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The current influenza vaccine provides narrow protection against the strains included in the vaccine, and needs to be reformulated every few years in response to the constantly evolving new strains. Novel approaches are directed towards developing vaccines that provide broader protection by targeting B and T cell epitopes that are conserved between different strains of the virus. In this paper, we focus on developing mathematical models to explore the CD8 T cell responses to influenza, how they can be boosted, and the conditions under which they contribute to protection. Our models suggest that the interplay between spatial heterogeneity (with the virus infecting the respiratory tract and the immune response being generated in the secondary lymphoid organs) and T cell differentiation (with proliferation occurring in the lymphoid organs giving rise to a subpopulation of resident T cells in the respiratory tract) is the key to understanding the dynamics of protection afforded by the CD8 T cell response to influenza. Our results suggest that the time lag for the generation of resident T cells in the respiratory tract and their rate of decay following infection are the key factors that limit the efficacy of CD8 T cell responses. The models predict that an increase in the level of central memory T cells leads to a gradual decrease in the viral load, and, in contrast, there is a sharper protection threshold for the relationship between the size of the population of resident T cells and protection. The models also suggest that repeated natural influenza infections cause the number of central memory CD8 T cells and the peak number of resident memory CD8 T cells to reach their plateaus, and while the former is maintained the latter decays with time since the most recent infection.