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    Numerical study and dynamics analysis of diabetes mellitus with co-infection of COVID-19 virus by using fractal fractional operator
    (Nature Portfolio, 2024) Farman, Muhammad; Akguel, Ali; Sultan, Muhammad; Riaz, Sidra; Asif, Hira; Agarwal, Praveen; Hassani, Murad Khan
    COVID-19 is linked to diabetes, increasing the likelihood and severity of outcomes due to hyperglycemia, immune system impairment, vascular problems, and comorbidities like hypertension, obesity, and cardiovascular disease, which can lead to catastrophic outcomes. The study presents a novel COVID-19 management approach for diabetic patients using a fractal fractional operator and Mittag-Leffler kernel. It uses the Lipschitz criterion and linear growth to identify the solution singularity and analyzes the global derivative impact, confirming unique solutions and demonstrating the bounded nature of the proposed system. The study examines the impact of COVID-19 on individuals with diabetes, using global stability analysis and quantitative examination of equilibrium states. Sensitivity analysis is conducted using reproductive numbers to determine the disease's status in society and the impact of control strategies, highlighting the importance of understanding epidemic problems and their properties. This study uses two-step Lagrange polynomial to analyze the impact of the fractional operator on a proposed model. Numerical simulations using MATLAB validate the effects of COVID-19 on diabetic patients and allow predictions based on the established theoretical framework, supporting the theoretical findings. This study will help to observe and understand how COVID-19 affects people with diabetes. This will help with control plans in the future to lessen the effects of COVID-19.
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    Study of COVID-19 SEWIR Model with Memory Effect of Fractal Derivative on Infectious Reaction Outbreak
    (2025-01-01) Farman, Muhammad; Akgül, Ali; Alshowaikh, Faisal; Hafez, Mohamed; Alkhazaleh, Shawkat; Asif, Hira
    The COVID-19 epidemic was a significant occurrence that had a significant influence on the global economic and health care systems. Machine learning techniques and mathematical models are being used to study the behaviour of the virus and make long and short term forecasts about the daily new cases. In this work, we construct a SEWIR epidemic model in this paper using the Mittag Lefler Kernel in terms of fractal fractional operator. The control rate and infectious force in this model are at their peak during the latent phase. We demonstrate the presence and originality of solutions and determine the model’s fundamental reproductive number R0. For the first and second derivative tests, a global stability investigation is started using the Lyapunov function. Quantitative analysis of the collapse of second derivative equilibrium points to demonstrate the impact of another wave of dynamical transmission. The model’s parameters are subjected to sensitivity analysis in order to the specific factors with the greatest effects on the propagation rate. Infections point analysis was thoroughly explained, and a Mittag Lefler Kernel-based mathematical framework was used to develop the model’s numerical solution.