As the pandemic progresses every day, each government reports the number of infected persons per day, the number of deaths and the critical state patients. But how does the the governments get to know the numbers? Basically every time someone reaches the healthcare system, and is a suspect, they will be tested. If positive, he or she we will be counted as a new infection. Also if the healthcare system test individuals without a reason and are positive they will also be counted.
The accuracy of the numbers with this approach will depend on how the pathogen operates. If the infected person detects symptoms before spreading it and contaminating others, or the infected person dies, the numbers will be quite accurate.
However on cases that transmission time is large and asymptomatic most of the infection period, the reported numbers are unrealistic.
The COVID-19 pathogen combines three important behaviours:
- It may or not produce symptoms;
- While asymptomatic the virus can spread until about 14 days;
- Produces symptoms similar to flue on mild to moderate cases and pneumonia on critical cases.
By the time the healthcare system detects a moderate or critical case, the infected individual has already spread the virus without knowing to many others… So the presented numbers will have a low correlation with the state of the spread.
Although the correlation isn’t the best, it is what’s possible to gather at the moment. I can imagine that the correlation will be higher in places the virus infects people which become moderate to critically sick. On places where the population is young, spread geographically and with an immune system capable to deal with the infection, might even pass unnoticed. The correlation will also improve if we test people as much as possible.
If 80% of the population has mild symptoms, these individuals do not go to the healthcare system and no preventive testing done, only 20% will actually call for help and be registered.
It is possible that values measured for total active cases of infection be 5 to 10 times higher than measured. This will depend on the aggressiveness of the virus and population fitness, considering we catch on the healthcare system 20% to 10% infections.
σ is our estimation ratio of the percentage of infected captured by the Healthcare system.
So multiplying the reported value by a number between 5 and 10 will give you a more accurate infection count.