Numerical dynamics of a size-structured influenza model with viral load transmission

Abstract

The multi-scale models provide a crucial theoretical framework for connecting immunology and epidemiology, which reveals how the interaction between the virus and the host’s immune response at the individual level affects the transmission dynamics of the disease in the population. Based on a multi-scale influenza model that integrates the influenza A viruses (IAVs) load within a host and the concentration of CD8 + T cells (CTLs), this paper establishes a dynamic link from the immune response to the population-level transmission and recovery rates. The resulting numerical system is analyzed using the linear implicit Euler method. Our analysis of its long-term dynamical properties demonstrates that the system is unconditionally positive, uniformly bounded, and first-order convergence. Furthermore, based on the numerical basic reproduction number, we prove the existence and stability of the numerical equilibria. Numerical experiments are conducted to verify the algorithmic convergence and to analyze trade-offs of the kinetics of the within a host and the transmission of between hosts, thus highlighting the key role of the immune response mechanism in shaping epidemic transmission dynamics.