Vaccine calculus: the missing variable

What we are lacking to do a proper risk-benefit analysis

Vaccine zealots claim that Covid is always worse than the vaccine, and therefore make rational sense for everyone to take. Even if vaccines do harm to children, they say, those harms are less than the harms done by Covid, so the equation still works out in favour of the vaccines.

Vaccine skeptics claim that vaccines do not prevent Covid and incur additional costs, and therefore only make sense for even the most at-risk populations, and even then might not be worth it.

My argument is that we don’t have the available evidence to answer the cost-benefit question, because everyone gets the calculus wrong.

Let’s define some terms:

Cv = Cost of vaccine

Cc = Cost of Covid infection

Pv = Probability of vaccine

Pc = Probability of Covid infection

With these terms, the costs for the unvaccinated can be defined as:

Cost = Cv*Pv + Cc*Pc

Where unvaccinated individuals have a Pv=0 and thus incur cost Cc*Pc (the cost of Covid only). There is good data on what the costs of Covid are for unvaccinated individuals - myocarditis, hospitalization, hypoxia, pulmonary hypertension, blood clots, cell damage, etc. But what are the costs to vaccinated individuals?

Is it Cv*Pv only? No, because we now know vaccinated people can still get Covid.

What we need to know is Cb - the cost of Covid breakthrough infection, and the probability of a breakthrough infection, Pb. As more and more data shows, Pb is not small - the vaccinated face a similar risk of breakthrough infections, particularly over > 6 month period. But the data I have seen on breakthrough cases focuses on how likely they are (Pb), not the relative harm done (Cb).

For all we know, Cb = Cc, or in other words, a breakthrough case of Covid in the vaccinated is just as harmful as a case of Covid in the unvaccinated, all else being equal.

With these terms, the costs in the vaccinated can be defined as:

Cost = Cv*Pv + Cb*Pb where Pv=1

In order to claim the cost-benefit analysis favours the vaccine, one must prove that, for any individual:

Cv + Cb*Pb < Cc*Pc

Where Cv + Cb*Pb = the costs incurred in the vaccinated,

and Cc*Pc = the costs incurred in the unvaccinated.

I have seen no such analysis, and it stands to reason that this very simple equation, a year into the vaccine campaign, has not been proven to be true.

The vaccinated eat the costs of the vaccines and the costs of breakthrough Covid, whereas the unvaccinated only eat the costs of Covid.

And when Cc can be lowered by using alternative treatments like ivermectin, quercetin, azithromycin, hydroxychloroquine, fluvoxamine, etc. it becomes even more likely that this equation will not hold true.

Therefore, we cannot say the vaccines are clearly worth it for anyone. In fact, it may very well turn out to be the case that the equation always tilts in favour of the unvaccinated.