Explaining rapid reinfections in multiple-wave influenza outbreaks: Tristan da Cunha 1971 epidemic as a case study

Camacho, Anton; Ballesteros, Sébastien; Graham, Andrea L.; Carrat, Fabrice; Ratmann, Oliver; Cazelles, Bernard

Our approach for evaluating the reinfection hypotheses rests on a statistical comparison of the corresponding statespace models to the shape and the dynamics of the observed daily incidence counts while, crucially, allowing for demographic stochasticity. For a time series y 1:T of T successive observations and a state-space model H i with parameter vector u, the likelihood is given by L(ujH i ) ¼ P( y 1:T j u, H i ). Parameter inference and model selection are based on an iterated filtering procedure that converges to the ML parameter estimate (u ML ) for each model to the incidence data [20] . We performed log-likelihood profiles in order to check convergence to the ML and to calculate 95% confidence intervals for parameter estimates. Finally, we used the corrected Akaike information criterion (AIC c ) to select the model that best explains the data: