Analysis and modeling with fractal-fractional operator for an epidemic model with reference to COVID-19 modeling

Abstract

Scientists and epidemiologists have been developing vaccines and immunizing people to stop the spread of COVID-19. Unfortunately, because of the emergence of new strains and persistent infections in different nations, the global effort to combat the disease is still only partially successful. This investigation calculates the epidemiological impact of COVID-19 under mitigation scenarios, which include non-pharmaceutical interventions. In this work, we develop a time-fractional COVID-19 pandemic model using a generalized Mittag-Leffler kernel. The fractal-fractional operator is used to analyze the fluctuation of the infection rate in society. The existence and uniqueness of the proposed scheme are addressed by applying the Banach contraction principle. The Ulam-Hyers stability of the fractal-fractional operator has been confirmed. In the end, numerical simulations of the COVID-19 model of fractional-order are carried out to lower the risk of negative effects of disease on society. As the fractional orders approach 1, the results approach the classical situation, in contrast to all other solutions, which differ and show the same behavior. Consequently, the fractal-fractional order COVID-19 model provides deeper insights into epidemic disease. Such research will help understand the behavior of the virus and help develop COVID-19 prevention strategies for a population.

Keywords

• COVID-19 model
• Banach contraction principle
• Unique solution
• Ulam-Hyers stability
• Two-step lagrange polynomial
• Modeling