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I am not a doctor or medical student, so I may understand this wrongly,

According to most article, corona vaccine success rate would be around 95%.

According to status, only around 2.5% died from covid-19. So roughly, 97.5% will survive. So I don't understand what is the purpose of having corona vaccine with 95% success rate since without a vaccine also 97.5% survive?

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Two major reasons and one minor:

  • Herd immunity: The 95% for which the vaccine works are not only spared from the disease, but they also do not infect others and thus do not contribute to spreading the virus. In absence of hygienic countermeasures, an average person infected with Covid-19 infects about 3 others on average (basic reproductive rate). As this number is bigger than 1, the virus can spread; otherwise it would die out. Now, if 95% of those 3 would be immune thanks to the vaccine, only 0.15 people would get infected on average, which is far less than 1 (and it gets even better with hygiene). If the entire population were vaccinated instantly (with 95% success rate), Covid-19 would die out in a few weeks, simply because it could not spread anymore.

  • Independence of probabilities: There is no reason to expect that the vaccine works exclusively for people who would also survive an infection. For a simple calculation, let’s assume that the vaccine is equally likely to work for everybody, i.e., independent of their chances to survive an infection¹. In that case the vaccine saves 95% of the 2.5% that would be killed by the virus and only 0.125% would die (0.05·0.025 = 0.00125).

  • It’s not only about deaths. Survivors of Covid-19 can still suffer from severe long-lasting or permanent damage. This is also something you want to avoid.


¹ This is a simplifying assumption, because whether the vaccine works for you depends on your immune system, which also influences whether you survive corona. However, probably nobody knows yet how strong this correlation is and what its direction is, i.e., whether the vaccine works better or worse for corona-sensitive people (this would also depend on the individual vaccine). The assumption is certainly closer to the truth than that the vaccine only works for those who would survive anyway.
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You seem to have misunderstood efficacy.

The 95% efficacy figure is a derived from a ratio of the number of cases in the control group (no vaccine) to the number of cases in the vaccine group. So, if both groups have 1000 people, perhaps 100 people in the control group become infected, while only 5 people in the vaccine group become infected. The vaccine efficacy is 95%, since the number of cases in the vaccine group is 95% lower than what you saw in the no-vaccine group (note that these numbers are illustrative and not actual figures).

A 95% efficacy does not mean that 5% of people will die from the disease. It doesn't even mean that 5% of people will become infected. It means that 95% of people who would have otherwise been infected will not be. If everyone was magically vaccinated today, you would expect the number of cases to drop by 95%, and the number of deaths from the disease to drop by a similar amount. Instead of 2.5% of the population dying, it might be more like 0.13%.

Note that there will be major downstream effects since viruses spread in an exponential manner - an important number you may have heard of is called R0, which represents the average number of new people an infected person will infect. A vaccine can cause R0 to drop below 1, meaning that the number of cases will dwindle over time. It's not just the case that a vaccine will prevent infection in 95% of people who would have otherwise gotten the disease, it also drastically lowers the number of people who "would have otherwise gotten the disease", since 95% of vaccinated individuals won't spread the disease.

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