Mathematical Modeling and Numerical Simulations of Influenza Transmission Dynamics with Structured Infectious Population

Abstract Influenza remains a major public health concern owing to its rapid evolution through antigenic drift and its potential to cause global pandemics. These factors contribute to widespread infection, severe health complications, and significant mortality worldwide. To understand the dynamics of the disease and control the dispersion of influenza, the existing susceptible, exposed, vaccinated, symptomatic infected, asymptomatic infected and recovered () framework is enhanced with a more complex mathematical model. This extension approach allows for the incorporation of multiple factors, including vaccination, waning immunity, and asymptomatic disease carriers. The estimation of , the basic reproduction number of the virus, is one of the outcomes vital to understanding the transmission of the virus. The virus's sensitivity to changes in control measures, such as antivirals and vaccination drives, is analyzed. The non‐standard finite difference method and Runge‐Kutta method are employed for numerical simulations. These results demonstrate a noticeable convergence and accuracy using the NSFD approach, particularly when observing different time intervals. By analyzing both disease‐free and endemic states, interventions aimed at eradicating or stabilizing the virus are assessed. This study provides valuable evidence for the development of effective health strategies. The insights and methods presented in this study can strengthen influenza control efforts and enhance global preparedness for future pandemics.