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It is often argued that because the number of infections is greater in the vaccinated
fraction of a population, compared to the unvaccinated fraction, the corresponding vaccine is not effective. But this is a simple logical error.
The point being that while the *number* of infections in the vaccinated can be greater, because of a high vaccinate rate,
the *percentage* will be lower unless the vaccine really is ineffective.

Another way to think about it, is to consider that a small percentage of a large fraction of a population can easily be greater than a large percentage of a small fraction of a population.

In the default scenario, the number of infections in the vaccinated is twice that of the unvaccinated, but the vaccine is still 90% effective; i.e. it reduces infections by 90%.

Use the sliders to set up your own scenario. Use the "Get Link" button to get a URL to your scenario.

Number of people in population

Background vaccination rate

Number of people infected who are vaccinated

Number of people infected who are unvaccinated

The NUMBER of infections is greater in the vaccinated

but the PERCENTAGE of infections is lower

and the vaccine is effective.

but the PERCENTAGE of infections is lower

and the vaccine is effective.

The vaccine is effective.

Percentage of those vaccinated who are infected

Percentage of those unvaccinated who are infected

Vaccine effectiveness