Stability and complex dynamical analysis of COVID-19 epidemic model with non-singular kernel of Mittag-Leffler law

One of the global problems and a number of societal challenges in the areas of social life, the economy, and international communications is COVID-19. In order to counteract the impact of sickness on society, we created a deterministic COVID-19 model in this study that uses real data to assess the impact of disease, dynamical transmission, quarantine impact, and hospitalized treatment. The model includes a generalized form of the fractal and fractional operator. This study aims to develop a fractal-fractional mathematical model suitable for the lifestyle of the Thai population facing the COVID-19 situation. The model divides the incubation period into the quarantine class and the exposed class, which later moved to the hospitalized infected class and the infected class. The fractal-fractional derivative is used to analyze the dynamics of the population in these classes, providing a more detailed understanding of the epidemic’s progression and the effectiveness of control measures. The existence and uniqueness of the solution were also determined with the Lipschitz condition and fixed point theory. With the use of simulations and functional analysis tools like Ulam-Hyers, we examine the sensitivity analysis of the fractal-fractional model with respect to each parameter effect. We develop a numerical scheme for the fractal-fractional model based on Newton polynomial for computational analysis and convergence solution to steady-state points of real data COVID-19 in Thailand. The verification of the examined fractional-order model with actual COVID-19 data for Thailand demonstrates the potential of the suggested paradigm in forecasting and comprehending the dynamics of the pandemic. Furthermore, the fractal fractional-order derivative gives rise to a range of chaotic behaviors that show how the species has changed over place and time. Fractional-order epidemiological models may help predict and understand the course of the COVID-19 pandemic and provide relevant management approaches.