Flattening the curve and the effect of atypical events on mitigation measures

On March 23rd and March 30th, 2020, the Mexican Federal government implemented social distancing measures to mitigate the COVID-19 epidemic. In this work a mathematical model is used to explore atypical transmission events within the confinement period, triggered by the timing and strength of short time perturbations of social distancing. Is shown that social distancing measures were successful in achieving a significant reduction of the epidemic curve growth rate in the early weeks of the intervention. However, “flattening the curve” had an undesirable effect, since the epidemic peak was delayed too far, almost to the government preset day for lifting restrictions (June 1st, 2020). If the peak indeed occurs in late May or early June, then the events of children's day and Mother’s Day may either generate a later peak (worst case scenario), a long plateau with relatively constant but high incidence (middle case scenario) or the same peak date as in the original baseline epidemic curve, but with a post-peak interval of slower decay.