'Comparing my simplistic spreadsheet to professional models, I find that around April 12 my spreadsheet departs far from reality, and becomes useles'
But I believe that professional models are not any better due to the lack of data.
No, the professional models are much better. They have been predicting the numbers accurately, weeks in advance. They have lots of good data, from China, Japan and Europe. Not such good data from U.S., but you can extrapolate even when the margin of error is large. The overall trends are clear. New York knows how many patients are in hospitals, and they can measure the growth rate of hospitalized patients and make educated guesses about how many there will be in a week, or two weeks, and when the peak will come. They can do this even when they can only estimate how many cases are outside the hospitals and unregistered.
If they start administering antibody tests, including some random testing of the general population, authorities will have a much better grasp of the overall infection rate, and the likely peak.
You can also extrapolate backwards, from deaths back to the total number of cases (with a lag). You couldn't do this weeks ago because there were few deaths. Now, unfortunately, U.S. has ~500 deaths a day, and in 3 days we will have 1,000, and six days 2,000. Those are statistically significant numbers. You can draw conclusions from them. There is now no way to avoid that number of deaths. Even if we could magically stop the infections, bringing the daily new cases down to zero, there are thousands of terminally ill people who will surely die over the next few weeks, and their numbers double every 3 days, exactly the same rate as the daily case rate was, back when this cohort of sick people got sick. (In other words, with a lag.) The daily case rate has declined recently, so it doubles every 7 days instead of every 3 days. If that keeps up, it means that in a few weeks, deaths will be doubling every 7 days instead of every 3 days.
The overall trend trend must stop fairly soon. In about a month. It can stop in two ways:
1. The lockdown is effective and it continues for as long a needed. The epidemic reaches the natural peak and declines, because a large fraction of the population gets sick, recovers or dies. The rate remains predictable because medical care is generally available. Case mortality is no worse than 3.5%. We hope it is 1% or 2%.
2. The lockdown fails, mainly because people ignore it, as they did in Italy until recently. Things go completely out of control. Deathly ill patients cannot get aspirin, and die in large numbers in tents in hospital parking lots or at home. We are back in the 14th century. The case mortality rate is somewhere between 6% and 10% -- the experts have no idea where it might be. Since 20% must be hospitalized now to survive, a large fraction of those people will die instead.
You can see why the doctors are so anxious to flatten the curve and keep things in Scenario 1. You can see why estimates of the total dead vary from hundreds of thousands up to 6 million. It is not that the models are inadequate or imprecise. The problem is that the people running the models cannot know whether the public will cooperate and stay locked down.
