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

The case of the InH hypothesis might seem surprising as its extinction probability remains null all along the epidemic. This result is in fact straightforward since reinfection in this model does not depend on a contact process and is not subject to demographic stochasticity. This reinfection mechanism is therefore very robust to the small population size but interestingly it is not supported by the statistical comparisons. This emphasizes the sensitivity and accuracy of our ML approach regarding the shape and the dynamics of the incidence time series (figure 4d). Finally, it is remarkable that the two best models perform almost equally well despite being based on antagonistic mechanisms. Indeed, the Win hypothesis assumes that 100 per cent of the infected hosts can be reinfected during a limited period lasting an average of 4.8 days, whereas the AoN hypothesis assumes that only 47 per cent of the infected hosts can be reinfected at any time. This superimposed dynamics is in fact specific to the epidemiological context of TdC and we show in electronic supplementary material, text S7, that the dynamics of these two models would differ both qualitatively and quantitatively in the epidemiological context of a large population. Win models (around 10), slightly lower for the PPI model, but more than twice as high for the InH model owing to an identifiability issue (electronic supplementary material, text S8). Overall, these high values for R 0 are somewhat unusual: R 0 is typically estimated around 2 for influenza, although exceptional cases have also been reported in closed populations [27] . We contend that a high value of R 0 as well as rapid spread (the first peak was reached after only 6 days) and a high attack rate (96%) can be expected in small, isolated communities [28] without pre-existing immunity [29] . Furthermore, estimates of the effective reproductive number from the TdC incidence time series [30] are in agreement with our estimates of R 0 (electronic supplementary material, text S9).