At the end of last month I took a look at the US case count to try to get an idea of how quickly this disease would be spreading. I just wanted to be able to make some plans regarding travel. So, I watched the numbers from the worldometer website. I found that the US case count doubled on a very regular pace. From March 1 I started recording the number each day and plotting it. It's amazing how predictible it has been. Since March 1 in the US it has been very tightly tracking an exponential growth pattern. The number of cases is doubling every 2.4 days. On this growth path, the number of US cases will reach over 420,000 by the end of March. However, in the US , bureaucratic and financial hurdles are resulting in very little testing being done. So the actual number of cases is likely much higher than the available numbers. If more extensive testing is done it will likely drive the numbers to go above the projection. If significant actions are taken to slow the spread, the data will track below the curve. So far, neither of these are seen in the data.
So, when will we see an inflection in the curve -- at the latest? Epidemiologists are saying to expect 60% to 80% infection rate before herd immunity takes effect. On the current growth path for the US, that will occur between April 21 and April 23. But, considering that the case count is likely higher than we know and that fear will probably grip the population and policy leaders before that prompting them to take some actions to slow the spread, I suspect we'll see an inflection point in the US in mid April. Unfortunately the inflection point will not be the peak. I think it's safe to say this epidemic will be with us for more than the next couple of months.
The epidemic (or pandemic) is already out of control. It is spreading in communities at exponential rate. Such exponential spread can only stop when majority of the population (on the order of magnitude of 50%) gets immunity either through contracting the disease or through vaccination. The latter is out of the question (vaccine is at least 12-18 month behind). So the actual spread will continue until most people get infected.
As for tracking test results... In open countries, like the US, there is the limit on how many positive tests the country can report each day (determined by the number of available test kits, lab throughput, qualification criteria determined by bureaucrats, etc.).
For example, 2 weeks before now the US had limited ability to perform tests: January through end of February they performed only ~1,500 tests in total in few CDC labs across the country, and that yielded few dozens domestic positive tests. Once million test kits were provide to health authorities of 50 states over the past few weeks, the number of positive tests in the US started climbing exponentially. This does not mean that there was no exponential community spread before the test kits were provide to states. The system was simply not able to gauge that spread with 1,500 tests they performed in 2 month.
Sooner or later the speed of the spread will outpace the current testing capacity in the US. The statistics will start flattening out in the US, but the exponential spread will continue.
As for authoritarian regimes - you simply cannot trust the numbers they produce. Recent figures from China are laughable, and they cannot be rationally explained. Another example is Russia. Russia has long history of manipulating its numbers. For example, in 2017 Russia reported 432 mortality case from flu and common cold. In the same year, CDC estimated mortality rate of 61,000 (95% CI 46K-95K) from flu in the US. Either vodka and cabbage are efficacious measured against flu, or Russian state-owned statistics agency spread misinformation. And, surprise surprise, the same agency reports laughable numbers of Covid-2019 cases in Russia now...