There are some countries that are deliberately suppressing their real numbers --- and can get away with this because they are effectively authoritarian states with limited free press - China, Iran, North Korea and other countries are examples.
It is more difficult to get away with fake numbers in western democracies since the press will eventually report on the actual toll.
However the numbers in western countries are still off for several reasons which include:
- A limited number of COVID-19 testing kits cause many people with symptoms not to be tested or counted. Leading to case under-count.
- People with mild cases just stay home and never contact officials and are not counted. Leading to case under-count.
- People afflicted with the flu, colds or other medical issues may be simply assumed to have COVID-19 due to lack of testing. Leading to case over-count.
- The number of deaths may be under-reported since people who die at home are not "post-tested" and simply not counted in the COVID-19 mortality count. One example of this is New York City. This leads to mortality under-count.
- In some places non COVID-19 deaths may simply be counted as COVID-19 since they died now and no post-testing was performed... and examiners just add this to death certificates This leads to mortality over-count.
The issues above show why there may be over-counts and under-counts even when a nation tries to do their best in this crisis. There can also be additional reasons for over-count & under-count including sloppy record keeping and tracking system computers being overwhelmed.
Until the U.S. follows the example of South Korea and Germany in terms of tracing every case, testing everyone who was near a COVID-19 patient, and carefully examining every death then we will not know the true numbers or have proper control over the pandemic. I will note that the mortality rate is also much lower in these two countries because they did proper testing, had medical facilities ready which were not overwhelmed, and took proper measures early.
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As a side note about China; both the U.S. and U.K. intelligence communities issued reports stating the counts in China are under-reported. The U.S. stated by a factor of 16 to 40 minimum. The Brits stated flatly it was definitely above a factor of 40 in the death count. Other estimates from media in Japan, Hong Kong, and other SE Asia countries for deaths and cases in China have the numbers much larger at 2 million dead and 40 million cases -- but there is no solid proof backing this.