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    Computational analysis of COVID-19 model outbreak with singular and nonlocal operator
    (Amer Inst Mathematical Sciences-Aims, 2022) Amin, Maryam; Farman, Muhammad; Akgul, Ali; Partohaghighi, Mohammad; Jarad, Fahd
    The SARS-CoV-2 virus pandemic remains a pressing issue with its unpredictable nature, and it spreads worldwide through human interaction. Current research focuses on the investigation and analysis of fractional epidemic models that discuss the temporal dynamics of the SARS-CoV-2 virus in the community. In this work, we choose a fractional-order mathematical model to examine the transmissibility in the community of several symptoms of COVID-19 in the sense of the Caputo operator. Sensitivity analysis of R0 and disease-free local stability of the system are checked. Also, with the assistance of fixed point theory, we demonstrate the existence and uniqueness of the system. In addition, numerically we solve the fractional model and presented some simulation results via actual estimation parameters. Graphically we displayed the effects of numerous model parameters and memory indexes. The numerical outcomes show the reliability, validation, and accuracy of the scheme.
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    Effect of vaccination to control COVID-19 with fractal fractional operator
    (Elsevier, 2022) Amin, Maryam; Farman, Muhammad; Akgul, Ali; Alqahtani, Rubayyi T.
    Currently, Atangana proposed new fractal-fractional operators that had extensively used to observe the unpredictable elements of an issue. COVID-19 is a pervasive infection today and is hard to fix. In this structure, the novel operators have been used to observing the effect of vaccination in the COVID-19 model with different values of eta(1), eta(2) which are used to show the effect of vaccination. The system will be converted into disease-free according to reproductive number. We used the Atangana-Baleanu fractal-fractional operator to investigate the COVID-19 model qualitatively and quantitatively. By using fixed point theorems we proved the existence and uniqueness of the model with the Atangana-Baleanue fractal- fractional operator. A non-linear assessment helped to find out the stability of the Ulam-Hyres. We simulate the mathematical outcomes, to understand the relationship of operators in several senses, for numerous arrangements of fractional and fractal orders. (C) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University.
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    Fractal-fractional operator for COVID-19 (Omicron) variant outbreak with analysis and modeling
    (Elsevier, 2022) Farman, Muhammad; Amin, Maryam; Akguel, Ali; Ahmad, Aqeel; Riaz, Muhammad Bilal; Ahmad, Sheraz
    The fractal-fraction derivative is an advanced category of fractional derivative. It has several approaches to real-world issues. This work focus on the investigation of 2nd wave of Corona virus in India. We develop a time-fractional order COVID-19 model with effects of disease which consist system of fractional differential equations. Fractional order COVID-19 model is investigated with fractal-fractional technique. Also, the deterministic mathematical model for the Omicron effect is investigated with different fractional parameters. Fractional order system is analyzed qualitatively as well as verify sensitivity analysis. The existence and uniqueness of the fractional-order model are derived using fixed point theory. Also proved the bounded solution for new wave omicron. Solutions are derived to investigate the influence of fractional operator which shows the impact of the disease on society. Simulation has been made to understand the actual behavior of the OMICRON virus. Such kind of analysis will help to understand the behavior of the virus and for control strategies to overcome the disseise in community.
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    Fractional order COVID-19 model with transmission rout infected through environment
    (Amer Inst Mathematical Sciences-Aims, 2022) Yao, Shao-Wen; Farman, Muhammad; Amin, Maryam; Inc, Mustafa; Akgul, Ali; Ahmad, Aqeel
    In this paper, we study a fractional order COVID-19 model using different techniques and analysis. The sumudu transform is applied with the environment as a route of infection in society to the proposed fractional-order model. It plays a significant part in issues of medical and engineering as well as its analysis in community. Initially, we present the model formation and its sensitivity analysis. Further, the uniqueness and stability analysis has been made for COVID-19 also used the iterative scheme with fixed point theorem. After using the Adams-Moulton rule to support our results, we examine some results using the fractal fractional operator. Demonstrate the numerical simulations to prove the efficiency of the given techniques. We illustrate the visual depiction of sensitive parameters that reveal the decrease and triumph over the virus within the network. We can reduce the virus by the appropriate recognition of the individuals in community of Saudi Arabia.
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    SIMULATIONS AND ANALYSIS OF COVID-19 AS A FRACTIONAL MODEL WITH DIFFERENT KERNELS
    (World Scientific Publ Co Pte Ltd, 2023) Yao, Shao-wen; Farman, Muhammad; Akgul, Ali; Nisar, Kottakkaran Sooppy; Amin, Maryam; Saleem, Muhammad Umer; Inc, Mustafa
    Recently, Atangana proposed new operators by combining fractional and fractal calculus. These recently proposed operators, referred to as fractal-fractional operators, have been widely used to study complex dynamics. In this paper, the COVID-19 model is considered via Atangana-Baleanu fractal-fractional operator. The Lyapunov stability for the model is derived for first and second derivative. Numerical results have developed through Lagrangian-piecewise interpolation for the different fractal-fractional operators. We develop numerical outcomes through different differential and integral fractional operators like power-law, exponential law, and Mittag-Leffler kernel. To get a better outcome of the proposed scheme, numerical simulation is made with different kernels having the memory effects with fractional parameters.