Multi-scale models improve the prediction of key epidemic factors and disease prevalence by capturing the interaction between individual immune responses and the spread of diseases among the population, helping to implement targeted control strategies for disease management. In this paper, we develop a novel size-structured influenza model based on the nested rules, aiming to explore how the replication of influenza virus affects its transmission at a population level. We calculate the basic reproduction numbers separately at the individual and population levels and rigorously prove the conditions under which the feasible equilibrium exists and is stable. Then, by evaluating the effectiveness of four measures consisting of individual antiviral treatment and population vaccination, we can determine an optimal treatment to minimize both the influenza cases and the total expenditure on influenza prevention. Numerical results reveal the complex interactions between the two interventions and the progression of the epidemic.