Critical Immune and Vaccination Thresholds in Heterogenous Populations

Laura Matrajt
Ira Longini


Previous influenza pandemics (1918, 1957, and 1968) have all had multiple waves. The current pandemic influenza A(H1N1) (pandemic H1N1) started in April 2009 and was followed, in the US and temperate Northern Hemisphere, by a second wave during the fall of 2009. The ratio of susceptibles and immunes in a population, at the end of a given wave, greatly determines the possibility and magnitude of a following wave. We developed a two-group epidemic model with vaccination that allows us to determine critical thresholds for vaccine-induced immunity and natural immunity for preventing further spread of influenza. We used this method to predict the possibility of a third wave of influenza in the US: If the basic reproduction number R0 were 1.6 or below, a third wave is very unlikely, plausible if the original R0 were 1.8, and likely if the original R0 were higher than 1.8.