After a year of the unprecedented COVID-19 pandemic in 2020, the world has been overwhelmed by COVID-19 resurgences in 2021. Resurgences usually cause longer, broader and higher waves of infection, with greater threat to societies and economies compared to first waves. They may be caused by late implementation or early relaxation of non-pharmaceutical interventions (NPIs) such as social restrictions, ineffective interventions, or virus mutations. Here we provide quantitative evidence to characterize epidemiological differences between waves, evaluate possible causes, and predict potential trends under virus mutations. We use an event-driven dynamic epidemiological model embedded with time-dependent intervention interactions to compare two waves of COVID-19 outbreaks, and we quantify the impacts of control or relaxation interventions (called events) on wave patterns. We show the second waves in late 2020 in Germany, France and Italy could have been better contained by either carrying forward the effective interventions from their first waves or implementing better controls and timing. We also obtain the quantitative effects of enforcing or relaxing interventions on various transmissibility levels of coronavirus mutants (like delta or lambda) in the second waves and in the next 30 days. Comprehensive analyses at four levels - vertical (between waves), horizontal (across countries), what-if (scenario simulations on second waves) and future (30-day trend) - in the two 2020 waves in Germany, France and Italy show that (1) intervention fatigue (government and community
reluctance to interventions), early relaxations and lagging interventions may be common reasons for the resurgences observed in many countries; (2) timely strong interventions such as full lockdown will contain resurgence; and (3) in the absence of
sufficient vaccination, herd immunity and effective antiviral pharmaceutical treatments and with more infectious mutations, the widespread early or fast relaxation of interventions including public activity restrictions will result in a COVID-19 resurgence.