Residual immunity and seasonality of an epidemic

Abstract We present a dynamical model of the onset and severity of cyclical epidemic disease taking account only of seasonal boosts of antibody during the infectious season and residual immunity remaining from one season to the next. We also compile data from public health sources on the annual number of cases of influenza A and peak infectivity month over a quarter century. In these data, we discover that there is a negative correlation between the change in number of cases from one year to the next and the shift of peak infectivity month between the two seasons, although this does not extend to a prediction of epidemic timing or case number based on the the previous season’s statistics. Simulating the mathematical model, we discover that there is also a negative correlation between the change in titer from one season to the next and the shift of peak infectivity month between the two seasons, suggesting that the empirical results can be explained by our minimal boost-and-wane model. In addition, the model predicts that suppressing the epidemic for one season, or witnessing a strong surge for one season, both have lasting effects for a number of successive seasons.