ABSTRACT
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.
ABSTRACT
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.
ABSTRACT
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.
ABSTRACT
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.
ABSTRACT
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.
ABSTRACT
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.
ABSTRACT
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.
ABSTRACT
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.
ABSTRACT
In this work, we formulate and analyze a new mathematical model for COVID-19 epidemic with isolated class in fractional order. This model is described by a system of fractional-order differential equations model and includes five classes, namely, S (susceptible class), E (exposed class), I (infected class), Q (isolated class), and R (recovered class). Dynamics and numerical approximations for the proposed fractional-order model are studied. Firstly, positivity and boundedness of the model are established. Secondly, the basic reproduction number of the model is calculated by using the next generation matrix approach. Then, asymptotic stability of the model is investigated. Lastly, we apply the adaptive predictor-corrector algorithm and fourth-order Runge-Kutta (RK4) method to simulate the proposed model. Consequently, a set of numerical simulations are performed to support the validity of the theoretical results. The numerical simulations indicate that there is a good agreement between theoretical results and numerical ones.
ABSTRACT
The deadly coronavirus continues to spread across the globe, and mathematical models can be used to show suspected, recovered, and deceased coronavirus patients, as well as how many people have been tested. Researchers still do not know definitively whether surviving a COVID-19 infection means you gain long-lasting immunity and, if so, for how long? In order to understand, we think that this study may lead to better guessing the spread of this pandemic in future. We develop a mathematical model to present the dynamical behavior of COVID-19 infection by incorporating isolation class. First, the formulation of model is proposed; then, positivity of the model is discussed. The local stability and global stability of proposed model are presented, which depended on the basic reproductive. For the numerical solution of the proposed model, the nonstandard finite difference (NSFD) scheme and Runge-Kutta fourth order method are used. Finally, some graphical results are presented. Our findings show that human to human contact is the potential cause of outbreaks of COVID-19. Therefore, isolation of the infected human overall can reduce the risk of future COVID-19 spread.