These two models use different methodology. Imperial College runs calculations based on how many people are susceptible, exposed, infected, and then recover (S.E.I.R.). Different models can include variables — like how infectious or how deadly the virus is — to change outcomes. If, for instance, we engage in social distancing, which dramatically lowers the chance that one is exposed, a model will show that we can expect a very different course.

I.H.M.E took data on changes in numbers of infected and dying from countries impacted earlier than the United States, such as China and Italy, and used those to predict the course of the disease. It assumed that America would have a similarly shaped experience (albeit with much different numbers) and presented a range of possible outcomes.

The models were all useful in helping to plan for worst-case scenarios. They were also useful for helping guide us into decisions to flatten the curve and prevent the health care system from being overwhelmed.

Even as they are updated, though, many of the models remain symmetric. Reality isn’t.

Let’s start with new cases. According to the Johns Hopkins Coronavirus Research Center, Italy had its worst day of new cases (6,557) in mid-March. A month before, it had almost none. More than a month later, it’s still having thousands a day. Spain started seeing an increase in cases in the beginning of March and peaked about three weeks later at 9,630. About a month after that, it’s still finding around 4,000 a day. Belgium rose and flattened, not dropped. So did the Netherlands.

None of them rose, peaked and fell smoothly.

The numbers of new cases can be influenced by testing. The less you test, the less you’ll find. It doesn’t appear, though, that the more-than-expected numbers of cases are because of increased testing after the peak. And deaths, while more of a lagging outcome, show a similar pattern.