Investigation of Numerical Solutions for a Fractional Seasonal Influenza Model in Deterministic Environments

ABSTRACT In this research, we study numerical solutions for a deterministic fractional seasonal influenza model. Using seasonal fluctuations and population dynamics, the model, which was formulated using the definition of Caputo fractional calculus, provides a nuanced view of the dynamics of the influenza transmission. We also demonstrate the existence and uniqueness of solutions by applying the fixed‐point theorem, which ensures the stability of our model. In addition, we employ a powerful approach to efficiently generate numerical solutions by the Laplace residual power series method. Further, we validate the precision and efficacy of our proposed approach by employing extensive numerical simulations and comparative analyses. This work advances our knowledge of fractional epidemiological models and aids in the management and containment of seasonal influenza outbreaks.