Mathematical analysis of publicly disclosed COVID-19 case data at Arizona State University indicates an out-of-control epidemic

While the numbers are presented as benign, a closer look shows an unfolding disaster

Academic Caveat: The following analysis and findings have not been peer-reviewed. All opinions are solely those of the author.

An update on more recent numbers can be found here, but the original text of this article will remain unaltered.

First: The Takeaways

• Under public pressure, Arizona State University disclosed limited COVID-19 case data on August 25 and August 28, 2020. However, the presentation was highly misleading, and a re-analysis of what is available suggests a rapidly spreading epidemic that is hitting students living on campus especially hard.
• ASU highlighted an estimate of the effective reproduction number, Rt, as 0.87 for Arizona as a whole; when this value is less than one the epidemic is shrinking. Analysis of the data disclosed by ASU suggests an Rt of almost 3 for the ASU community, implying instead a rapidly growing epidemic.
• COVID-19 positivity rates are misleadingly presented as 0.2% confirmed positive for ASU faculty/staff and 0.6% confirmed positive for the student body. This refers to the percentage of these populations that have had a positive test. Actual test positivity percentage is inferred to be 7.22% from August 25 through August 27. Also, an extremely worrisome 2.13% of the Tempe on-campus student population has tested positive just one week after classes began.
• Per capita case rates over the last few days are many times higher in all ASU populations than in the general Arizona population. Our best estimate is that the on-campus student population case rate is 64 times that of the general Arizona population.
• Doubling time for the current epidemic at ASU is inferred to be 1.9 days. If this does not change, the majority of ASU students, especially those living on campus, will be infected in a matter of weeks. While transmission dynamics do typically evolve in ongoing epidemics such that spread slows, intervention is still needed, and previous studies suggest that even small delays in control interventions can mean large differences in total cases.

Intro: Re-analyzing data from ASU

Universities across the country are reporting increasing coronavirus cases, and many have already closed to in-person classes. Arizona State University’s decision to re-open its campus to in-person learning and invite students to live on campus has met with controversy. Especially contentious was the university’s initial decision to disclose no case data, either to the public or to the vast majority of students, staff, and faculty.

Apparently under public pressure, the university has now made two disclosures (on August 25 and August 28) with lumped case data but relatively little detail [1,2]. The text of the latter disclosure suggests that there is little cause for concern, with test positivity rates less than 1% and a reproduction number less than one. I performed an independent analysis of the data in these disclosures to estimate case rates, test positivity rates, case doubling times, and effective reproduction numbers for the ASU population in general and the on-campus Tempe student population in particular. I found that, rather than being under control, all data available to the public indicates instead an epidemic that is out of control and spreading rapidly, especially in the on-campus student population.

Overview of the Results

I estimate that the case rate per 100,000 per day, over the three day interval between the two disclosures is 122 cases per 100,000 per day, about 16 times higher than Arizona overall. My best estimate for the Tempe on-campus population is 470 cases per 100,000 per day, or 64 times the Arizona average. Overall test positivity is calculated to be 7.22% over the three-day interval. The university’s emphasis on positivity as a fraction of positive cases divided by the total population, not tests performed, is therefore profoundly misleading.

The emphasis on the reproduction number (Rt) for Arizona as a whole, which is indeed likely less than one (an Rt less than one implies cases will decline exponentially, while Rt greater than one implies exponential growth in cases), is similarly misleading. I estimate that Rt is well over one for the lumped ASU population, likely just under 3, and most likely substantially higher for the Tempe on-campus population. I infer a doubling time of 1.9 days for cumulative cases in the ASU population. This inferred doubling time suggests that, if current trends continue, over 25% of the on-campus population will be infected within a single week, and most of the ASU population will be infected in two weeks time.

Coronavirus epidemics have thus far been characterized by very rapid growth in the early phases that tapers, and so these rapid transmission dynamics may not persist for long. Students may spontaneously modify behavior in light of these statistics, and the early surge in cases is likely concentrated in those most likely to catch the disease. Therefore, while no firm future predictions can be made, the present numbers suggest dramatic intervention to interrupt transmission is urgently required at ASU in general, and the Tempe on-campus population in particular. Moreover, other work (e.g. [3]) has concluded that the earlier non-pharmaceutical interventions (e.g. lockdowns, etc.) are implemented, the greater the benefit to controlling COVID-19 epidemics; even a single week’s delay may mean nearly twice as many infections [3]. If these calculations are even roughly accurate, I do not believe continued large scale student presence on campus can be justified at this time.

There is necessarily a great deal of uncertainty to my calculations, as virtually no data on daily case rates or demographics has been disclosed by ASU. I ask the ASU administration to help clarify, confirm, or refute our conclusions by disclosing detailed, daily case data, along with any internal epidemiologic analysis. Based on what is publicly available, these are the best estimates concerning the basic quantitative epidemiology of the unfolding epidemic at ASU that can currently be made.

Finally: All the Details!

Here are all the details on the calculations, in boring academic-ese…

Limited quantitative case data was disclosed on August 25, 2020 [1], and August 28, 2020 [2]. In the first disclosure, it was reported that, since August 1, 32,729 tests of ASU students and faculty were collected with 161 positive results. No further temporal, spatial, or demographic data was disclosed, nor was the end date of testing, but it may be reasonable to assume data coverage was up to August 24, 2020. In the second disclosure it was stated 37,149 tests had been conducted from August 1 to August 27, and the following data was provided:

• 28 total known positives among 12,400 total faculty and staff. No information on number of tests was provided.
• 452 total known positives among our total campus immersion student body of 74,500. No information on the number of tests was provided.
• More than half of these positive cases reside off campus in the metropolitan Phoenix area. 205 (out of 9,645 living on the Tempe campus) are in isolation on the Tempe campus.

We can infer 4,420 tests (37,149–32,729) were conducted between August 25 and August 27, resulting in 319 positive tests (480–161), giving an overall positivity rate of 7.22%. This is obviously quite different than a reported “0.2%’’ positive rate for faculty/staff or “0.6%’’ positive rate for the student body [2]. We can infer minimum and maximum daily case rates per 100,000, over the dates of August 25 though August 27, by either allocating all or none of the first 161 cases to different subpopulations. We derive a central estimate by assuming the same fractional allocations of total cases through August 27 as through August 24. For example, 205 out of 480 cases (42.7%) on August 27 were in the on-campus Tempe population, so we similarly assume 69 of the initial 161 cases occurred on-campus. Ranges with central estimates in parentheses are given as follows:

• 122.36 cases per day per 100,000 for total faculty/staff/student population (319 cases, 3 days, 86,900 total population).
• 130.20–142.7 (134.23) cases per day per 100,000 for the overall student body (between 291 and 319 student cases since August 24, 300 new cases as central estimate, student body of 74,500)
• 152.07–708.48 (470.02) cases per day per 100,000 for students living on Tempe campus (44 to 205 cases, 136 new cases as central estimate, population 9,645)
• 44.20–126.95 (84.29) cases per day per 100,000 for students not living on the Tempe campus (86 to 247 cases, 164 new cases as central estimate, population 64,855)
• 0–75.27 (51.08) for ASU faculty and staff (0 to 28 cases, 19 new cases as central estimate, population 12,400)

As of August 29, Arizona as a whole saw 7.4 cases per day per 100,000 averaged over the last seven days, and even at the height of the Arizona epidemic in late June and early July, daily cases hovered around 50 per 100,000 [4]. Thus, daily case rates over the last several days are at least 17.5 times greater than the AZ average in the student body as a whole, and at least 20 times and possibly almost 100 times as great in the Tempe on-campus student body; rates may be as much as tenfold higher in ASU faculty and staff population as well. Therefore, it is reasonable to infer that transmission among the ASU community is being driven by student cases, especially among the on-campus population.

If cumulative cases did indeed go from 161 to 480 in just three days, this yields a doubling time of 1.9 days, for an exponentially growing epidemic, which in turn corresponds to a basic reproduction number, R0 (similar to Rt early in epidemic time), of almost 3, according to the following formula [5]

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

where td is the doubling time and g is the case generation time, which is about 5.0 days as an overall mean [6]. Thus, we get R0 of 2.82 if we assume a generation time of 5.0 days and td of 1.9 days.

We can also determine an absolute minimum doubling time of 8.6 days and minimum reproduction number of 1.40 for Tempe on-campus students as follows: Since at most 161 on-campus students had been diagnosed with COVID-19 as of the first disclosure, an increase to 205 over three days gives an 8.6 day doubling time and 1.40 R0 value. Similarly, going from 161 cases to 247 for off-campus students yields a doubling time of 4.9 days and reproduction number of 1.71.

These are strictly minimums, and the calculations simply serve to show that we can decisively rule-out a reproduction number less than 1 for either on or off-campus student populations. Since transmission appears to be overwhelmingly concentrated in the smaller on-campus population, it is virtually certain that the doubling time is smaller and the reproduction number greater for this subpopulation, compared to overall ASU averages.

If ASU case numbers continue to grow exponentially at the same rate, we can expect a cumulative 6,141 cases across the ASU population in seven days time, and 2,623 cases in the Tempe on-campus group. Virtually every on-campus student and the majority of the ASU population will be infected in less than two weeks if these trends continue. However, as noted above it unlikely that such virulent transmission will persist long-term.

Finally, as a hypothetical exercise, we can also calculate the minimum number of “locked-in’’ cases from the current case load and the baseline Arizona reproduction number, purportedly 0.87 [2]. Since this value represents the number of new cases created by each current case, in a single transmission generation we must go from 480 cases to 418 cases, which themselves generate an additional 363 cases, and so on. Summing until transmission ceases yields 1,577 total cases in the on-campus population, and 3,692 total cases overall. Again, this is assuredly a gross underestimate, but is a best-case scenario when using the inappropriate reproduction number cited by ASU.

References

[1] An Update on ASU’s COVID-19 Management Strategy. August 25, 2020. https://president.asu.edu/statements/an-update-on-asu%E2%80%99s-covid-19-management-strategy

[2] UPDATE: ASU COVID-19 management strategy. August 28, 2020.
https://president.asu.edu/statements/update-asu-covid-19-management-strategy

[3] Pei, S., Kandula, S., \& Shaman, J. (2020). Differential Effects of Intervention Timing on COVID-19 Spread in the United States. medRxiv. doi: https://doi.org/10.1101/2020.05.15.20103655

[4] New York Times. Arizona Coronavirus Map and Case Count.
https://www.nytimes.com/interactive/2020/us/arizona-coronavirus-cases.html

[5] Britton, T. Basic estimation-prediction techniques for Covid-19, and a prediction for Stockholm. medRxiv. doi: https://doi.org/10.1101/2020.04.15.20066050

[6] Ganyani, T., Kremer, C., Chen, D., Torneri, A., Faes, C., Wallinga, J., & Hens, N. (2020). Estimating the generation interval for coronavirus disease (COVID-19) based on symptom onset data, March 2020. Eurosurveillance, 25(17), 2000257.