Infections seem to slow down drastically in South Korea, given a policy response and a lockdown, so let's look at South Korea's numbers.
South Korea superspreader diagnosed on 18th February, which leads to clusters of infection there, and strong policy response follows soon afterward.
In South Korea, The peak of infection occurred on 1st March,
It took around ten days from the start of governmental and community response to the peak of infection. Now it seems the total number of cases(n~8200) would peak at the double at the inflection point (n=4212) in South Korea.
In Italy, the nation-wide lockdown was implemented on 9th March.
Assuming a ten-day delay on the inflection point after policy response, the inflection point would be around 19th March. Given the current trend of 20% daily increase of cases in Italy, the number of cases would be around 50 thousand at the inflection point and slowly converge to 100 thousand eventually. The number of new cases on the day of inflection point would be around 7 - 10 thousand and would take over a week to get this number back to around 1000 by the end of March/ Early April. Consequently, the nation-wide lockdown cannot be lifted before mid-April.
In Spain, the nation-wide lockdown was imposed on 14th March, so we could hope to see an inflection point on 24th March. Given a 20 % daily increase before the inflection point, we could see the total number of cases converged at 80 thousand eventually by mid-April.
These numbers are very optimistic, given a lack of containment measures in Switzerland (and the U.K., but it is not part of the Schengen area, so it doesn't matter too much.).
I do not want to speculate how bad the situation will become in the U.K. due to the "herd immunity" policy response.
If there are no social distancing or hand-washing practices, we could see an overload in NHS by the end of this week and a hike in the case-fatality rate.
I also do not want to speculate on the situation in the U.S.; the policy response is inadequate due to incoordination between various states and cities. The lack of travel restriction within the U.S. would remain a major challenge to the containment. One particular way to spread is short-haul flights. Both the U.S. and Canada would follow the exponential curves in the number of cases. The U.S. should see the ten-thousandth cases by Thursday, and thousandth cases in Canada the same day. I do not speculate the infection point in both countries due to a lack of adequate policy reponse to-date.
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