A caputo fractional order epidemic model for evaluating the effectiveness of high-risk quarantine and vaccination strategies on the spread of COVID-19.

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.

Assessing the impact of SARS-CoV-2 infection on the dynamics of dengue and HIV via fractional derivatives.

A new non-integer order mathematical model for SARS-CoV-2, Dengue and HIV co-dynamics is designed and studied. The impact of SARS-CoV-2 infection on the dynamics of dengue and HIV is analyzed using the tools of fractional calculus. The existence and uniqueness of solution of the proposed model are established employing well known Banach contraction principle. The Ulam-Hyers and generalized Ulam-Hyers stability of the model is also presented. We have applied the Laplace Adomian decomposition method to investigate the model with the help of three different fractional derivatives, namely: Caputo, Caputo-Fabrizio and Atangana-Baleanu derivatives. Stability analyses of the iterative schemes are also performed. The model fitting using the three fractional derivatives was carried out using real data from Argentina. Simulations were performed with each non-integer derivative and the results thus obtained are compared. Furthermore, it was concluded that efforts to keep the spread of SARS-CoV-2 low will have a significant impact in reducing the co-infections of SARS-CoV-2 and dengue or SARS-COV-2 and HIV. We also highlighted the impact of three different fractional derivatives in analyzing complex models dealing with the co-dynamics of different diseases.

Some theoretical and computation results about COVID-19 by using a fractional-order mathematical model

The SARS-CoV-2 coronavirus is spreading with very high speed throughout the world. The WHO has declared it a pandemic. In this regard, various researchers are working to develop a procedure or medications to control and cure it. For this, mathematical models have been developed to understand the transmission dynamics of the disease. Since the disease is transmitted from person to person, experts advise to keep social distance and to avoid unnecessary migration so that transmission may be reduced. This chapter is devoted to population dynamical models of fractional order and fuzzy population models to investigate COVID-19. Investigation of the proposed models corresponding to different values of migration of healthy and infected populations is carried out using different techniques. Also some existence results are established by using a fixed point theory approach and nonlinear analysis. Moreover, some semianalytical results related to approximate solution of both proposed models are investigated by using Laplace transform coupled with the Adomian decomposition method. The results are presented graphically. © 2022 Elsevier Inc. All rights reserved.

Investigation of a time-fractional COVID-19 mathematical model with singular kernel.

We investigate the fractional dynamics of a coronavirus mathematical model under a Caputo derivative. The Laplace-Adomian decomposition and Homotopy perturbation techniques are applied to attain the approximate series solutions of the considered system. The existence and uniqueness solution of the system are presented by using the Banach fixed-point theorem. Ulam-Hyers-type stability is investigated for the proposed model. The obtained approximations are compared with numerical simulations of the proposed model as well as associated real data for numerous fractional-orders. The results reveal a good comparison between the numerical simulations versus approximations of the considered model. Further, one can see good agreements are obtained as compared to the classical integer order.

Applying Laplace Adomian decomposition method (LADM) for solving a model of Covid-19.

In this study, we apply the Laplace Adomian decomposition method (LADM) for the mathematical model of Covid-19. The mathematical model includes a system of nonlinear ordinary differential equations. Therefore, the model cannot be solved analytically but only by approximation. The application of LADM approximates the solution profiles of the dynamical variables of the Covid-19 model by an analytical power series. The conventional way to calculate the expressions of the approximation solutions is complicated both in terms of mathematical calculations and in terms of computer run time. In this paper, we propose a new algorithm for implementing the LADM method combined with the singularly perturbed vector field (SPVF) method. The new algorithm we offer is significantly reducing the running time of both the computer and the mathematical calculations. We compared the results obtained from the LADM to the numerical simulations. Some plots are presented to show the reliability and simplicity of the new algorithm.

Theoretical and numerical analysis of novel COVID-19 via fractional order mathematical model.

In the work, author's presents a very significant and important issues related to the health of mankind's. Which is extremely important to realize the complex dynamic of inflected disease. With the help of Caputo fractional derivative, We capture the epidemiological system for the transmission of Novel Coronavirus-19 Infectious Disease (nCOVID-19). We constructed the model in four compartments susceptible, exposed, infected and recovered. We obtained the conditions for existence and Ulam's type stability for proposed system by using the tools of non-linear analysis. The author's thoroughly discussed the local and global asymptotical stabilities of underling model upon the disease free, endemic equilibrium and reproductive number. We used the techniques of Laplace Adomian decomposition method for the approximate solution of consider system. Furthermore, author's interpret the dynamics of proposed system graphically via Mathematica, from which we observed that disease can be either controlled to a large extent or eliminate, if transmission rate is reduced and increase the rate of treatment.