Mathematical modeling of influenza dynamics: A novel approach with SVEIHR and fractional calculus

Viral infections pose a significant risk to public health all around the world. Knowledge of their transmission and epidemiology therefore forms the basis of prevention and control measures. Models are essential components to develop and quantify the characteristics of new pathogens, to evaluate the risks of emerging diseases, and to design strategies to control epidemics. This study investigates the validity of the fractional-order SVEIHR influenza model in predicting seasonal influenza outbreaks in Saudi Arabia using Atangana–Baleanu–Caputo (ABC) operators. The first part of our analysis was examining the positivity, boundedness, and global stability of the disease-free equilibrium of the model. The effective reproduction number of vaccination was calculated, indicating a decrease in the spread of the virus due to vaccination. Additionally, we determined that the reproduction number in the absence of vaccination suggests a higher rate of virus transmission. Therefore, we concluded that a reduction in [Formula: see text] occurs when vaccination rates increase. Our findings underscore the critical impact of vaccination on controlling the spread of influenza. Then raising coverage of protective vaccines becomes a logical goal for decreasing the basic reproduction number and thus mitigating the epidemic of influenza. We suggest that we extend this model by incorporating additional factors such as antiviral treatments and social behavior changes, which may further influence the dynamics of influenza transmission.