**By Jerald Hughes**

**(Scott Robinson and Scott LaJoie contributed to this analysis)**

With COVID-19 infections spreading in the U.S. at an extraordinary rate, it is useful to be able to predict what lies ahead.

The nearest term is the hospitalizations which follow as a result of increased cases of infection. This lag is about 12 days, and the ratio of currently hospitalized patients to daily average cases is about 79%.

On November 13 the 7-Day average of daily cases was 136,408. This means that by Thanksgiving Day we should expect about 107,762 patients hospitalized - a dramatic increase caused by the skyrocketing case numbers.

Further out, we have seen that there is about an 18-day lag between daily case numbers and daily deaths. The mortality rate at this time lag has been varying between 1.55% and 2.15%. In the most recent two weeks, we have observed 1.61% mortality. That means that by December 2 we should expect about 2196 daily deaths.

But what about further out? One important future milestone is the peak of the third wave now currently in progress. For the analysis which follows, the two research questions are:

1) When will the third wave peak?

2) How high will the third wave peak?
For projections created with sophisticated, detailed epidemiological models, see __https://covid19.healthdata.org/united-states-of-america?view=total-deaths&tab=trend__ and __https://www.cdc.gov/coronavirus/2019-ncov/cases-updates/forecasts-cases.html____.__
Here, we will use the historical data available from the two previous waves to attempt to predict the progress of a third wave.

We can see the entire history of COVID-19 daily cases in the US in this graph:

**Figure 1. COVID-19 Cases, full history**

We can see the first two waves in their entirety. They show similar phases:

Phase 1: Uncontrolled, swiftly increasing spread, as the line curves upwards Phase 2: Constant spread, as the line continues upward at a fairly stable angle Phase 3: Coming under control, as the line curves toward horizontal, reaching a peak. The end of Phase 3, where the line hits its peak, represents the highest count of daily cases for that wave, and the beginning of reducing the daily count.

For our massive third wave on the right side and highest-ever part of this graph, we are either still in Phase 1, or at best, just barely starting Phase 2.

We can now analyze these phases of the first two waves already recorded as historical data, to get a sense of what lies ahead for the third wave in the Fall of 2020.

In order to understand the size and progress of these three phases during the first two waves, we will look at the slope of the daily cases line. The graph below charts the slope of the red line above, which represents the 7-day average of the daily cases numbers:

**Figure 2. Slope, Daily Cases**

The first wave began with individual cases arriving from overseas. Uncontrolled spread, with the daily cases line curving upward, began about March 15.

We can see the slope first top out on March 26. It bounces around for a few days, but still around the 2000 mark until April 4, when it begins to plunge downward, arriving at 0 – the daily cases peak of Wave 1 – on April 11. The following graph marks these three phases:

**Figure 3. First wave.**

Now we start to see a sense of the scale of the first wave, and how it changed over time, as the nation struggled with measures to contain the epidemic. This table shows the periods marked in the chart above:

**Table 1. COVID first wave periods.**

This gives us a first historical baseline on how COVID-19 developed in the first wave. The entire period from the start of uncontrolled spread to peak, lasted just 28 days. Measuring the average slopes separately for phases 2 and 3 allows us to create a basis for estimating how many additional cases are added during those periods. We can also see below that the average slope of Phase 3, as the curve flattens out to its peak, is considerably below that of Phase 2—as we should expect, since Phase 3 ends at 0 slope:

**Table 2. COVID first wave baseline.**

Next, we run the same analysis on the second wave. Like the first wave, it also has three distinct phases, which we can identify from the historical data. The chart below shows the graph of the slope of the line of the daily cases 7-day average:

**Figure 4. COVID second wave phases.**

The second wave was larger in many respects: it started from a higher point, it lasted longer in all phases, and of course it reached a much higher number of daily cases at its peak. This line also displays a disruption caused by the long July 4th weekend, which is an artifact of data reporting delays. The following tables show the corresponding measures for this second wave.

**Table 3a. COVID second wave phase measure.**

**Table 3b. COVID second wave peak, slopes.**

Here we notice that the second wave took 15 days longer to get from uncontrolled spread to peak, and spent nearly twice as long in Phase 2. However, the slope of Phase 2 during this second wave was less steep than seen in the first wave. This squares with our memory of the first wave, when we understood very little about COVID-19, but responded with a lockdown measures. By the time of the second wave, many citizens were already aware of protective measures, but the lockdown policies were much more relaxed. This second wave took longer to reach its peak, but also took longer to control.

Now we have two historical baselines to use in trying to answer our research questions:

1) When will the third wave peak?

2) How high will the third wave peak?

Unfortunately, we’re either still in Phase 1 of the third wave, or Phase 1 has just ended. The following chart shows the graph of what we know up to Nov 13:

**Figure 5. COVID third wave, Phase 1.**

The third wave began to see uncontrolled spread on Oct 5, and continued to curve upwards all the way through to at least Nov 11. While it is too soon to tell whether we will see the slope steepen even further, the remainder of this analysis will assume that Phase 1 lasted 38 days, ending on Nov 11, and that we are now just two days into Phase 2. Right away the scaling problem is apparent. This Phase 1 period is far larger than that of either the first or second wave, and consequently our daily case numbers have reached staggering heights. We will explore three possible scenarios.

**Minimal Scenario**

For a *very* optimistic analysis, we will calculate the numbers assuming that this third wave will finish phases 2 and 3 with lightning speed, just 10 and 7 days respectively. That gives us a (rosy) scenario answer to the question of when this wave will peak: by Dec 1:

**Table 4. COVID third wave, minimal scenario.**

We know the [proposed] length of Phase 1, the baseline from which this wave began, and the present 7-day average of daily cases on Nov 13.

The Phase 2 slope was calculated as the average of the most recent 5 days – very steep! Assuming 10 days in Phase 2 and given this slope, we can calculate an estimated additional daily cases to be added during Phase 2.

In the first wave, the slope of Phase 3 was 35% of the slope of Phase 2, so we assume that historical number here, and arrive at the estimated average slope of Phase 3. Assuming just 7 days in Phase 3, that gives us the additional daily cases to be added as we approach the peak. The sum of our present level plus our estimates of phases 2 and 3 gives us a possible number of where we arrive at the peak: 7-day average of 208,251 new cases per day.

The peak daily deaths estimate was derived also from an optimistic scenario, where the mortality rate is assumed to be the same as the lowest fatality rate observed over the entire period since August 1, 1,55%.

Notice that this yields a predicted average daily death number of 3,228, already a staggering level. The next two scenarios are much worse.

The second scenario is also somewhat optimistic, assuming that we can control this wave at levels no worse than those scene during the second wave. The major difference here is the lengths of phases 2 and 3. These push our peak date out to Dec 11. This scenario still assumes a very swift recovery to 0 slope, given where we are on Nov 13:

**Table 6. COVID third wave, middle scenario.**

The numbers added during Phase 2 in this scenario are higher because the period is much longer than wave 1, 19 days instead of just 10. This scenario also uses a somewhat higher estimate adjustment for the average slope during Phase 3, 42% instead of 35%. Instead of the optimistic 1.55% mortality rate, this scenario uses the mortality rate calculated as the rate observed for the most recent two weeks, at an 18-day lag, which is 1.61%.

Notice that this mortality rate thereby factors in all of the most recent medical improvements in treatments and protocols. Whatever the best methods available are, they are being used now, and that is the basis for our historical observed mortality rate. The consequent daily deaths prediction soars into numbers not yet seen during this pandemic.

The final scenario takes the possibility of scaling up seriously. We have already seen that Phase 1 has been both longer and dramatically higher than the previous wave. Despite the first two scenarios above, we have no serious basis for believing that the remaining phases of this third wave will not also scale larger. The final scenario takes a conservative approach to scaling. The scaled-up third wave takes a total of 77 days, of which 38 have already passed, putting our 3rd wave peak on Dec 21. The scaling here was done by observing the scale of change between waves 1 and 2, then conservatively assuming that this third wave will only scale by a factor half that size. So while the second wave Phase 2 was 90% longer than the first wave Phase 2, here we produce an estimate with only a 45% increase in the number of days, yielding 28 days in Phase 2. The scale factor for Phase 3 was much more modest – 5%, which is half of the factor of increase observed between wave 1 and wave 2. The Phase 3 average slope in wave 2 was of greater relative magnitude than that of the first wave. Here we conservatively scale up by only half as much:

**Table 7. COVID third wave, scaled scenario.**

The resulting peak numbers are beyond staggering, even compared to the very worst days of either of the previous waves. At this point, an innate human difficulty in grasping large numbers begins to set in. One way of thinking about these levels is to consider that the first wave was intensely focused on a few hotspots, mainly on both coasts. The second wave, while enormous, saw dozens of severe hotspots. But for the third wave, we may be beyond the point of looking at hotspots: COVID-19 is in so many places, with increasing infections nearly everywhere in the entire United States, that the cumulative effect may dwarf anything seen before.

In summary, the United States faces in the coming weeks a health crisis of unprecedented proportions. The media - and the federal government - are certainly under-reporting the potential consequences of the accumulating third wave, and the danger cannot be overstated. The nation is in peril.

Jerald Hughes is Chair of the Department of Information Systems, University of Texas RGV.

Scott Robinson is a data scientist in Louisville, Kentucky.

Scott LaJoie is Associate Professor of Health Sciences at the University of Louisville.

*All opinions expressed in this blog are solely those of the authors, and do not reflect those of University of Texas Rio Grande Valley or the University of Louisville, or any organizations of which the contributors are members.*

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