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 PPI hypothesis is more complicated. A previous analysis of a similar but deterministic model [12] has revealed that dynamics depend on a reinfection parameter sR 0 . When this parameter is well above a reinfection threshold (sR 0 . 1), reinfection becomes selfsustained and dynamics are SIS-like, whereas below this threshold primary infection dominates and leads to SIRlike dynamics. Our stochastic PPI model estimates sR 0 ¼ 1.18 and indicates critical dynamics: the reinfection parameter must be sufficiently high to reduce stochastic extinctions during the inter-wave period, but at the same time it must be sufficiently low to avoid sustained reinfection and therefore more than two epidemic waves. Put another way, epidemic fade-out after the second wave can only be reproduced near the reinfection threshold (sR 0 p1), which simultaneously generates a significant inter-wave extinction probability.