Seasonal influenza appears as annual oscillations in temperate regions of the world, yet little is known as to what drives these annual outbreaks and what factors are responsible for their inter-annual variability. Recent studies suggest that weather variables, such as absolute humidity, are the key drivers of annual influenza outbreaks. The rapid, punctuated, antigenic evolution of the influenza virus is another major factor. We present a new framework for modelling seasonal influenza based on a discrete-time, age-of-infection, epidemic model, which allows the calculation of the model's likelihood function in closed form. This framework may be used to perform model inference and parameter estimation rigorously. The modelling approach allows us to fit 11 years of Israeli influenza data, with the best models fitting the data with unusually high correlations in which r > 0.9. We show that using actual weather to modulate influenza transmission rate gives better results than using the inter-annual means of the weather variables, providing strong support for the role of weather in shaping the dynamics of influenza. This conclusion remains valid even when incorporating a more realistic depiction of the decay of immunity at the population level, which allows for discrete changes in immunity from year to year.
Keywords: antigenic drift; epidemic modelling; maximum likelihood; model fitting; seasonal influenza; weather.