Dynamics and Optimal Control of a Size-Structured Influenza Model Linking Within-Host and Between-Host

Abstract

Multi-scale models improve the prediction of key epidemic factors and dis- ease prevalence by capturing the interaction between individual immune responses and the spread of diseases among the population, helping to implement targeted con- trol strategies for disease management. In this paper, we develop a novel size-structu- red 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 rigor- ously prove the conditions under which the feasible equilibrium exists and is stable. Then, by evaluating the effectiveness of four measures consisting of individual antivi- ral 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.

Keywords

Multi-scale influenza model / size-structure / optimal control / cost-effectiveness