Mechanistic modelling of multiple waves in an influenza epidemic or pandemic

Multiple-wave outbreaks have been documented for influenza pandemics particularly in the temperate zone, and occasionally for seasonal influenza epidemics in the tropical zone. The mechanisms shaping multiple-wave influenza outbreaks are diverse but are yet to be summarized in a systematic fashion. For this purpose, we described 12 distinct mechanistic models, among which five models were proposed for the first time, that support two waves of infection in a single influenza season, and classified them into five categories according to heterogeneities in host, pathogen, space, time and their combinations, respectively. To quantify the number of infection waves, we proposed three metrics that provide robust and intuitive results for real epidemics. Further, we performed sensitivity analyses on key parameters in each model and found that reducing the basic reproduction number or the transmission rate, limiting the addition of susceptible people who are to get the primary infection to infected areas, and limiting the probability of replenishment of people who are to be reinfected in the short term, could decrease the number of infection waves and clinical attack rate. Finally, we introduced a modelling framework to infer the mechanisms driving two-wave outbreaks. A better understanding of two-wave mechanisms could guide public health authorities to develop and implement preparedness plans and deploy control strategies.