Deep learning-based predictions and analysis of Norovirus dynamics using a fractional-order mathematical model

Norovirus, which is extremely contagious and has a significant impact on the gastrointestinal tract, has also been one of the main potential threats to health in the population. The use of fractional calculus has received much interest in the past few years with regard to the modeling of infectious diseases, especially because it allows modeling the memory and nonlocal processes in a dynamic system. In this study, a mathematical model is developed to investigate the transmission dynamics of norovirus. The proposed model consists of five epidemiological compartments: susceptible, exposed, infected, vaccinated, and recovered populations. The existence and uniqueness of the mathematical model are proven by a fixed-point theorem. The findings demonstrate that the sustainability of the disease-free equilibrium increases with a decrease in fractional order. In order to observe the effects of the fractional order on the dynamics of disease, numerical simulations are carried out based on the three-step Adams-Bashforth procedure, which supports the theoretical results with graphical illustrations. Moreover, the results are validated through the comparison with deep neural networks. The comprehensive nature of numerical simulations carried out at different fractional orders and transmission parameters indicates that the dynamics of fractional orders are effective in describing memory and heterogeneity of the disease transmission, which are characterized by classical integer-order models only to a limited extent. The results also indicate that the high coverage of vaccination and improvement in the effectiveness of treatment will greatly decrease the prevalence of infections. Further, the model has been demonstrated to be numerically stable and positive in real parameter disclosures. Altogether, this study provides a reliable mathematical approach and better understanding for analyzing disease dynamics and may be extended to other applications in epidemiology and related scientific fields.