Modelling Immune Memory Development.

The cellular adaptive immune response to influenza has been analyzed through several recent mathematical models. In particular, Zarnitsyna et al. (Front Immunol 7:1-9, 2016) show how central memory CD8+ T cells reach a plateau after repeated infections, and analyze their role in the immune response to further challenges. In this paper, we further investigate the theoretical features of that model by extracting from the infection dynamics a discrete map that describes the build-up of memory cells. Furthermore, we show how the model by Zarnitsyna et al. (Front Immunol 7:1-9, 2016) can be viewed as a fast-scale approximation of a model allowing for recruitment of target epithelial cells. Finally, we analyze which components of the model are essential to understand the progressive build-up of immune memory. This is performed through the analysis of simplified versions of the model that include some components only of immune response. The analysis performed may also provide a theoretical framework for understanding the conditions under which two-dose vaccination strategies can be helpful.