Epidemiological analysis of fractional order COVID-19 model with Mittag-Leffler kernel

• DOI: 10.3934/math.2022046
• Publication Date: 2021-10-16T05:51:53Z
• Authors: Muhammad Farman; ; Ali Akgül; Kottakkaran Soopp...; Dilshad Ahmad; Aqeel Ahmad; Sarfaraz Kamangar; C Ahamed Saleel
• Keywords: Economics; fractal operator; mittag-leffler law; Infectious disease (medical specialty); Operator (biology); Mathematical analysis; Biochemistry; Gene; 01 natural sciences; abc derivative; Health Sciences; QA1-939; FOS: Mathematics; Pathology; Disease; 0101 mathematics; Fixed-point theorem; Anomalous Diffusion Modeling and Analysis; Order (exchange); Mittag-Leffler function; Modeling the Dynamics of COVID-19 Pandemic; Public Health, Environmental and Occupational Health; Fractional calculus; Pure mathematics; Applied mathematics; 3. Good health; Coronavirus disease 2019 (COVID-19); Fractional Derivatives; Chemistry; covid-19; Modeling and Simulation; Disease Transmission and Population Dynamics; Physical Sciences; Kernel (algebra); Repressor; stability and uniqueness; Medicine; Uniqueness; Transcription factor; sumudu transform; Fractal; Mathematics; Finance

<abstract> <p>This paper derived fractional derivatives with Atangana-Baleanu, Atangana-Toufik scheme and fractal fractional Atangana-Baleanu sense for the COVID-19 model. These are advanced techniques that provide effective results to analyze the COVID-19 outbreak. Fixed point theory is used to derive the existence and uniqueness of the fractional-order model COVID-19 model. We also proved the property of boundedness and positivity for the fractional-order model. The Atangana-Baleanu technique and Fractal fractional operator are used with the Sumudu transform to find reliable results for fractional order COVID-19 Model. The generalized Mittag-Leffler law is also used to construct the solution with the different fractional operators. Numerical simulations are performed for the developed scheme in the range of fractional order values to explain the effects of COVID-19 at different fractional values and justify the theoretical outcomes, which will be helpful to understand the outbreak of COVID-19 and for control strategies.</p> </abstract>