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The “big picture” of the overall pandemic
I am going to collect here my analysis of daily COVID-19 cases (C), hospitalizations (H), and deaths (D) in Fairfax County, Virginia, between March 17, 2020, and Sept. 1, 2021, along with a simple model (M) I developed for each of these based on the data; I have updated one model parameter derived from the data between March 17, 2020, to March 17, 2021. The data are taken from the public database maintained by the Virginia Department of Health for each county in Virginia, and may differ slightly from a local database maintained separately by Fairfax County. You can convert to per capita cases for comparing to other places if you use the population of Fairfax County in 2020 and 2021 of 1.15 Million.
The figure below for the 533 days from 3/17/20 to 8/31/21 shows the actual data for cases along with solid lines reflecting 2-week averages of the C, H, and D data. The dotted lines give the predictions CM, HM, and DM for each of these from my model M explained below the figure. The model follows all the trends in H and C and evens out the statistical fluctuations, although these persist even in 14-day averages.
The quantitative assumptions of the model are designed to be simple and to capture several basic aspects of the pandemic:
- Since there were many uncounted cases in the early data due to a lack of adequate testing, the key model assumption is that hospitalization H tracks actual cases CM by a fixed ratio rh; the model also assumes a fixed death ratio DM/CM=rd. This assumption allows the model to adjust model cases CM based on known hospitalizations. To keep the hospitalization ratio HM/CM fixed at rh, the model needs to take CM = 5xC at the peak in C for day 50 and then assumes case counting was approaching accuracy exponentially and was 90 percent accurate by day 200. These are plausible assumptions that allow the model to fit all the data trends fairly well.
- The Model is
- The formula is CM = C x [ 1 + 4×10-(day-50)/150 ]. This is shown as a dotted black line, which is indistinguishable from the reported cases on the graph by around day 200.
- HM = CM/33, that is, rh=1/33 corresponding to 1 hospitalization for every 33 actual cases; the dotted green line shows HM.
- DM = CM-14/120, that is, there is rd=1/120 corresponding to 1 death for every 120 actual cases, counted from 14 days earlier. This shift in days is needed since deaths lag cases. This assumes a 2-week difference between case onset and average death. The dotted red line shows DM. Note: my former model assumed rd=1/200, but that lower rate undercounted total deaths (when summed over all days), and therefore needed to be adjusted to fit the data.
- The model predicts that there have been 139000 total cases in Fairfax County between 3/17/21 and 8/31/21 compared to 83000 reported cases. The ratios rh and rd are such that the total hospitalizations and deaths from the model agree with the actual reported values, 4180 and 1140 respectively.
- If my model should miss uncounted cases (that is, the Fairfax case count beyond day 200 is an undercount), then the fixed ratios rh and rd will need to be corrected to account for such cases. If rd is correct, then the death rate of 1 in 120 cases implies that COVID-19 is 8 times more deadly than the seasonal flu, which has a lower death rate of 1 in 1000 cases.
- The ratios rh=1/33 and rd=1/120 can be compared to the pandemic averages for the whole Commonwealth of Virginia, for which rh=1/23 and rd=1/65. In both cases, the Fairfax rates are significantly smaller (and thus better) than those for Virginia as a whole. I do not have an rh for the USA, but rd=1/61 (642000 deaths in 39.5 million cases), quite similar to the rate in Virginia. If I only used reported cases for Fairfax (83000) instead of model cases including uncounted ones (139000), I would have rd=1/72. Thus, based on reported cases alone, Fairfax, Virginia, and the USA have similar magnitudes for their case death rates, 1/72, 1/65, and 1/61. This suggests that all three entities may have similar errors due to uncounted cases. I take my model rd=1/120 to be more realistic, since the model accounts for data after around day 200 when testing for cases became generally available and widespread in Fairfax and also accounts for the estimated uncounted cases prior to day 200.
The model and the actual data do not agree in every detail, but this is precisely what is expected for such a very simple mathematical model based on fixed ratios rh and rd. It can not track fluctuations and fine details. But it is remarkably good in tracking the overall trends using the fixed rh and rd ratios.
The total number of reported cases, hospitalizations and deaths in Fairfax County between 3/17/20 and 8/31/21 are 82955, 4179, and 1137. “Reported cases” refer to persons who have tested positive for COVID-19. With a population of 1.15 Million, that means that 1 in 14 of our residents have tested positive. However, the 67 percent larger number of cases, 139000, that my model predicts implies that 1 in 8 of our residents has actually been positive for COVID-19. This higher number of total cases is based on the known number of hospitalizations and the assumed fixed hospitalization rate of rh=1/33.
The data clearly have some broad trends. First, there have been three major peaks, the first being the initial ramp-up of cases in the spring of 2020. The second from October 2020 through January 2021 is likely due to many more indoor social events due to the onset of fall and winter and the Thanksgiving and Christmas holidays, since it is known that the airborne mode of transmission of COVID-19 is favored indoors. The third ramp-up starting in early July 2021 is surely due to circulation of the highly contagious new Delta variant.
A number of studies from many different countries and times have noted an approximately 2-month ramp-up to a peaks in cases followed by a drop-off. This relatively consistent pattern has no known explanation and remains a puzzle. It might have something to do with how the virus finds susceptible people until it runs out of a ready supply of such. It might also have something to do with people adopting behavior changes, like more masking, distancing, and hand washing when everyone knows cases are rising rapidly. Whatever the cause, it seems realistic to expect a halt in cases and a drop-off after a rapid ramp-up. The details of a drop-off will depend on time and place.
Interestingly, the time between the end of June and beginning of October 2020 had relatively low case rates near or below 100 cases per day. Following the winter peak, there was a rapid decrease in cases once vaccinations started to ramp up in February 2021, especially evident from late April 2021 when partial and full vaccinations in Fairfax County approached and exceeded 40 and 25 percent respectively. By the last couple weeks of June 2021, the pandemic seemed nearly over: cases had nearly halted, with only very few cases per day in Fairfax (the graph shows an artificial dip towards zero cases in this time period; this is because the Department of Health removed some previously reported cases, causing even a negative case count for some days). Hospitalizations dropped to an average of less than 1 per day in early July, and deaths did the same later in July, reaching a rate of less than one per week. Presumably the few deaths that did occur in early July were due to lingering cases from previous weeks or months. Since with a few cases, statistical fluctuations and outlier cases affect the data, the model predictions do not track the details very well when case rates are small, say below 10 or 20 cases per day.
Differences by age group
Fairfax County maintains data by age group. The distribution of cases among the 4 age groups 0-17, 18-49, 50-64, and 65+ is the following: 15, 55, 20, and 10 percent of reported cases respectively. The distribution of deaths among the same age groups is 0.1, 4, 14, and 82 percent respectively. Thus, the 65+ age group has 82 percent of the deaths but only 10 percent of the cases. This translates to a very high death rate of 1 death for every 9 cases of people age 65+. This is where vaccinations help a lot. Fairfax does not report cases or deaths by vaccination status, but data from elsewhere indicate that for fully vaccinated people of age 65+ the death rate is closer to 1 in 50 cases, much better odds. Vaccinations are known to lower cases, hospitalizations, and deaths in ALL age groups, but this is especially significant for those over 65, since this group has by far the highest death rate of any age group.
The new data I have been collecting for the past 2 weeks (see below) show that cases in the under 18 age group are up by 73 percent in Fairfax County, whereas cases over age 50 are down by 23 percent. There is a definite shift to younger age groups. There is a hint of this in the data on death by age group, which I have been keeping from the daily Fairfax reports since Aug. 15. Of the 11 deaths between Aug. 15 and Aug. 31, the distribution by age group 0-17, 18-49, 50-65, 65+ is 1, 1, 3, and 6 respectively. This recent death of a person under 18 is tragically the very first in that age group in Fairfax County since Fairfax started keeping data back in March 2017. The 6 deaths from the over 65 group represents 55 percent of the 11 total, a significant drop from the pandemic average of 82 percent. With a caveat about statistical fluctuations, it appears that deaths are shifting younger too, correlating with the higher fraction of cases among younger people, who are much less likely to be vaccinated than people over 65. This is another argument for the need for vaccinations in all age groups for reducing needless deaths from COVID-19.
Recent trends June – August, 2021
The graph below magnifies the above graph for Fairfax County from June through August 2021 (except I changed averaging to 7-day averaging for this shorter time span). The graph also adds the predictions of exponential doubling models with doubling times of 8 and 10 days. While the initial Delta ramp-up indicated a doubling time around a week, the actual data have bent away from that rapid increase and are leveling now, consistent with the idea of a leveling in cases after around 2 months of ramping up (see above). Only time will tell whether cases remain low, given that schools are just now restarting in Fairfax, potentially a source of new infections.
The average hospitalization rate has tended to remain lower than my model predictions by roughly 50 percent, or half of the predicted value. While I do not have a specific explanation, it may be related to vaccinations, since breakthrough cases in vaccinated people tend to lead to less severe illness. In any case, it would be good if H now turns out to be nearer C/60 instead of C/33.
The rate of reported deaths has started increasing significantly, from less than 1 per week to 7 per week in the last week (equivalent to 1 per day). On the graph, the discrete integer values (1, 2, 3, …) of H and D in the data are evident (although zero does not show up on a log graph), whereas averages can take on any value, including between 0 and 1. Currently hospitalizations lie in the range of 0 to 6 per day, with an average around 3 per day, whereas my model predicts around 5 per day. The number of deaths per day are more typically 0 or 1, but we had 4 in one day last week, and 7 deaths in the 7-day period ending Aug. 31. My model now predicts a daily rate of around 7 deaths per week. The model is surely in “the right ballpark,” and can be used for guidance, but can not predict daily statistical fluctuations, only long term trends when there are 20 or more cases per day.