Influenza A virus infection of the respiratory epithelium triggers an antiviral innate immune response. This entails secretion of type-1 interferons, INF-a/b, from infected epithelial cells and release of an array of inflammatory and chemotactic cytokines from alveolar macrophages and wandering neutrophils and dendritic cells upon phagocytosis of newly-synthesized virus particles produced by the infected epithelial cells. The process leads to activation of natural killer (NK) cells and gives rise to viral antigen-bearing macrophages and dendritic cells that, in turn, activate and clonally expand multiple influenza A-specific cytotoxic T lymphocytes (CTLs). Activated NK cells can kill newly-infected epithelial cells whereas anti-influenza CTLs destroy virus-producing epithelial cells. We present a simple spatial model for the influenza virus infection of respiratory epithelium, represented as a hexagonal (maximally close-packed) lattice, to describe a previously undefined relationship between the rate of death of infected epithelial cells due to (i) virus replication, (ii) activated NK cells, and (iii) CTLs, and the spread of infection in respiratory tract. Without modelling the detailed kinetics of various processes, it is possible to gain valuable insights into critical mechanisms implicit in the control of virus infection. We analyze this model for linear stability and show how the same techniques may be extended to a more comprehensive model of immune response, including conditions that would prevent the generation of unwanted “cytokine storm” and ensuing inflammation in the respiratory tract.