Table 1.

Model comparison. See Figure 1 for a diagram of the general epidemiological model. The ‘basic’ model is the well-known SIRS model with the transmission rate β(t) including only the seasonal forcing function and the loss of immunity rate ε(t) set to a constant. The ‘basic-H1’ model includes R_H1 as an additional class to incorporate the loss of susceptible due to previous infection by H1N1, and use the observed incidence of H1N1 as a covariate determining the flux of individuals into this class. The ‘refined’ model additionally considers a different reporting error for the summer and winter seasons, and allows for the sub-exponential growth of the epidemic curve with an exponent α (smaller than 1) on I in the force of infection. The ‘humidity’ model replaces the spline-based seasonal forcing function with a humidity-based function. The next series of models includes the influence of the evolutionary index E(t) on the transmission rate β(t) and/or the loss of immunity ε(t). Among these evolutionary models (the ‘immunity loss/transmission’ model, the ‘transmission’ model, and the ‘immunity loss’ model), the best model (the ‘continuous’ model, compared to models without evolutionary compartment) based on the Akaike information criterion (AIC) is the one that incorporates a continuous dependence on E(t) only in the loss of immunity. A further improvement is achieved by the cluster model which incorporates evolutionary change as a discrete event for seasons with an antigenic transition (the ‘cluster’ model). AIC was calculated as: AIC = 2k − 2ln(L), where k is the number of parameters and L is the maximum likelihood. The likelihood ratio test was used for model selection. Based on p values (smaller than 0.05), the basic-H1 and refined models are significantly better than the basic model, and the refined model is in turn significantly better than the basic-H1 model. Models with evolution, include the cluster model, are significant better than those without it (shaded). Among models with evolutionary information, the continuous and cluster model is significant better than the transmission model.

Models	Epidemiology			Evolution		Number Parameters	AIC
	H1N1	α ≠ 1 ρwinter & ρsummer	Seasonal forcing	Loss of Immunity ωε ≠ 0	Transmission ωβ ≠ 0
Basic	×	×	Periodic splines	×	×	14	4493
Basic-H1	√	×	Periodic splines	×	×	17	4478
Refined	√	√	Periodic splines	×	×	19	4471
Humidity	√	√	Specific humidity	×	×	15	4484
Immunity loss/Transmission	√	√	Periodic splines	√	√	22	4450
Transmission	√	√	Periodic splines	×	√	21	4458
Immunity loss (continuous)	√	√	Periodic splines	√	×	21	4448
Immunity loss (cluster)	√	√	Periodic splines	√	×	20	4445