linear problem is presented in terms of theorems. A new analysis of epidemic peaks in Brazil with the help of parameter values cited from a real data is effectuated. Graphical simulations show the obtained results to classify the importance of the classes of projected model. We observed that the proposed fractional technique is smoothly work in the coding and very easy to implement for the model of non-linear equations. By this study we tried to exemplify the roll of newly proposed fractional derivatives in mathematical epidemiology. The main purpose of this paper is to predict the epidemic peak of COVID-19 in Brazil at different transmission rates. We have also attempted to give the stability analysis of the proposed numerical technique by the reminder of some important lemmas. At last we concluded that when the infection rate increases then the nature of the diseases changes by becoming more deathly to the population.

Projections and fractional dynamics of COVID-19 with optimal control strategies.

When the entire world is eagerly waiting for a safe, effective and widely available COVID-19 vaccine, unprecedented spikes of new cases are evident in numerous countries. To gain a deeper understanding about the future dynamics of COVID-19, a compartmental mathematical model has been proposed in this paper incorporating all possible non-pharmaceutical intervention strategies. Model parameters have been calibrated using sophisticated trust-region-reflective algorithm and short-term projection results have been illustrated for Bangladesh and India. Control reproduction numbers ( R c ) have been calculated in order to get insights about the current epidemic scenario in the above-mentioned countries. Forecasting results depict that the aforesaid countries are having downward trends in daily COVID-19 cases. Nevertheless, as the pandemic is not over in any country, it is highly recommended to use efficacious face coverings and maintain strict physical distancing in public gatherings. All necessary graphical simulations have been performed with the help of Caputo-Fabrizio fractional derivatives. In addition, optimal control strategies for fractional system have been designed and the existence of unique solution has also been showed using Picard-Lindelof technique. Finally, unconditional stability of the fractional numerical technique has been proved.

Forecasting of COVID-19 pandemic: From integer derivatives to fractional derivatives.

In this work, a new compartmental mathematical model of COVID-19 pandemic has been proposed incorporating imperfect quarantine and disrespectful behavior of citizens towards lockdown policies, which are evident in most of the developing countries. An integer derivative model has been proposed initially and then the formula for calculating basic reproductive number, R 0 of the model has been presented. Cameroon has been considered as a representative for the developing countries and the epidemic threshold, R 0 has been estimated to be  ~ 3.41 ( 95 % CI : 2.2 - 4.4 ) as of July 9, 2020. Using real data compiled by the Cameroonian government, model calibration has been performed through an optimization algorithm based on renowned trust-region-reflective (TRR) algorithm. Based on our projection results, the probable peak date is estimated to be on August 1, 2020 with approximately 1073 ( 95 % CI : 714 - 1654 ) daily confirmed cases. The tally of cumulative infected cases could reach  ~ 20, 100 ( 95 % CI : 17 , 343 - 24 , 584 ) cases by the end of August 2020. Later, global sensitivity analysis has been applied to quantify the most dominating model mechanisms that significantly affect the progression dynamics of COVID-19. Importantly, Caputo derivative concept has been performed to formulate a fractional model to gain a deeper insight into the probable peak dates and sizes in Cameroon. By showing the existence and uniqueness of solutions, a numerical scheme has been constructed using the Adams-Bashforth-Moulton method. Numerical simulations have enlightened the fact that if the fractional order α is close to unity, then the solutions will converge to the integer model solutions, and the decrease of the fractional-order parameter (0  <  α  <  1) leads to the delaying of the epidemic peaks.

A new study of unreported cases of 2019-nCOV epidemic outbreaks.

2019-nCOV epidemic is one of the greatest threat that the mortality faced since the World War-2 and most decisive global health calamity of the century. In this manuscript, we study the epidemic prophecy for the novel coronavirus (2019-nCOV) epidemic in Wuhan, China by using q-homotopy analysis transform method (q-HATM). We considered the reported case data to parameterise the model and to identify the number of unreported cases. A new analysis with the proposed epidemic 2019-nCOV model for unreported cases is effectuated. For the considered system exemplifying the model of coronavirus, the series solution is established within the frame of the Caputo derivative. The developed results are explained using figures which show the behaviour of the projected model. The results show that the used scheme is highly emphatic and easy to implementation for the system of nonlinear equations. Further, the present study can confirm the applicability and effect of fractional operators to real-world problems.

Solution of a COVID-19 model via new generalized Caputo-type fractional derivatives.

In this manuscript, we solve a model of the novel coronavirus (COVID-19) epidemic by using Corrector-predictor scheme. For the considered system exemplifying the model of COVID-19, the solution is established within the frame of the new generalized Caputo type fractional derivative. The existence and uniqueness analysis of the given initial value problem are established by the help of some important fixed point theorems like Schauder's second and Weissinger's theorems. Arzela-Ascoli theorem and property of equicontinuity are also used to prove the existence of unique solution. A new analysis with the considered epidemic COVID-19 model is effectuated. Obtained results are described using figures which show the behaviour of the classes of projected model. The results show that the used scheme is highly emphatic and easy to implementation for the system of non-linear equations. The present study can confirm the applicability of the new generalized Caputo type fractional operator to mathematical epidemiology or real-world problems. The stability analysis of the projected scheme is given by the help of some important lemma or results.