A novel comparative fractional-order modeling of omicron dynamics: Vaccination impact and control strategies in the USA

This article presents a new mathematical model to look into how the COVID-19 Omicron variant spreads, taking into account the impact of vaccination campaigns. Using a compartmental approach, we divide the population into nine epidemiological groups: susceptible, exposed, asymptomatic, symptomatic, Omicron-infected, vaccinated, clinically recorded, quarantined, and recovered individuals. We then use first- and second-order ordinary differential equations to model the interactions between these groups. The ABC derivative is used to extend the model into a fractional as well as fractal–fractional order system. Moreover, we investigate fractional and fractal fractional order systems for the proposed model in a comparative sense. The inclusion of fractional and fractal–fractional order systems allows for a more nuanced understanding of the dynamics within each epidemiological group. By exploring these alternative mathematical frameworks, we can gain insights into the complex interactions that shape the spread and control of infectious diseases like Omicron. Apart from our research, it also concentrates on the stability of equilibrium points, the basic reproduction number, and the success of vaccination campaigns. Solutions and behaviors are shown using MATLAB produced graphical representations. For public health decision-makers, this study clarifies the dynamics of the Omicron outbreak and the consequences of vaccination, so guiding their decisions.