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

(c) Simulation and model selection Given the small population of TdC, demographic stochasticity is expected to play a significant role in the epidemic dynamics, especially during the inter-wave period when the number of infected hosts is low and epidemic fade-out is likely to happen. We therefore used the stochastic framework of continuous-time Markov chains that naturally allows demographic stochasticity to be taken into account. The Markov chain events and the transition rates used to simulate the six models are provided in electronic supplementary material, text S1.5. Numerical simulations were performed using the exact algorithm provided by Gillespie [19] . Model-predicted incidence is computed by counting the daily number of new hosts entering the infectious class I. Since the dataset reports only 85 per cent of the total number of attacks and in order to take account of possible unreported asymptomatic cases, the observation process must also be modelled. More precisely, after having checked that the data were not overdispersed (electronic supplementary material, text S1.6), we assumed a Poisson process observation whose reporting rate parameter (r) was also inferred [20] .