Progress and trends in mathematical modelling of influenza A virus infections

Mathematical modelling of influenza A virus infection has seen increased use over the last several years. Models applied to both in vitro and in vivo data have provided important new understanding of the kinetics of the virus, the role of different components of the immune response, the importance of non-infectious influenza A virus particles, the issue of drug treatment and resistance, and the interaction mechanisms during bacterial co-infections. We review these contributions by mathematical models, with a focus on studies performed in the last several years. For continued progress, we emphasize robust data and parameter estimation approaches.