Posts Tagged COVID-19
This post is about a simple idea that came to us from Reverend Thomas Bayes (b. 1701) who studied statistics (now called Bayesian Method) . Here is the basic idea:
If a disease is very common, the test for it can be very simple.
If a disease is very uncommon, the test for it needs to be very accurate.
In regard to the 2020 COVID-19 pandemic in the U.S., the virus is very common. So, at this time the easiest and most accurate test is a simple questionnaire. In this questionnaire if you have two or three of the symptoms then you likely have COVID-19. If you have been in contact with someone with known COVID-19 and have any symptoms, then you likely have COVID-19. Is testing a symptomatic person absolutely needed? No. But, that’s not the end of the story, see the connected issues below.
☐ Fever or chills
☐ Shortness of breath or difficulty breathing
☐ Muscle or body aches
☐ New loss of taste or smell
☐ Sore throat
☐ Congestion or runny nose
☐ Nausea or vomiting
So, if this simple check list is so great, why do some people need the nasal or oral swab testing (PCR viral test)? Because the virus sometimes causes no symptoms — early or late in the disease and sometimes never. Note that the check list did not have “
☐ No Symptoms” as a selection. That makes sense, there is no way a person would think they are sick if they feel fine — yet they may be spreading virus to many other people.
The concern about “silent spreaders” is a huge problem. Once a person is known to have COVID-19 (diagnosed or suspected) then that person needs immediate quarantine for 14 days and must get in contact with the health department to start tracking down contacts that MAY OR MAY NOT have symptoms. Those contacts without symptoms should have the nasal or oral PCR testing if available. As they wait for the results (which can take hours to days) they must be quarantined.
Some silent spreaders can be tough to track down: taxi drivers, doormen, receptionists, grocery clerks, and bus drivers. Essentially, people who have huge numbers of contacts that people often forget to mention. Here is a scary thought: if people around you are getting COVID-19, maybe you are the silent spreader.
The Health Department has a huge job, and they need everybody’s help. Do what they say, don’t waste their time, and become informed by reading about the disease online. The 130,000 deaths so far in the U.S. is very serious business.
Someday COVID-19 will be uncommon (that would be nice), then we will need a very accurate test for the disease. That very accurate test sadly does not exist right now (PCR currently has about 30% false negatives — meaning the test is negative, but you actually have it).
When the vaccine is available, take it ,and in the mean time, wear your mask and practice social distancing.
China has run the gauntlet with the novel Coronavirus. They do not report any new cases now and the population is cautiously and gradually returning to normal activity. China has reported on the number of cases and deaths despite very difficult times. One problem they have had as will other countries is how to report deaths that did not happen in a hospital or without testing to verify the presence of COVID-19.
The main question currently in the United states is when will the population be free from restrictions to stay at home? As mentioned in the previous post the experience from china gives some clues. The following are two graphs; the first shows an overview of number of new cases over time (left axis) and the number of deaths (right axis). The data becomes erratic at the peak of the curve when the hospitals and healthcare workers were overwhelmed. The bell-shaped red is a fairly good fit to the number of new cases. The yellow curve is from a similar effort at fitting a curve (see below) to the numbers of deaths per day.
The disease started sometime at the end of December 2019 and spread. Millions of people were confined to their residences finally leading to no new cases about 2 months later. The peak of cases happened around February 8 while the peak of deaths was about 1 week later. The deaths subsided about 2 weeks after the peak, marking continued hospital overload and a reservoir of virus that could escape and threaten the population again.
China has been criticized for the reporting of deaths, and the irregularities are easy to see around the peak of deaths probably related to a saturation of the health care system. Patients likely died at home since admission to hospitals was not possible and furthermore an exact diagnosis based on PCR testing was lacking. Nevertheless, the picture is sufficiently clear to be a guide for other countries regarding what to expect.
In a region such a one of the States in the US several milestones should be reached before social distancing is eased:
- No new cases in a State
- Borders to the State remain closed if adjacent states still have active cases (people could leave states but would likely need 2 weeks of quarantine if they return).
- Hospitals only have a few remaining cases of COVID-19 patients and have the staffing to receive emergencies if needed (this could take about 2 weeks from the last new case).
- The State Health department has the capacity to rapidly trace any new cases and institute strict quarantine.
- Adequate and rapid viral testing is available to the health department and physicians.
Social distancing allowed many persons to avoid infection, associated illness and death. A resurgence of COVID-19 is easily possible in the populations of uninfected individuals.
Healthcare workers and any other workers who have survived the illness could return to work at any time, even now. They are at very low risk due to the immunity developed to clear the virus from their bodies. At some point, a test for immune status based on antibodies present in the blood would be helpful because a large number of persons were probably infected and not diagnosed at the time with PCR testing (the mouth or nose swab). Persons with adequate antibodies also could safely return to work now.
So what does the crystal ball suggest: many people will be returning to work toward the end of April, 2020. There will be states that lag because the virus started in those states later — that’s going to be a difficult pill to swallow. Predictions about what will happen are subject to lots of unknowns. With time, the end-game will be more clear.
At the height of the novel Coronavirus infection the transmission rate is about one to three. Meaning that one person infects three. When that rate drops from three to less than one then the virus is losing ground and will fade away. When no new cases happen then the virus has no way to reproduce and is gone (yea!).
An individual who contracts the virus (sorry) the illness lasts about two weeks. A small percent (less than 2%) may die. The good news is that surviving the virus means the body fought it off leaving lots of antibodies floating around in the blood to prevent reinfection with the same virus (at least for several years).
The initial fear was that the virus might mutate (change it’s structure) quickly so that a person’s antibodies would not be effective for very long. Fortunately for humans, the little devil does not seem to mutate quickly (needs more observation to be sure). Surviving persons cut the transmission rate since they don’t catch the virus.
That brings us back to the original question: exactly when will the pandemic end? We can only guess because the answer is up to the virus and how well people avoid each other. Effective drugs against this virus or immunizations are simply not available now and almost certainly will not be available for at least a year (perhaps in 2021).
Did you say guess? Yes. So let’s make an educated guess. China was a huge experiment. In that country the virus went away (with great effort) in about sixty days. That’s roughly what to expect in the United States.
The Chinese experience revealed the course of the virus followed a ubiquitous mathematical progression called a Gaussian curve, otherwise known as the “bell-shaped curve”. The number of new cases goes up, hits a peak and then declines. The mathematical equation for the Gaussian curve is a little complicated:
y = a * exp( 0 – (x – b)^2 / (2 * c^2))
where y it the number of cases on the vertical axis
x is the day on the horizontal axis (1,2,3,4,5…)
a is the height of the peak
b is the day where the peak happens
c is the width of the bell.
Once some of the actual data is known (e.g. the numbers of new cases) a curve fitting program can figure out a,b and c. Here is an example for the State of Colorado in the United States at the time this post was written: (see updated graphs at end of post)
In the graph the blue dots are the number of new cases each day and the red line is the Gaussian curve fitted to the available data. The best “guess” is that new cases will stop at the end of April where the red curve hits zero. Of course, the medical havoc from the virus in those final few people infected would last for another two weeks. The peak of new cases happens at about April 5th. Unfortunately, the peak of deaths occurs about a week after the peak of new cases.
The end of new cases for the United States overall is more complicated than China since the virus started in the various states at different times. The sum of all the bell-shaped curves from each State may create a US curve that shows several small delayed peaks or just a skewed curve with a longer tail on the right side — time will tell.
Once the virus has subsided in one area it is possible a flare-up could happen due to travel of infected persons into an area that had many non-infected people. If that happens, the State health department should quickly quarantine the area — another mini bell-shaped curve will happen in that area.
Whether the virus will come back later this year or next year or never is unknown. If it does, many people will be immune and laboratories may have a greater ability to test for it. Hopefully pharmaceutical companies will manufacture an immunization. Is this the last pandemic? NO. We must do a better job of preparation and acting on the warning signs. Will humans remember this lesson? (no answer).
Updated graph of cases per day in Colorado, USA as of 4-14-2020
Update for Colorado, USA as of 4-21-20
Observation: as more testing is done more asymptomatic cases are being found. This has the effect of hiding stay-at-home measures with an artifactual bump in numbers if new cases. The aberration should be less with time and with lower number of cases. At this point many analysts believe the rate of hospitalizations may be the best indicator of disease activity. Steve Goodman, Stanford Professor of Epidemiology & Medicine, gave an interview to KPIX, a local TV station 3/25/2020, supporting the importance of hospitalization data:
A graph of current COVID-19 cases is below and now includes hospitalizations (and a 4-point smoothing curve).
Update for Colorado, USA as of 5-1-2020
Today the state will begin to allow some workers to return to work and stores to offer limited (curbside) service. The new case and new hospitalization data have reached a variable level that is much lower than most models (without stay-at-home orders) predicted. The stay-at-home strategy appears to have reached the goal of “flattening” the curve. Unfortunately, restrictions of movement are being lessened while the virus is still at peak activity. An additional concern both nationally and in Colorado is the late reporting of cases which has muddied the waters.
Some modeling experts predict a resurgence is in the offing. Below is the latest graph without the Gaussian prediction for new cases and with the use of a 7-day smoothing (necessary due to the erratic reporting). The “dump” of “unreported” deaths confuses the overall picture — such deaths probably happened over several weeks, not on one day.
The success of stopping the virus in New Zealand, Australia, Vietnam and China was due to forceful stay-at-home orders. In Colorado and the US as a whole, such force of law and will is lacking and stems from a huge concern about economics. The sentiment among retired people is to stay-at-home to minimize risk; consequently, many new deaths will likely be in members of the workforce.
At the start of this post the “assumption” was the US would try to stop the virus. That made predicting an “end” a reasonable endeavor — now that is no longer the case and some time will need to pass for a new pattern to emerge. Only when hospitalizations are near zero will we feel Colorado is close to the end of the pandemic.