Brief update on publicly available COVID-19 case data at Arizona State University

The epidemiologic picture has improved, but student case rates remain quite high, and ASU’s zip code is now at the epicenter of the Arizona epidemic; future case counts at ASU are highly uncertain

Final Update, Sep. 10, 2020: ASU has confirmed elsewhere that it is indeed reporting active cases, but will now includes cumulative cases from August 1, 2020 to (presumably) the date of the most recent update. Historical data has not been provided. From Sep. 9 on, new cases and percent positives will presumably be possible to calculate, but no reliable analysis can be performed on the historical data as previous cumulative case counts remain unknown.

Update Sep. 7, 2020: ASU’s data disclosure today, reporting “807 total known positives” in the student body, down from 957 four days priors, shows that the typical interpretation (and the one I have followed) that reported numbers represented cumulative case counts, is false. Numbers must represent some version of “active cases,” but it is impossible to know. This may explain the lower than expected case increase in the previous data disclosure. This, and the previous deceptive reporting of percent positivity imply that the data currently being disclosed by ASU is fundamentally unreliable unless much more detail and a thorough explanation of all terms is disclosed.

No data disclosed by ASU, currently publicly available, can be used to calculate new cases, cumulative cases, or true percent positive (except potentially to give lower bounds for these quantities). The analysis below is no longer reliable (excepting that based on zip code data), and can be interpreted as a kind of “best case scenario” for ASU. To preserve the record, the original text below will not be altered.

Usual caveat: The following is not peer-reviewed, and all work and opinions are solely those of the author.

Update Overview

Since I originally posted an analysis of ASU case disclosures, ASU has made two new data disclosures (on August 31 and September 3), which show high ongoing rates of COVID-19 transmission rates, though not nearly as dire as extrapolation from the initial two disclosures suggested. The release of additional data is applauded, and the slowdown in new cases is a welcome (but very tenuous) development; however, daily updates would still be preferable, and true test percent positive is still not reported.

It is indeed typical for epidemics to evolve toward slower transmission, as those most likely to be infected are removed from the susceptible pool, while policy and spontaneous behavioral changes further reduce transmission rates. Hopefully this has indeed occurred and continues to happen, but the data continues to paint a concerning picture. Per capita case rates in the student population remain 10–20 times greater than the Arizona average, and the most recent interval testing percent positive is 6.0%; overall percent positive since August 25 is inferred to be 7.7% (either 822 or 824 new positive cases, 10,696 test). About 3.8% of the Tempe on-campus student body has also now tested positive for COVID-19 since the school year began two weeks ago.

It is also very likely that the effective reproduction number, Rt, remains above 1 for the ASU student population, based on the fact that per capita cases are at least an order of magnitude higher than the Arizona average, and Arizona’s Rt is currently estimated at 0.95. Additionally, crude exponential growth fits to student data, as well as preliminary susceptible-exposed-infected-recovered (SEIR) model-fits to Tempe zip code 85281 (main zip code for ASU) case data, and a coarse version of daily student cases inferred from ASU’s disclosures, suggest a reproduction number greater than one. However, the fit to student data is sensitive to fitting details, and either large decreases or increases in daily case count appear possible in the coming days. It does appear that 85281 is now the epicenter of Arizona’s ongoing COVID-19 epidemic.

Since the September 3 disclosure, announcements with prior case and testing numbers (excepting the August 25 disclosure of 161 cases) do not appear to be available anymore through ASU, but I previously made a record of most the data, which is tabulated and summarized here for the four data updates. Inferred case doubling times and basic reproduction numbers under an assumption of exponential case growth are also provided, but as noted later, with the slowing growth in caseload, this is probably not appropriate at this point. As mentioned, I fit instead a basic SEIR model to coarse student data and daily Tempe zip code 85281 data (from May 18 through September 3, 2020), with these fits suggesting that a serious epidemic is still occurring, but there is great uncertainty about the future.

Summary of four data disclosures from August 25 through September 3

August 25.

ASU disclosed: 32,729 tests since August 1. 161 total positives (no further breakdown)

• Interval percent positive (all tests): 0.49%
• 7.7 cases per day per 100,000 (assuming 86,900 total population and end date of August 24); comparable to AZ average

August 28.

ASU disclosed: 37,149 tests since August 1; data up to August 27.

Cumulative positive results (total population in parentheses):

• 28 student/faculty positives (pop. 12,400)
• 452 total student (pop. 74,500)
• 205 Tempe on-campus positives (pop. 9,645).

Interval percent positive (4,420 new tests, 319 new positives): 7.2%

Case rates over interval (new cases over interval in parentheses; given are central estimates, see prior post for details):

• Faculty/staff: 51.1 cases per day per 100,000 (19 new cases)
• Tempe on-campus: 470 cases per day per 100,000 (136 new cases)
• Student, other: 84.3 cases per day per 100,000 (164 new cases)
• Student, overall: 134.2 cases per day per 100,000 (300 new cases)
• AZ 7-day average: 7.4 cases per day per 100,000 (per NY Times)

Inferences for total population:

• Inferred (overall) doubling time under exponential growth: 1.9 days
  Inferred Rt: 2.8

Rt inferred using formula:

R0 = 1 + g ln(2)/(td),

where td is the doubling time and g is the case generation time, assumed to be 5.0 days.

August 31.

ASU disclosed: 40,402 tests since August 1; data up to August 30.

Cumulative positive results (total population in parentheses):

• 775 total student positives (pop. 74,500)
• 323 Tempe on-campus (pop. 9,645)
• 452 off-campus/other positives (pop. 64,855)
• 28 faculty/staff (pop. 12,400)

Interval percent positive (3,253 new tests, 323 new positives): 9.9%

Case rates over interval (new cases over interval in parentheses):

• Tempe on-campus: 158.7 cases per day per 100,000 (46 new cases)
• Student, other: 69.9 cases per day per 100,000 (136 new cases)
• Student, overall: 81.4 cases per day per 100,000 (182 new cases)
• AZ 7-day average: 7.4 cases per day per 100,000 (NY Times)

Inferences for total student population:

1. Using 452 positives 3 days prior as baseline

Inferred doubling time under exponential growth: 3.9 days
Inferred Rt: 1.9

2. Using 161 positives 6 days prior as baseline
Inferred doubling time under exponential growth: 2.6 days
Inferred Rt: 2.3

September 3.

ASU disclosed: 43,425 tests since August 1; data up to September 2.

Of note, all prior update documents no longer appear to be available on ASU’s website. Also of note, on-campus Tempe population changed to 9,662. Total faculty/staff positives were reported as 26, an anomalous 2 test decrease since the 28 cases given the last two updates.

Cumulative positive results (total population in parentheses):

• 957 total student positives (pop. 74,500)
• 369 Tempe on-campus (pop. 9,662)
• 588 off-campus/other positives (pop. 64,838)
• 26 faculty/staff (pop. 12,400)

Interval percent positive (3,023 new tests, 182 new positives): 6.0%

Case rates over interval (new cases over interval in parentheses):

• Tempe on-campus: 158.7 cases per day per 100,000 (46 new cases)
• Student, other: 69.9 (136 new cases)
• Student, overall: 81.4 cases per day per 100,000 (182 new cases)
• AZ 7-day average: 7.4 cases per day per 100,000 (NY Times)

Inferences for total student population:

1. Using 775 positives 3 days prior as baseline
Inferred doubling time under exponential growth: 9.9 days
Inferred Rt: 1.35

2. Using 452 positives 6 days prior as baseline
Inferred doubling time under exponential growth: 5.5 days
Inferred Rt: 1.63

3. Using 161 positives 9 days prior as baseline
Inferred doubling time under exponential growth: 3.5 days
Inferred Rt: 1.99

Some Simple Model Fits to Coarse Student and Zip Code 85281 Data

Brief Model Description and Student Data Fits

Figure 1. Simple processing of disclosed data into daily interpolated cumulative cases loads and daily new case rates; case data is for the entire student population. Figure by the author.

Obviously, as new data becomes available, we get different estimates for our doubling times and Rt. It is also likely not appropriate to assume exponential case growth at this point. Therefore, I have assumed a constant per-day case rate for each disclosure interval, and linearly interpolated to get a very crude representation of possible daily cases (see Figure 1). From there, I fit a classical susceptible-exposed-infected-recovered (SEIR) model, which is characterized by three basic parameters:

1. Infectious contact rate
2. Latent period from infection to infectiousness
3. Recovery rate

The basic reproduction number can be estimated as the ratio of infectious contact rate to recovery rate. Assuming a mean latent period of 5.1 days and an effective recovery rate of 1/(3 days) (assuming cases are detected relatively quickly and quarantined), I perform a piecewise fit on the infectious contact rate, as well as the initial infected population. Total student population is fixed at 74,500.

Depending upon how data cutoffs are chosen for the piecewise fit, it is possible to conclude that the current reproduction number is either well above one, or has crashed to well below one at the end of the data series, with very different implications for the future. This is probably related to the crude nature of the data and the short time window. Two example fits with the model run an additional 7 days, yielding very different predictions, are given in Figure 2. Since this exercise is inconclusive, I turned to the Arizona case data by zip code.

Figure 2. Two potential SEIR model fits (that are then run an additional 7 days) to the student case data also given in Figure 1. Very different outcomes are possible with the same model and data. Figure by the author.

85210 Data and Model Fits

Figure 3. Daily cases (as a 7-day moving average) for the top 100 zip codes in Arizona with the most total COVID-19 cases. Tempe zip code 85281 is highlighted in red. Figure by the author.

For this part, I have performed a piecewise fit to cumulative daily case data for Tempe zip code 85281 (main zip code for ASU), obtained via the Tempe City government data portal at this link. But first, note that this zip code has seen a large increase in cases compared to other large zip codes, with Figure 3 showing the 7-day average daily case count for the 100 zip codes with the highest COVID-19 case counts in Arizona; 85281 is a clear outlier.

A piecewise fit to the data was performed using the same SEIR model framework, with a total zip code population assumed to be 57,348. Figure 4 shows the raw data and piecewise model fits (unlike the student data, results are highly insensitive to the exact fitting choices). Final infectious contact rate is estimated at about 1.36 contacts per day with an effective recovery rate of 1 / (3 days). This yields an approximate basic reproduction number of 4.1 (just divide the two numbers).

Figure 4. Raw data and SEIR model fits (with infectious contact rate fitted piecewise) for zip code 85281. Daily cases are on the left panel, cumulative cases on the right. Figure by the author.

Some serious caveats are in order. This model-fitting exercise does suggest a rapidly spreading epidemic in zip code 85281, but it is likely these cases are primarily concentrated in the smaller ASU community, so a simple model that does not distinguish populations could be misleading. Furthermore, it takes a few days for policy/behavioral changes to become apparent in data, so this exercise may also overestimate transmission. In any case, the data thus far continues to suggest a serious epidemic centered around ASU, with a reproduction number most likely over 1, but future trajectories are highly uncertain. The downtrend in new case rates is encouraging, but the situation remains highly tenuous.

Code Availability

MATLAB and Python code to reproduce these results will be made available on GitHub, pending the author’s recovery from exhaustion. Stand by for updates.