ABSTRACT
The present article studies the agitation scenario of SARS‐CoV‐2 (COVID‐19), the current pandemic around the globe, by applying Atangana–Baleanu–Caputo (ABC)$$ \left(\mathcal{ABC}\right) $$ derivative operator where 0<κ≤1$$ 0<\kappa \le 1 $$. Using classical notions, we study various qualitative features, like existence, uniqueness and investigate Hyers–Ulam stability analysis of the model under consideration. Lagrange's polynomial approach is used for the approximation of nonlinear terms of the system. We carry out numerical simulations for different values of the fractional‐order κ$$ \kappa $$. The results obtained are compared with those of the classic order derivatives. It is observed that the results obtained with fractional order are better as compared to the classical order. [ABSTRACT FROM AUTHOR] Copyright of Mathematical Methods in the Applied Sciences is the property of John Wiley & Sons, Inc. and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
ABSTRACT
This research discusses the analysis and simulation of SIR model for COVID-19 spreading with regards to the effect of offline learning and vaccination. The results of the analysis shows that the COVID-19 case in Indonesia is at a stable stage. The SIR model was chosen because it is one of the basic methods in the epidemiological model like COVID-19. The simulation results shows that if offline learning is not enforced but 99% of the students are vaccinated, the rate of spread of COVID-19 slows down and the rate of recovery has increased in just five months. The results also shown that if 50% offline learning is carried out, the basic reproduction number is R0 = 3.3715, which means that a student infected with COVID-19 can infect 11 other people and if 99% offline learning is carried out, the basic reproduction number is obtained R0 = 6.6757, which means that a student infected with COVID-19 can infect 22 other people in Indonesia. Copyright © 2023 Inderscience Enterprises Ltd.
ABSTRACT
This study proposes a corona pandemic model that incorporates both reported and unreported cases of virus to be more realistic. In addition, it is advised to employ both preventive measures: vaccination and treatment and applied them at the simultaneously. The optimal controls were characterized with the maximum Pontryagin principle. Finally, the results of the numerical simulations demonstrate the utility of the proposed control mechanisms and this modeling. © 2023, SCIK Publishing Corporation. All rights reserved.
ABSTRACT
In this article, we consider a Covid-19 model for a population involving diabetics as a subclass in the fractal–fractional (FF) sense of derivative. The study includes: existence results, uniqueness, stability and numerical simulations. Existence results are studied with the help of fixed-point theory and applications. The numerical scheme of this paper is based upon the Lagrange's interpolation polynomial and is tested for a particular case with numerical values from available open sources. The results are getting closer to the classical case for the orders reaching to 1 while all other solutions are different with the same behavior. As a result, the fractional order model gives more significant information about the case study. © 2023 The Author(s)
ABSTRACT
In this paper, the dynamics of an autonomous mathematical model of COVID‐19 depending on a real bifurcation parameter is controlled by the parameter switching (PS) algorithm. With this technique, it is proved that every attractor of the considered system can be numerically approximated and, therefore, the system can be determined to evolve along, for example, a stable periodic motion or a chaotic attractor. In this way, the algorithm can be considered as a chaos control or anticontrol (chaoticization) algorithm. Contrarily to existing chaos control techniques that generate modified attractors, the obtained attractors with the PS algorithm belong to the set of the system attractors. It is analytically shown that using the PS algorithm, every system attractor can be expressed as a convex combination of some existing attractors. Interestingly, the PS algorithm can be viewed as a generalization of Parrondo's paradox. [ FROM AUTHOR]
ABSTRACT
COVID-19, a novel coronavirus disease, is still causing concern all over the world. Recently, researchers have been concentrating their efforts on understanding the complex dynamics of this widespread illness. Mathematics plays a big role in understanding the mechanism of the spread of this disease by modeling it and trying to find approximate solutions. In this study, we implement a new technique for an approximation of the analytic series solution called the multistep Laplace optimized decomposition method for solving fractional nonlinear systems of ordinary differential equations. The proposed method is a combination of the multistep method, the Laplace transform, and the optimized decomposition method. To show the ability and effectiveness of this method, we chose the COVID-19 model to apply the proposed technique to it. To develop the model, the Caputo-type fractional-order derivative is employed. The suggested algorithm efficacy is assessed using the fourth-order Runge-Kutta method, and when compared to it, the results show that the proposed approach has a high level of accuracy. Several representative graphs are displayed and analyzed in two dimensions to show the growth and decay in the model concerning the fractional parameter α values. The central processing unit computational time cost in finding graphical results is utilized and tabulated. From a numerical viewpoint, the archived simulations and results justify that the proposed iterative algorithm is a straightforward and appropriate tool with computational efficiency for several coronavirus disease differential model solutions. © 2022 the author(s), published by De Gruyter.
ABSTRACT
In this article, we consider a Covid-19 model for a population involving diabetics as a subclass in the fractal–fractional (FF) sense of derivative. The study includes: existence results, uniqueness, stability and numerical simulations. Existence results are studied with the help of fixed-point theory and applications. The numerical scheme of this paper is based upon the Lagrange's interpolation polynomial and is tested for a particular case with numerical values from available open sources. The results are getting closer to the classical case for the orders reaching to 1 while all other solutions are different with the same behavior. As a result, the fractional order model gives more significant information about the case study.
ABSTRACT
This paper deals with the global dynamics of deterministic-stochastic COVID-19 mathematical model with quarantine class and incorporating a preventive vaccination. Lyapunov functions are utilized for the global stability of disease free equilibrium point and the graph theoretic method is used for the construction of Lyapunov function for positive equilibrium point. The stability of model is discussed regarding the reproductive number. Utilizing the non-standard finite difference scheme for the numerical solution of the deterministic model, the obtained results are shown graphically. Further, environmental noises are added to the model for description of stochastic model. Then we take out the existence and uniqueness of positive solution with extinction for infection. Finally, we solve numerically the stochastic model using Newton Polynomial scheme and present the results graphically.
ABSTRACT
The coronavirus disease 2019 (COVID-19) is a recent outbreak of respiratory infections that have affected millions of humans all around the world. Initially, the major intervention strategies used to combat the infection were the basic public health measure, nevertheless, vaccination is an effective strategy and has been used to control the incidence of many infectious diseases. Currently, few safe and effective vaccines have been approved to control the inadvertent transmission of COVID-19. In this paper, the modeling approach is adopted to investigate the impact of currently available anti-COVID vaccines on the dynamics of COVID-19. A new fractional-order epidemic model by incorporating the vaccination class is presented. The fractional derivative is considered in the well-known Caputo sense. Initially, the proposed vaccine model for the dynamics of COVID-19 is developed via integer-order differential equations and then the Caputo-type derivative is applied to extend the model to a fractional case. By applying the least square method, the model is fitted to the reported cases in Pakistan and some of the parameters involved in the models are estimated from the actual data. The threshold quantity ( R 0 ) is computed by the Next-generation method. A detailed analysis of the fractional model, such as positivity of model solution, equilibrium points, and stabilities on both disease-free and endemic states are discussed comprehensively. An efficient iterative method is utilized for the numerical solution of the proposed model and the model is then simulated in the light of vaccination. The impact of important influential parameters on the pandemic dynamics is shown graphically. Moreover, the impact of different intervention scenarios on the disease incidence is depicted and it is found that the reduction in the effective contact rate (up to 30%) and enhancement in vaccination rate (up to 50%) to the current baseline values significantly reduced the disease new infected cases.
ABSTRACT
In this study, we estimate the basic reproduction number (R0 ) for the ongoing COVID-19 pandemic for 10 seriously affected states and for the whole country for the lockdown period. For this, we formulate a SEIQHR mathematical model and fitted it to cumulative COVID-19 cases. The Government of India implemented the first phase of nationwide lockdown from March 25, 2020 to April 14, 2020 and extended the same from April 15, 2020 to May 3, 2020. We measure the effectiveness of the nationwide lockdown on the spread of COVID-19 in India. For this, we have estimated the basic reproduction number for three phases;namely March 14–31, 2020 (Phase I), April 1–15, 2020 (Phase II), and April 16–30, 2020 (Phase III). Our study finds that, in all the cases, the value of the R0 is minimum at the end of phase III. This demonstrates the success of the implementation of lockdown in reducing the value of the basic reproduction number. © 2021, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
ABSTRACT
In this article, we are studying a Covid-19 mathematical model in the fractal-fractional sense of operators for the existence of solution, Hyers-Ulam (HU) stability and computational results. For the qualitative analysis, we convert the model to an equivalent integral form and investigate its qualitative analysis with the help of iterative convergent sequence and fixed point approach. For the computational aspect, we take help from the Lagrange's interpolation and produce a numerical scheme for the fractal-fractional waterborne model. The scheme is then tested for a case study and we obtain interesting results.
ABSTRACT
In this paper, a mathematical model is formulated to study the transmission dynamics of the novel coronavirus infection under the effect of treatment. The compartmental model is firstly formulated using a system of nonlinear ordinary differential equations. Then, with the help of Caputo operator, the model is reformulated in order to obtain deeper insights into disease dynamics. The basic mathematical features of the time fractional model are rigorously presented. The nonlinear least square procedure is implemented in order to parameterize the model using COVID-19 cumulative cases in Saudi Arabia for the selected time period. The important threshold parameter called the basic reproduction number is evaluated based on the estimated parameters and is found R 0 ≈ 1.60 . The fractional Lyapunov approach is used to prove the global stability of the model around the disease free equilibrium point. Moreover, the model in Caputo sense is solved numerically via an efficient numerical scheme known as the fractional Adamas-Bashforth-Molten approach. Finally, the model is simulated to present the graphical impact of memory index and various intervention strategies such as social-distancing, disinfection of the virus from environment and treatment rate on the pandemic peaks. This study emphasizes the important role of various scenarios in these intervention strategies in curtailing the burden of COVID-19.
ABSTRACT
In the present investigations, we construct a new mathematical for the transmission dynamics of corona virus (COVID-19) using the cases reported in Kingdom of Saudi Arabia for March 02 till July 31, 2020. We investigate the parameters values of the model using the least square curve fitting and the basic reproduction number is suggested for the given data is â0 ≈ 1.2937. The stability results of the model are shown when the basic reproduction number is â0 < 1. The model is locally asymptotically stable when â0 < 1. Further, we show some important parameters that are more sensitive to the basic reproduction number â0 using the PRCC method. The sensitive parameters that act as a control parameters that can reduce and control the infection in the population are shown graphically. The suggested control parameters can reduce dramatically the infection in the Kingdom of Saudi Arabia if the proper attention is paid to the suggested controls.