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
In this paper, we convert the recent COVID-19 model with the use of the most influential theories, such as variable fractional calculus and fuzzy theory. We propose the fuzzy variable fractional differential equation for the COVID-19 model in which the variable fractional-order derivative is described using the Caputo-Fabrizio in the Caputo sense. Furthermore, we provide the results on the existence and uniqueness using Lipschitz conditions. Also, discuss the stability analysis of the present new COVID-19 model by employing Hyers-Ulam stability.
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).
ABSTRACT
The real world is filled with uncertainty, vagueness, and imprecision. The concepts we meet in everyday life are vague rather than precise. In real-world situations, if a model requires that conclusions drawn from it have some bearings on reality, then two major problems immediately arise, viz. real situations are not usually crisp and deterministic;complete descriptions of real systems often require more comprehensive data than human beings could recognize simultaneously, process and understand. Conventional mathematical tools which require all inferences to be exact, are not always efficient to handle imprecisions in a wide variety of practical situations. Following the latter development, a lot of attention has been paid to examining novel L-fuzzy analogues of conventional functional equations and their various applications. In this paper, new coincidence point results for single-valued mappings and an L-fuzzy set-valued map in metric spaces are proposed. Regarding novelty and generality, the obtained invariant point notions are compared with some well-known related concepts via non-trivial examples. It is observed that our principal results subsume and refine some important ones in the corresponding domains. As an application, one of our results is utilized to discuss more general existence conditions for realizing the solutions of a non-integer order inclusion model for COVID-19.
ABSTRACT
A fractional order COVID-19 model consisting of six compartments in Caputo sense is constructed. The indirect transmission of the virus through susceptible populations by the shedding effect is studied. Equilibrium solutions are calculated, and basic reproduction ratio (that depends both on direct and indirect mode of transmission), existence and uniqueness, as well as stability analysis of the solution of the model, are studied. The paper studies the effect of optimal control policy applied to shedding effect. The control is the observation of standard hygiene practices and chemical disinfectants in public spaces. Numerical simulations are carried out to support the analytic result and to show the significance of the fractional order from the biological viewpoint.
ABSTRACT
In this article, Euler's technique was employed to solve the novel post-pandemic sector-based investment mathematical model. The solution was established within the framework of the new generalized Caputo-type fractional derivative for the system under consideration that serves as an example of the investment model. The mathematical investment model consists of a system of four fractional-order nonlinear differential equations of the generalized Liouville–Caputo type. Moreover, the existence and uniqueness of solutions for the above fractional order model under pandemic situations were investigated using the well-known Schauder and Banach fixed-point theorem technique. The stability analysis in the context of Ulam—Hyers and generalized Ulam—Hyers criteria was also discussed. Using the investment model under consideration, a new analysis was conducted. Figures that depict the behavior of the classes of the projected model were used to discuss the obtained results. The demonstrated results of the employed technique are extremely emphatic and simple to apply to the system of non-linear equations. When a generalized Liouville–Caputo fractional derivative parameter (ρ) is changed, the results are asymmetric. The current work can attest to the novel generalized Caputo-type fractional operator's suitability for use in mathematical epidemiology and real-world problems towards the future pandemic circumstances.
ABSTRACT
In this paper, we study a Caputo-Fabrizio fractional order epidemiological model for the transmission dynamism of the severe acute respiratory syndrome coronavirus 2 pandemic and its relationship with Alzheimer's disease. Alzheimer's disease is incorporated into the model by evaluating its relevance to the quarantine strategy. We use functional techniques to demonstrate the proposed model stability under the Ulam-Hyres condition. The Adams-Bashforth method is used to determine the numerical solution for our proposed model. According to our numerical results, we notice that an increase in the quarantine parameter has minimal effect on the Alzheimer's disease compartment.Copyright © 2022 The Author(s)
ABSTRACT
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
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.
ABSTRACT
The deadly coronavirus disease 2019 (COVID-19) has recently affected each corner of the world. Many governments of different countries have imposed strict measures in order to reduce the severity of the infection. In this present paper, we will study a mathematical model describing COVID-19 dynamics taking into account the government action and the individuals reaction. To this end, we will suggest a system of seven fractional deferential equations (FDEs) that describe the interaction between the classical susceptible, exposed, infectious, and removed (SEIR) individuals along with the government action and individual reaction involvement. Both human-to-human and zoonotic transmissions are considered in the model. The well-posedness of the FDEs model is established in terms of existence, positivity, and boundedness. The basic reproduction number (BRN) is found via the new generation matrix method. Different numerical simulations were carried out by taking into account real reported data from Wuhan, China. It was shown that the governmental action and the individuals' risk awareness reduce effectively the infection spread. Moreover, it was established that with the fractional derivative, the infection converges more quickly to its steady state.
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
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.
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
In this paper, we consider a mathematical model of a coronavirus disease involving the Caputo-Fabrizio fractional derivative by dividing the total population into the susceptible population S ( t ) , the vaccinated population V ( t ) , the infected population I ( t ) , the recovered population R ( t ) , and the death class D ( t ) . A core goal of this study is the analysis of the solution of a proposed mathematical model involving nonlinear systems of Caputo-Fabrizio fractional differential equations. With the help of Lipschitz hypotheses, we have built sufficient conditions and inequalities to analyze the solutions to the model. Eventually, we analyze the solution for the formed mathematical model by employing Krasnoselskii's fixed point theorem, Schauder's fixed point theorem, the Banach contraction principle, and Ulam-Hyers stability theorem.
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
Arrival of a new disease marks a yearlong destruction of human lives and economy in general, and if the disease turns out to be a pandemic the loss is frightening. COVID-19 is one such pandemic that has claimed millions of lives till date. There is a suffering throughout the world due to various factors associated with the pandemic, be it loss of livelihoods because of sudden shutdown of companies and lockdown, or loss of lives due to lack of medical aid and inadequate vaccination supplies. In this study, we develop a six-compartmental epidemiological model incorporating vaccination. The motivation behind the study is to analyze the significance of higher vaccination efficacy and higher rate of population getting vaccinated in controlling the rise in infectives and thereby the untimely demise of various individuals. The work begins with an ordinary differential equation model followed by stability analysis of the same, after which a fractional-order derivative model of the same is formulated and the existence of uniformly stable solution for the system is proved. In addition to this, we present the stability of the equilibria in general for the fractional model framed. The sensitivity analysis of the basic reproduction number along with its correlation with various parameters is presented. In addition to this, sensitivity of certain state variables in the fractional model with respect to different fractional orders as well with respect to different infection rate is exhibited in this work. Factors related to lockdown and usage of face shields are incorporated in the entire study, and importance of these is highlighted in the study as well. The major takeaway from the study is that mere vaccination will not suffice in eradication of the virus. The vaccine efficacy plays a major role along with other intervention included in the model. The numerical simulations are carried out in MATLAB software using ode45 and fde12. [ FROM AUTHOR] Copyright of International Journal of Biomathematics is the property of World Scientific Publishing Company 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
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
Resource availability plays a pivotal role in the fight against emerging infections such as COVID-19. In the event where there are limited resources the control of an epidemic disease tends to be slow and the disease spread faster in the human population. In this paper, we are motivated to formulate and investigate a mathematical model via the Caputo derivative which incorporates the impact of limited resources on COVID-19 transmission dynamics in the population. We analyze the fractional model by computing the equilibrium points, and basic reproduction number, (R0), and also used the Banach-fixed point theorem to prove the existence and uniqueness of the solution of the model. The impact of each parameter on the dynamical spread of COVID-19 was examined by the help of Sensitivity analysis. Results from mathematical analyses depict that the disease-free equilibrium is stable if R0 < 1 and unstable otherwise. Numerical simulations were carried out at different fractional order derivatives to understand the impact of several model parameters on the dynamics of the infection which can be used to establish the influential parameter driving the epidemic transmission path. Our numerical results show that an increase in the recovery rate of hospitalization increases the number of infected individuals. The results of this work can help policymakers to devise strategies to reduce the COVID-19 infection. © 2023, SCIK Publishing Corporation. All rights reserved.
ABSTRACT
In this work, we present a model that uses the fractional order Caputo derivative for the novel Coronavirus disease 2019 (COVID-19) with different hospitalization strategies for severe and mild cases and incorporate an awareness program. We generalize the SEIR model of the spread of COVID-19 with a private focus on the transmissibility of people who are aware of the disease and follow preventative health measures and people who are ignorant of the disease and do not follow preventive health measures. Moreover, individuals with severe, mild symptoms and asymptomatically infected are also considered. The basic reproduction number (R0) and local stability of the disease-free equilibrium (DFE) in terms of R0 are investigated. Also, the uniqueness and existence of the solution are studied. Numerical simulations are performed by using some real values of parameters. Furthermore, the immunization of a sample of aware susceptible individuals in the proposed model to forecast the effect of the vaccination is also considered. Also, an investigation of the effect of public awareness on transmission dynamics is one of our aim in this work. Finally, a prediction about the evolution of COVID-19 in 1000 days is given. For the qualitative theory of the existence of a solution, we use some tools of nonlinear analysis, including Lipschitz criteria. Also, for the numerical interpretation, we use the Adams-Moulton-Bashforth procedure. All the numerical results are presented graphically. © 2023 Tech Science Press. All rights reserved.