Is it true that the quarantine must be extended to at least 49 days to be sure there are no reocurrences of the virus?

Hi @Lucas great question! Unfortunately, this is untrue and there is no basis for that recommendation. The modelling techniques are flawed and do not reflect real-world events as they unfold, as techniques like these are purely experimental. Whereas in the real-world, there are many other considerations and factors influencing behaviour that can affect the epidemiologic "curve" and behavioural responses to measures like Quarrantine.

Such an extensive, and prolonged quarrantine  can have many unintended effects. For example, it may place many casual workers and daily-wage individuals in a desperate financial situation, in which they may choose to overlook symptoms and continue working in an effort to feed families (presenting late - spreading to more people along the way). This will be detrimental to essential public health efforts such as contact tracing to fight the infection.

Ultimately, public health measures (like quarrantine/social distancing) are most essential to "flatten the curve" - that is primarily to reduce the RATE of new infections and not the NET NUMBER when the former gets too high. The reason for this is that health systems have fixed capacity to attend to cases at any one time. If the RATE is too high i.e. people are disseminating the infections quickly and the new cases are presenting quickly and all at the same time, healthcare services will be quickly overwhelmed.

To achieve their intended effect, public health measures need to be tailored based on many factors about the target population, some of which may be dynamic in the context of an unfolding outbreak (e.g. daily inter-city transport/mobility of the population, capacity of existing healthcare services, availability of financial support, proportion of incident cases identified through contact tracing, etc). Quarrantine is a targeted measure to reduce spread from high risk individuals, however more evidence is required to justify prolonging beyond the 2 weeks, given the potential detrimental effects of extended quarrantines. More important is for individuals to be empowered in being responsible and present early to medical professionals once they are symptomatic.

For instance, quarrantine measures or even a temporary lockdown for the duration of 2 weeks (covering the incubation period reported in over 90% of reported cases) applied at the time that infections are rising quickly can be a timely response to help to reduce the RATE of infection and thereby the speed of incident cases as they turn symptomatic in the following two weeks, in certain populations. These can help to regulate the case load such that the health system would be better positioned to attend to those that are falling ill. More about this at this link: https://www.cdc.gov/csels/dsepd/ss1978/lesson1/section11.html