Forecasting infectious disease emergence subject to seasonal forcing
The structure of school terms is well known to influence seasonality of transmission rates of childhood infectious diseases in industrialized countries. A less well-studied aspect of school calendars that influences disease dynamics is that all children enter school on the same day each year. Rather than a continuous inflow, there is a sudden increase in the number of susceptible individuals in schools at the start of the school year. Based on the standard susceptible-exposed-infectious-recovered (SEIR) model, we show that school cohort entry alone is sufficient to generate a biennial epidemic pattern, similar to many observed time series of measles incidence. In addition, cohort entry causes an annual decline in the effective transmission that is evident in observed time series, but not in models without the cohort effect. Including both cohort entry and school terms yields a model fit that is significantly closer to observed measles data than is obtained with either cohort entry or school terms alone (and just as good as that obtained with Schenzle's realistic age-structured model). Nevertheless, we find that the bifurcation structure of the periodically forced SEIR model is nearly identical, regardless of whether forcing arises from cohort entry, school terms and any combination of the two. Thus, while detailed time-series fits are substantially improved by including both cohort entry and school terms, the overall qualitative dynamic structure of the SEIR model appears to be insensitive to the origin of periodic forcing.