It helps to start with a mental model of the variables and how they relate to one another. If you remember your grade school math, you might remember the Venn diagram. Basically, a person must be part of the potentially exposed group to contract the virus. Among those that contract, some will have severe symptoms, some of those will be hospitalized, and some of those will die. Now it is possible to die without going to the hospital or be hospitalized without severe symptoms. So the model is imperfect but descriptive for the relationships. The question is how to define the step from one group to another.
You might notice that there is a cloud-like line between the general population and the contracted or symptomatic group. Perhaps the biggest issue today is identifying those in the population that have contracted the virus form the general population.
Questioning the Variables
The model seems simple but there are multiple issues. This section looks at variables starting from the center and moving out.
Death/Hospitalized/Severe: There are two issues with defining death in relation to the virus. First, causality, the virus seems to have a greater impact on those with certain pre-existing conditions. Did the person die of the virus or of pneumonia or diabetes or age?
Especially early in the progression of COVID-19, people may have a bad case and it is simply not recognized. A person without good insurance may tough it out – assuming it is the flu. Even hospitalized patients may be misdiagnosed – partially due to the lack of tests.
Second, time frame, we get daily reports of number of cases and the number of deaths. There is a natural urge think these two numbers are related because they are both going up. The problem is that death occurs at a specific point in time.
A person with a case of COVID-19 may be active for at least two weeks and longer for those severely ill. The counts for contracted, severe, hospitalized, and death should be moving at different speeds because it takes a different amount of time to be in each of these groups. As a region build from one to 10 to 100 to 1000 cases, there should be a lag time between diagnosis and death. The combination of causality and time frame make it difficult to determine the rate of severe reactions.
Contracted or Symptomatic: Around the world has been the biggest problem. It is impossible to know the number of cases without testing. China, the United States, and others have denied the existence of the problem or had been unable to produce tests until reaching an emergency level of possible cases. Even today, the United State cannot test people that are not systematic.
Rate of infection, rate of hospitalization, severe reaction, and death are all proportions that depend on two relatively unknown numbers. At the same time, calculating the rates are essential for planning. If this week there are 1,000 known positive cases, 50 have been hospitalized, 20 have needed ventilators, and ten have died, it is easy to make assumptions and plan for resources. Assumption errors are multiplied as case grow from 1,000 to 100,000.