Contact networks are more realis models for human contact than the homogeneous mixing model that classical disease models adopt. Developing mathematical models that faithfully reproduce the mean dynamics of the disease spread process on a contact network is crucial to understand when and why we must conside the underlying network contact structure, and how disease dynamics differ from the prediction of classical models.

There have been 4 influenza A pandemics in the 20th century. The 1918 pandemic introduced the subtype H1N1 that replaced the previously circulating subtype; the 1957 pandemic introduced H2N2 subtype that replaced the previously seasonal H1N1 subtype. The H3N2 subtype introduced in the 1968 pandemic replaced the then seasonal H2N2 subtype. In 1977, the H1N1 was reintroduced and coexisted with the H3N2 subtype since then. We develop mathematical models to understand the interaction between teh pandemic and seasonal subtypes, and investigate the condition that caused the replacement and coexistence of the subtypes.