Computational analysis of a Caputo–Fabrizio fractal–fractional Norovirus model with optimal control

Norovirus is a highly contagious pathogen responsible for numerous outbreaks of gastrointestinal disease and poses a significant public health challenge. In this study, we propose a modified Caputo–Fabrizio fractal–fractional model of norovirus. This model consists of seven compartments (NoV7), including susceptible [Formula: see text], exposed [Formula: see text], infected [Formula: see text], quarantined [Formula: see text], clinically-positive [Formula: see text], vaccinated [Formula: see text], and recovered [Formula: see text] individuals and has been developed to explain the transmission dynamics of norovirus. We have determined the basic reproduction number, [Formula: see text], which estimates the virus’s ability to spread. Both local and global stabilities have been investigated at the infection-free equilibrium point. Furthermore, sensitivity analysis is conducted to evaluate the influence of each parameter on [Formula: see text], providing insights into how changes in these parameters ([Formula: see text]) affect the virus’s transmission dynamics. The basic mathematical model has been expanded to include time-dependent control variables, leading to the development of an optimal control model using various control strategies. Analysis utilizing the Pontryagin maximum principle has determined the conditions for optimal pandemic control. Numerical results indicate that applying control strategies to the fractal–fractional mathematical model in the sense Caputo–Fabrizio, specifically vaccination ([Formula: see text]) and hospitalization ([Formula: see text]), results in a decreased rate of norovirus transmission. The fractal–fractional model provides a more comprehensive understanding of the dynamical behavior and memory effects. This study aids in understanding the dynamic behavior of the mathematical model and the impact of control strategies, which can minimize the spread of infection.