Once the virus died out in Wuhan, it did not spread widely in China, and doesn't seem to be re-initiating as the Chinese go back to work. Scientists seem pretty puzzled by this, but it's an optimistic development when we look at our future path. There is some research on whether a second strain developing has affected the reduced spread. There's no agreement on this right now.
South Korea seems to have quickly limited their infection rate with a lack of acceleration of new cases.
A study by Chinese scientists just came out that quantified the response of the contagion of this virus to temperature and humidity. It seems to be a fairly standard corona virus that loses its virulence in the heat and humidity. They produced their estimates based on a fairly small sample, and those estimates would stop the virus by the end of June. They believe their numbers are on the conservative side due to testing limitations and comparison with other coronaviruses. The slower spread in some warm, humid countries seems to support this.
In Germany, where there is and has been very widely available testing, they have over 6000 positive-testing cases and only 13 deaths, a case-fatality rate of around 0.25%, which is extremely encouraging. There seem to be no agreed-upon explanations for this.
There are a boatload of drugs and vaccines in development, and the private sector has really come through quickly on testing once the CDC and FDA got out of the way. If we can really fast track those we may be able to avoid a second cycle of infection (2nd cycle was worse with the "Spanish" flu in 1918). (Links to drugs and testing below)
(God Bless Thermo-Fisher!)
On the other hand, American people are not doing a good job (broadly) of socially distancing, and we seem to expect distancing to "fix" the problem immediately, when distancing will actually take about a full contagion cycle to be effective at all, at least 14 days. In the meantime the case rate will go up, and people will become skeptical of the effectiveness of distancing.