Overall, it is difficult to predict when cases will diminish, particularly in the US. Some experts have suggested a seasonal role. Infectious disease physician at Johns Hopkins Center for Health Security Amesh Adalja suggests that COVID-19 is akin to the seasonal cold and predicts some "tapering off of cases" as we head into spring and summer in the northern hemisphere, while the virus may have increased transmission in parts of the southern hemisphere. Director of the National Institute of Allergy and Infectious Diseases Dr. Anthony Fauci is also hopeful that cases will diminish as the weather becomes warmer, but both he and others caution that we don't have enough information to predict the seasonal behavior of the virus (see Australia, which is currently in its warm season, yet still experiencing COVID-19 outbreaks).
If we look to the timelines of other countries for comparison: in the US, the rapidly increasing number of cases resembles the beginning of an exponential curve - similar to Italy. However, cases in China and South Korea are beginning to decrease, suggesting they may have begun to "plateau." It took approximately two months for China to reach this stage from the beginning of the outbreak and South Korea roughly half a month, although due to differences in response times, testing, and approaches to tracing cases / public health interventions, it may be difficult to extrapolate what has happened in other countries to the US.
In the US, it is difficult to tell when the peak will arrive, partly due to the limitations in testing. Additionally, we may see second or third waves of outbreaks even after cases begin to decrease. Therefore, while it may not be unreasonable to hope for an end sometime in late April or May based on these predictions and cases, we simply do not have enough information to say for certain.
More information can be found in the sources below:
Drafted 19 March 2020