Tracking Covid-19

Based on the professional literature available, there are some inconvenient truths about Covid-19 that are not always considered in the chorus of confusion that exists today. Here we summarize what is known, what has already happened, and what is to be expected based on the analysis of the data and the epidemiological models.

Background

An analysis of the first 425 laboratory-identified cases of a novel coronavirus infected pneumonia (Covid-19) is presented by Qun Li, et.al.¹. The first cases were identified at Wuhan hospitals as a "pneumonia of unknown etiology" when the patients met the following criteria: fever in excess of 100.4°F, radiographic evidence of pneumonia, low or normal white-cell count or low lymphocyte count, and no symptomatic improvement after antimicrobial treatment for 3 to 5 days according to standard clinical guidelines. On Jan. 7, 2020, the outbreak was confirmed as a new coronavirus infection².

The analysis of these 425 initial cases revealed an average incubation time of 5.2 days, with a 95th percentile at 12.5 days. In its early stages, this outbreak had a doubling time of 7.4 days and an average time between successive infections of 7.5 days. For those who were hospitalized, the average time between the onset of illness and admission was 12.5 days. While 24 of the 45 cases identified by Jan. 1, 2020, were connected to the Huanan Seafood Wholesale Market, the closing of this market on that date did not stop the spread of the infection. Clearly this infection could be transmitted person-to-person among close contacts. On Feb. 11, 2020, The World Health Organization (WHO) named it Covid-19 and by March 11 had declared a pandemic².

The Covid-19 Response Team at Imperial College London published on March 16 what one of our colleagues called "the best study so far available"³. This team used epidemiological models to look at how nonpharmaceutical interventions (NPIs) are likely to affect what happens in both the United Kingdom and the United States. We will discuss these NPIs and the team’s findings later. We mention this study now because it is the source for much of the following information.

The basic reproduction number for this infection appears to be in the neighborhood of 2.2 to 2.4 ^1,3. This is an estimate of how many new people in an uninfected population are likely to be infected by each person with Covid-19 on the average. For comparison, the seasonal flus have a basic reproduction number between 1.0 and 2.1. Analysis of data from China and from those returning on repatriation flights suggest that up to 40 percent to 50 percent of Covid-19 infections were not identified as such because of infections with no symptoms and persons with mild disease ³.

The infection fatality ratio (IFR) for Covid-19 is estimated to be about 1 percent, which is about 10 times that of typical seasonal flu. However, this is not uniform for all ages. Those in their 60s have an IFR of 2.2 percent. Those in their 70s have an IFR of 5.1 percent, and those in their 80s have an IFR of 9.3 percent³.

Tracking Covid-19

No data have any meaning apart from their context. When we are presented with numbers one value at a time we have trouble interpreting them. When we place those numbers in context they help us to understand where we have been and where we are going. When tracking the actual course of a pandemic this need for context is crucial. The situation is changing and the question is no longer "Has a change occurred?" but rather "How fast are things changing?" To this end we do not need anything more than a simple running record, but it helps to know what kind of running record to draw. 

When working with exponential growth phenomena, the primary graph has always been the semi-log plot. The actual counts are plotted on a logarithmic scale while the dates are plotted on a linear scale. This plot preserves the nature and interpretability of the data since it plots the actual values, but it turns the exponential growth curves into straight lines. Since it is much easier to see when the slope of straight a line changes than it is to tell when a curved line changes shape, the semi-log plot is more easily understood. Moreover, it is easier to extend a straight line to make reasonable, data-based short-term predictions than it is to try to extend an exponential growth curve on a traditional graph⁴.

(For those who are not familiar with a semi-log graph, these graphs can be created in Excel using the scatterplot tool and choosing one axis to use a logarithmic scale. There is even a YouTube video on how to do this.)

Figure 1 lists the number of confirmed Covid-19 cases in the United States as reported by the European CDC⁵.

Figure 1: Number of confirmed Covid-19 cases in United States

These values show that in the United States the number of confirmed Covid-19 cases has increased a thousand-fold in 25 days (from 103 to 104,686 between March 3 and March 28).  Since 2 raised to the tenth power is 1024, a thousand-fold increase represents 10 doublings. Ten doublings in 25 days gives an average doubling time of 2.5 days. The numbers in figure 1 double every two to three days throughout most of March. Figure 2 shows the data of figure 1 on a semi-log graph.

The straightness of the line shows a fairly stable exponential growth.  However, the last few days show some slight change in the angle of the plot. Changes where the growth curve becomes more horizontal are known as "flattening the curve." Changes like this represent slower growth for the pandemic. Here the counts double between March 28 and April 2, so the current doubling time is estimated to be about five days.

Figure 2: Confirmed Covid-19 cases in the United States

What can be done?

While several pharmaceutical treatments are being tried, none have yet proven to be effective for Covid-19⁶. Thus the only thing left is prevention which depends upon nonpharmaceutical interventions. There are five NPIs that were considered by the Imperial College task force when they ran their epidemiological models:³:

The first NPI model was case isolation in the home. Symptomatic cases stay at home for seven days. The second NPI model was voluntary home quarantine for 14 days for members of a household with a symptomatic case.

The third NPI model was social distancing of those over 70 years of age. This model assumed the reduction of workplace contacts by 50 percent and the reduction of other contacts outside the household by 75 percent.

The fourth NPI model was social distancing of the entire population. This model assumes this will reduce contacts outside the household, school, or workplace

The fifth NPI model was the closure of all schools and 75 percent of all universities.

These five NPI models were aimed at reducing contact rates within the population and thereby reducing the transmission of the virus. The microsimulation epidemiological models show that the effectiveness of any one intervention is likely to be limited, requiring multiple interventions to be combined to have a substantial impact on transmission.

The first three intervention models—case isolation, home quarantine, and social distancing of those at risk of severe disease—make up an optimal mitigation policy. Mitigation has the potential to slow the epidemic spread, reduce the peak healthcare demand by two-thirds, and cut the number of deaths in half³. However, since this will still overwhelm the intensive-care units and result in thousands of preventable deaths, the alternative of suppression has to be considered. Suppression has the aim of reducing the effective reproduction number (the average number of secondary cases each case generates) to below 1.0³.

The epidemiological models for the United States show that suppression will require no less than social distancing of the entire population, home isolation of cases, and household quarantine of their family members. The major challenge of suppression is that this type of intensive intervention package will need to be maintained until a vaccine becomes available. If the interventions are relaxed, the models show that the transmission of Covid-19 is likely to quickly rebound³.

New Rochelle

New Rochelle is a suburban city of 80,000 in Westchester County which is just north of New York City. The numbers of confirmed Covid-19 cases reported by the Westchester County Health Department for New Rochelle are given in Figure 3.

Patient One for New Rochelle had been sick since February 27, but was only identified as being infected with Covid-19 on March 2. After his test came back positive several interventions were instituted, beginning with the closure of his synagogue, the quarantine of 100 families from that synagogue, and the tracing of Patient One’s contacts. On March 12, after 122 people had been found to be infected, an isolation zone with a one-mile radius from the synagogue was established by special order and all places where people could congregate were closed. The National Guard was called upon to deliver food to people sequestered at home and to clean gathering places within the zone. On March 13 a drive-thru testing center was set up near New Rochelle⁷. On March 25 the mayor announced plans to relax the isolation zone restrictions, but this was superseded by the governor’s stay-at-home order which was already in place.

Figure 3:  Number of confirmed Covid-19 cases in New Rochelle

As may be seen in figure 4, the growth curve began to flatten out on March 7, after the initial surge. While the curve continued to climb, it was climbing much more slowly than previously.

Figure 4:  Confirmed Covid-19 cases in New Rochelle

Between March 19 and March 30 the number of cases doubled from 172 to 346. Thus, these data show a doubling time for New Rochelle of 11 days. This doubling time is comparable with what is happening in countries that are doing a good job of mitigating the pandemic such as Japan, Taiwan, and Singapore⁵.  (At this time, among those countries with more than 100 cases, only China, South Korea, and San Marino have suppressed the pandemic by getting the graph horizontal and reducing the effective reproduction number down to 1.0 or less⁵.)

A traditional way of looking at epidemiological data is to track the number of new cases each day. When we do this for New Rochelle we get the graph in figure 5. There we see three surges in the number of cases.

Figure 5:  Number of new cases each day in New Rochelle

While the spread of Covid-19 was effectively suppressed for two short periods, each time it rebounded. Another aspect of the Covid-19 pandemic is illustrated by this graph—declines in new cases of Covid-19 lag behind the interventions. Accordingly, these data cannot be used to establish cause-and-effect relationships.

In addition, deaths from Covid-19 lag even further behind. On March 27 there had been a cumulative total of 9 deaths from Covid-19 cases in all of Westchester County. Three days later this total had climbed to 19 deaths. The next day, March 31, there had been a total of 25 deaths from this outbreak. All of this suggests that while non-pharmaceutical interventions can be used to mitigate, or even suppress, the Covid-19 pandemic, these interventions have to be maintained until pharmaceutical interventions become available.

What lies ahead?

Returning to confirmed Covid-19 cases for the U.S. shown in Figure 2, the slight flattening of the most recent points is encouraging. The last few days show a doubling time of about 5 days, which is better than the earlier doubling time of 2.5 days. However, Figure 6 shows that this doubling time still puts us on track to hit one million confirmed cases by April 14 or 15.

Figure 6:  Confirmed Covid-19 cases in the United States

Hopefully we will continue to flatten this curve, but we have a long way to go. Effective mitigation will require a more rigorous adherence to the nonpharmaceutical interventions than we have practiced in the past. If we do not flatten this curve, when should we expect to hit 10 million confirmed cases? 

Covid-19 fatalities

As of April 3, the United States had 6053 Covid-19 fatalities⁵. Figure 7 shows the plot of these Covid-19 fatalities. The projection arrow is based on the last seven values.

Figure 7:  Covid-19 fatalities in the United States

If this curve does not get flattened further, we could have as many as 100,000 deaths as soon as April 17. Since this does not consider the impact of finite medical resources, we cannot continue to simply wait for things to improve on their own. 

Download this Excel spreadsheet, enter the daily numbers yourself, and have a similar graph automatically updated for you.

Also, this simple Excel spread sheet should help show the difference between a linear vs. semilog chart for showing exponential data.

References

1. "Early Transmission Dynamics in Wuhan, China, of Novel Coronavirus-Infected Pneumonia," Qun Li, et. al., New England Journal of Medicine, v.382, No. 13, March 26,2020.

2. Liu Xia, Na Risha, Bi Zhengiang. "Challenges in the prevention and control of new coronavirus pneumonia" [J/OL].  Chinese Journal of Epidemiology, 2020, 41 (2020-03-28) <http://rs.yilgle.com/yufabiao/1186569.htm.DOI:10.3760/cma.j.cn112338-20200216-00108. [Internet pre-publishing].

3. "Impact of nonpharmaceutical interventions (NPIs) to reduce Covid-19 mortality and healthcare demand," Imperial College, London task force

4. "Single Subject Studies in Prostate Cancer: How Graphing the Data Can Provide Insight and Guide Clinical Decisions," Al Pfadt and Don Wheeler,
Oncogen Journal 2(2) 10, March 14, 2019.

5. Website of the European Centre for Disease Prevention and Control

6. "A Trial of Lopinavir–Ritonavir in Adults Hospitalized with Severe Covid-19," B Cao, et. al., New England Journal of Medicine, March 20, 2020.

7. "A Cluster Site Sees Progress After Isolation" Sharon Otterman and Sarah Maslin Nir, The New York Times, Saturday, March 28, 2020, vol.CLXIX, no. 58,646.

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