We propose and analyse a model for the dynamics of a single strain of an influenza-like infection. The model incorporates waning acquired immunity to infection and punctuated antigenic drift of the virus, employing a set of differential equations within a season and a discrete map between seasons. We show that the between-season map displays a variety of qualitatively different dynamics: fixed points, periodic solutions, or more complicated behaviour suggestive of chaos. For some example parameters we demonstrate the existence of two distinct basins of attraction, that is the initial conditions determine the long term dynamics. Our results suggest that there is no reason to expect influenza dynamics to be regular, or to expect past epidemics to give a clear indication of future seasons' behaviour.

Blood malignancies arise from the dysregulation of haematopoiesis. The type of blood cell and the specific order of oncogenic events initiating abnormal growth ultimately determine the cancer subtype and subsequent clinical outcome. HOXA9 plays an important role in acute myeloid leukaemia (AML) prognosis by promoting blood cell expansion and altering differentiation; however, the function of HOXA9 in other blood malignancies is still unclear. Here, we highlight the biological switch and prognosis marker properties of HOXA9 in AML and chronic myeloproliferative neoplasms (MPN). First, we establish the ability of HOXA9 to stratify AML patients with distinct cellular and clinical outcomes. Then, through the use of a computational network model of MPN, we show that the self-activation of HOXA9 and its relationship to JAK2 and TET2 can explain the branching progression of JAK2/TET2 mutant MPN patients towards divergent clinical characteristics. Finally, we predict a connection between the RUNX1 and MYB genes and a suppressive role for the NOTCH pathway in MPN diseases.