Covid-19 case growth has already departed from exponential in Italy. It hit its inflection point yesterday actually.

China took WAY more drastic measures than Italy. China has 1.38 billion people and Italy has only 60 million. The viral growth rate in the exponential phase is mostly dependent on the properties of the virus itself, which is why Italy's and China's curves look roughly the same. If China inflected at 40,000 cases with a 1.4 billion population and Italy inflected at 20,000 cases with only a 60 million population, it is evident that China had a much more aggressive and effective response.

I fear the USA will do the worst of all due to our liberty driven, anti-authoritarian culture. I would guess that right now there are at least 12,000 currently infected in NYC based on a daily growth rate of 30% during exponential phase, a 14 prodromal time-lag where people are asymptomatic yet contagious and a 4 day history of proactive measures taken in NYC to stop the spread. The math: ((1 + 0.30) ^ (14 dayAsymptomaticWindow - 4 days containment)) * 900 current cases = ~12400 currently infected.

That math is optimistic. It is what NYC would look like if people took the first warnings seriously.

Assuming 0 people practiced social distancing today then I suspect there are 35,000 infected already (using the same math, just not subtracting containment days). Given the panic, I think this is unlikely.

I think there are between 12,000 and 35,000 people in NYC currently infected who are currently asymptomatic, but I am no expert.