ABSTRACT
Throughout history, infectious diseases have been the cause of outbreaks and the deaths of people. It is crucial for endemic disease management to be able to forecast the number of infections at a given moment and the frequency of new infections so that the appropriate precautions can be taken. The COVID-19 pandemic has highlighted the value of mathematical modeling of pandemics. The susceptible–infected–quarantined–recovered–vaccinated (SIQRV) epidemic model was used in this work. Symmetrical aspects of the proposed dynamic model, disease-free equilibrium, and stability were analyzed. The symmetry of the population size over time allows the model to find stable equilibrium points for any parameter value and initial conditions. The assumption of the strong symmetry of the initial conditions and parameter values plays a key role in the analysis of the fractional SIQRV model. In order to combat the pandemic nature of the disease, control the disease in the population, and increase the possibility of eradicating the disease, effective control measures include quarantine and immunization. Fractional derivatives are used in the Caputo sense. In the model, vaccination and quarantine are two important applications for managing the spread of the pandemic. Although some of the individuals who were vaccinated with the same type and equal dose of vaccine gained strong immunity thanks to the vaccine, the vaccine could not give sufficient immunity to the other part of the population. This is thought to be related the structural characteristics of individuals. Thus, although some of the individuals vaccinated with the same strategy are protected against the virus for a long time, others may become infected soon after vaccination. Appropriate parameters were used in the model to reflect this situation. In order to validate the model, the model was run by taking the COVID-19 data of Türkiye about a year ago, and the official data on the date of this study were successfully obtained. In addition to the stability analysis of the model, numerical solutions were obtained using the fractional Euler method. © 2023 by the authors.
ABSTRACT
In this article, we investigate the dynamics of COVID-19 with a new approach of piecewise global derivative in the sense of singular and non-singular kernels. The singular kernel operator is a Caputo derivative, whereas the non-singular operator is an Atangana-Baleanu Caputo operator. The said problem is investigated for the existence and uniqueness of a solution with a piecewise derivative. The approximate solution to the proposed problem has been obtained by the piecewise numerical iterative technique of Newton polynomials. The numerical scheme for piecewise derivatives in the sense of singular and non-singular kernels is also developed. The numerical simulation for the considered piecewise derivable problem has been drawn up against the available data for different fractional orders. This will be useful for easy understanding of the concept of piecewise global derivatives and the crossover problem dynamics.
ABSTRACT
We investigate a mathematical system of the recent COVID-19 disease focusing particularly on the transmissibility of individuals with different types of signs under the Caputo fractional derivative. To get the approximate solutions of the fractional order system we employ the fractional-order Alpert multiwavelet(FAM). The fractional operational integration matrix of Riemann-Liouville (RLFOMI) employing the FAM functions is considered. The origin system will be transformed into a system of algebraic equations. Also, an error estimation of the supposed scheme is considered. Satisfactory results are gained under various values of fractional order with the chosen initial conditions (ICs).
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The preeminent target of present study is to reveal the speed characteristic of ongoing outbreak COVID-19 due to novel coronavirus. On January 2020, the novel coronavirus infection (COVID-19) detected in India, and the total statistic of cases continuously increased to 7 128 268 cases including 109 285 deceases to October 2020, where 860 601 cases are active in India. In this study, we use the Hermite wavelets basis in order to solve the COVID-19 model with time- arbitrary Caputo derivative. The discussed framework is based upon Hermite wavelets. The operational matrix incorporated with the collocation scheme is used in order to transform arbitrary-order problem into algebraic equations. The corrector scheme is also used for solving the COVID-19 model for distinct value of arbitrary order. Also, authors have investigated the various behaviors of the arbitrary-order COVID-19 system and procured developments are matched with exiting developments by various techniques. The various illustrations of susceptible, exposed, infected, and recovered individuals are given for its behaviors at the various value of fractional order. In addition, the proposed model has been also supported by some numerical simulations and wavelet-based results.
ABSTRACT
In this manuscript, the mathematical model of COVID-19 is considered with eight different classes under the fractional-order derivative in Caputo sense. A couple of results regarding the existence and uniqueness of the solution for the proposed model is presented. Furthermore, the fractional-order Taylor's method is used for the approximation of the solution of the concerned problem. Finally, we simulate the results for 50 days with the help of some available data for fractional differential order to display the excellency of the proposed model.
ABSTRACT
The recent global Coronavirus disease (COVID-19) threat to the human race requires research on preventing its reemergence without affecting socio-economic factors. This study proposes a fractional-order mathematical model to analyze the impact of high-risk quarantine and vaccination on COVID-19 transmission. The proposed model is used to analyze real-life COVID-19 data to develop and analyze the solutions and their feasibilities. Numerical simulations study the high-risk quarantine and vaccination strategies and show that both strategies effectively reduce the virus prevalence, but their combined application is more effective. We also demonstrate that their effectiveness varies with the volatile rate of change in the system's distribution. The results are analyzed using Caputo fractional order and presented graphically and extensively analyzed to highlight potent ways of curbing the virus.
ABSTRACT
Coronavirus disease 2019 (COVID-19), an infection that is highly contagious. It has a regrettable effect on the world and has resulted in more than 4.6 million deaths to date (July 2021). For this contagious disease, numerous nations implemented control measures. Every country has vaccination programs in place to achieve the best results. This research is done in two stages, including partial and complete vaccination, to enhance the efficiency and effectiveness of the vaccination. Our study found that receiving this vaccination lowers the risk of contracting a disease and its side effects, such as severity, hospitalization, need for oxygen, admission to the intensive care unit, and infection-related death. Taking into account, the system is built using fractional-order Caputo sense nonlinear differential equations. A basic reproduction number is calculated to determine the transmission rate. The bifurcation analysis predicts chaotic behavior of a system for this threshold value. The suggested system's recovery rate is optimized using fractional optimum controls. For the fractional-order differential equation, numerical results are simulated using MATLAB software using real-validated data (July 2021).
ABSTRACT
In the given manuscript, the fractional mathematical model for the current pandemic of COVID-19 is investigated. The model is composed of four agents of susceptible (S), infectious (I), quarantined (Q) and recovered (R) cases respectively. The fractional operator of Atangana-Baleanu-Caputo (ABC) is applied to the considered model for the fractional dynamics. The basic reproduction number is computed for the stability analysis. The techniques of existence and uniqueness of the solution are established with the help of fixed point theory. The concept of stability is also derived using the Ulam-Hyers stability technique. With the help of the fractional order numerical method of Adams-Bashforth, we find the approximate solution of the said model. The obtained scheme is simulated on different fractional orders along with the comparison of integer orders. Varying the numerical values for the contact rate ζ, different simulations are performed to check the effect of it on the dynamics of COVID-19.
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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.
ABSTRACT
Currently, the entire planet is suffering from a contagious epidemic infection, 2019-nCOV due to newly detected coronavirus. This is a lethal infectious virus that has destroyed thousands of lives all over the world. The important aim of this study is to investigate a susceptible-infected-treatment-recovered (SITR) model of coronavirus (2019-nCOV) with bi-modal virus spread in a susceptible population. The considered 2019-nCOV model is analyzed by two fractional derivatives: the Caputo and Atangana-Baleanu-Caputo (ABC). For the Caputo model, we present a few basic mathematical characteristics such as existence, positivity, boundedness and stability result for disease-free equilibria. The fixed-point principle is used to establish the existence and uniqueness conditions for the ABC model solution. We employed the Adams-Bashforth-Moulton (ABM) numerical technique for the Caputo model solution and the Toufik-Atangana (TA) numerical approach for the ABC model solution. Finally, using MATLAB, the simulation results are shown to highlight the impact of arbitrarily chosen fractional-order and model parameters on infection dynamics. © 2022 The Author(s).
ABSTRACT
In this work, we generalize the multi-vaccination for COVID-19 mathematical model to the variable-order fractional derivative case by replacing the first-order derivative with the variable-order fractional Atangana-Baleanu-Caputo operator. Moreover, the parameters of the proposed model are dependent on the variable-order fractional derivative. We use an amended numerical technique to build an asymptotically stable difference scheme. The proposed scheme accurately simulates the behavior of the solution of the presented model. Some properties, boundedness, and positivity of the studied system are proved analytically. The introduced scheme preserves these properties of the analytic solutions. Numerical treatment is run out for testing the reliability, applicability, and simplicity of this scheme. Comparitive study bettween the obtained results using the discretization of Atangana-Baleanu-Caputo derivative and nonstandard finite differeance method with the results which obtained using the discretization of the operator Yang-Abdel-Cattani is given.
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New atypical pneumonia caused by a virus called Coronavirus (COVID-19) appeared in Wuhan, China in December 2019. Unlike previous epidemics due to the severe acute respiratory syndrome (SARS) and the Middle East respiratory syndrome coronavirus (MERS-CoV), COVID-19 has the particularity that it is more contagious than the other previous ones. In this paper, we try to predict the COVID-19 epidemic peak in Japan with the help of real-time data from January 15 to February 29, 2020 with the uses of fractional derivatives, namely, Caputo derivatives, the Caputo-Fabrizio derivatives, and Atangana-Baleanu derivatives in the Caputo sense. The fixed point theory and Picard-Lindel of approach used in this study provide the proof for the existence and uniqueness analysis of the solutions to the noninteger-order models under the investigations. For each fractional model, we propose a numerical scheme as well as prove its stability. Using parameter values estimated from the Japan COVID-19 epidemic real data, we perform numerical simulations to confirm the effectiveness of used approximation methods by numerical simulations for different values of the fractional-order gamma, and to give the predictions of COVID-19 epidemic peaks in Japan in a specific range of time intervals.
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In this paper, we analyzed and found the solution for a suitable nonlinear fractional dynamical system that describes coronavirus (2019-nCoV) using a novel computational method. A compartmental model with four compartments, namely, susceptible, infected, reported and unreported, was adopted and modified to a new model incorporating fractional operators. In particular, by using a modified predictor–corrector method, we captured the nature of the obtained solution for different arbitrary orders. We investigated the influence of the fractional operator to present and discuss some interesting properties of the novel coronavirus infection. © 2022 by the authors. Licensee MDPI, Basel, Switzerland.
ABSTRACT
In this paper, we develop a mathematical model with a Caputo fractional derivative under fuzzy sense for the prediction of COVID-19. We present numerical results of the mathematical model for COVID-19 of most three infected countries such as the USA, India and Italy. Using the proposed model, we estimate predicting future outbreaks, the effectiveness of preventive measures and potential control strategies of the infection. We provide a comparative study of the proposed model with Ahmadian’s fuzzy fractional mathematical model. The results demonstrate that our proposed fuzzy fractional model gives a nearer forecast to the actual data. The present study can confirm the efficiency and applicability of the fractional derivative under uncertainty conditions to mathematical epidemiology. [ FROM AUTHOR] Copyright of Journal of Intelligent & Fuzzy Systems is the property of IOS Press 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 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 . (Copyright applies to all s.)
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
Extended orthogonal spaces are introduced and proved pertinent fixed point results. Thereafter, we present an analysis of the existence and unique solutions of the novel coronavirus 2019-nCoV/SARS-CoV-2 model via fractional derivatives. To strengthen our paper, we apply an efficient numerical scheme to solve the coronavirus 2019-nCoV/SARS-CoV-2 model with different types of differential operators.
Subject(s)
COVID-19 , SARS-CoV-2 , HumansABSTRACT
In this paper, we investigate the fractional epidemic mathematical model and dynamics of COVID-19. The Wuhan city of China is considered as the origin of the corona virus. The novel corona virus is continuously spread its range of effectiveness in nearly all corners of the world. Here we analyze that under what parameters and conditions it is possible to slow the speed of spreading of corona virus. We formulate a transmission dynamical model where it is assumed that some portion of the people generates the infections, which is affected by the quarantine and latent time. We study the effect of various parameters of corona virus through the fractional mathematical model. The Laguerre collocation technique is used to deal with the concerned mathematical model numerically. In order to deal with the dynamics of the novel corona virus we collect the experimental data from 15th-21st April, 2020 of Maharashtra state, India. We analyze the effect of various parameters on the numerical solutions by graphical comparison for fractional order as well as integer order. The pictorial presentation of the variation of different parameters used in model are depicted for upper and lower solution both.
ABSTRACT
The current work is of interest to introduce a detailed analysis of the novel fractional COVID-19 model. Non-local fractional operators are one of the most efficient tools in order to understand the dynamics of the disease spread. For this purpose, we intend as an attempt at investigating the fractional COVID-19 model through Caputo operator with order χ ∈ ( 0 , 1 ) . Employing the fixed point theorem, it is shown that the solutions of the proposed fractional model are determined to satisfy the existence and uniqueness conditions under the Caputo derivative. On the other hand, its iterative solutions are indicated by making use of the Laplace transform of the Caputo fractional operator. Also, we establish the stability criteria for the fractional COVID-19 model via the fixed point theorem. The invariant region in which all solutions of the fractional model under investigation are positive is determined as the non-negative hyperoctant R + 7 . Moreover, we perform the parameter estimation of the COVID-19 model by utilizing the non-linear least squares curve fitting method. The sensitivity analysis of the basic reproduction number R 0 c is carried out to determine the effects of the proposed fractional model's parameters on the spread of the disease. Numerical simulations show that all results are in good agreement with real data and all theoretical calculations about the disease.
ABSTRACT
The new emerged infectious disease that is known the coronavirus disease (COVID-19), which is a high contagious viral infection that started in December 2019 in China city Wuhan and spread very fast to the rest of the world. This infection caused million of infected cases globally and still pose an alarming situation for human lives. Pakistan in Asian countries is considered the third country with higher number of cases of coronavirus with more than 200,000. Recently, many mathematical models have been considered to better understand the coronavirus infection. Most of these models are based on classical integer-order derivative which can not capture the fading memory and crossover behavior found in many biological phenomena. Therefore, we study the coronavirus disease in this paper by exploring the dynamics of COVID-19 infection using the non-integer Caputo derivative. In the absence of vaccine or therapy, the role of non-pharmaceutical interventions (NPIs) is examined on the dynamics of theCOVID-19 outbreak in Pakistan. First, we construct the model in integer sense and then apply the fractional operator to have a generalized model. The generalized model is then used to present the detailed theoretical results. We investigate the stability of the model for the case of fractional model using a nonlinear fractional Lyapunov function of Goh-Voltera type. Furthermore, we estimate the values of parameters with the help of least square curve fitting tool for the COVID-19 data recorded in Pakistan since March 1 till June 30, 2020 and show that our considered model give an accurate prediction to the real COVID-19 statistical cases. Finally, numerical simulations are presented using estimated parameters for various values of the fractional order of the Caputo derivative. From the simulation results it is found that the fractional order provides more insights about the disease dynamics.
ABSTRACT
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.