Back of envelope calculation: the number and the costs of freezers needed for the Pfizer vaccine.

I always love back of envelope calculations so I thought I would do some for the number of freezers needed for the Pfizer vaccine which, as I pointed out in my last post, needs a -80C medical grade freezer. First off, let’s assume we want to have lots of vaccination stations and we want to get everyone vaccinated within a few months. That means I will assume each vaccine station gets a 3 cubic foot -80C freezer- they cost about 13k each retail, say 10k wholesale?

https://www.thermofisher.com/order/catalog/product/ULT390-10-A#/ULT390-10-A

Each box holds 6,300 2ml vials which I will assume are roughly enough for one person’s dose, round down to 6,000 as is customary in a back of envelope calculation. (And yes I know it’s possible they will use larger vials that hold more individual doses but for a back of envelope calculation, I don’t think that is relevant.)

Since the vaccine requires two doses a month apart, for the sake of this back of envelope calculation, I’m just going to assume we want to have storage for 125 million doses per treatment center at a time because we want to distribute 500 million doses over a month. We need to distribute the vaccines via a truck that would also store the vaccine at -80C so let’s assume we will have the capacity for 75 million doses stored on trucks as they move to the treatment centers from the manufacturing centers. So the trucks themselves need a fair number of freezers because ordinary refrigerated trucks don’t come close to -80C.

O.K. we need to store 200 million doses by assumption because we need to duplicate some capacity to deal with both transport and treatment stations. So we get about 34,000 of these freezers needed at a cost of about 340 million. Not bad $$ wise, but that’s a lot of freezers that we will need to manufacture relatively quickly – and these are not your garden variety chest freezers, since they have to be ultra-reliable at -80C. Also, we need to equip each of the delivery trucks with a 50amp diesel generator to power the freezers – they probably run about 3k each and let’s assume each truck gets two large 20 cubic feet -80C freezers that each hold roughly 40,000 doses, so each truck can deliver 80,000 doses. (Turns out the cost of a 20 cubic foot freezer isn’t much more than a 3 cubic ft freezer interesting enough: https://www.thermofisher.com/order/catalog/product/ULT390-10-A#/ULT390-10-A) 

Anyway, we then need roughly 1,000 diesel generator equipped trucks then to transport the vaccine doses around,, so using a figure of say $3,000/per generator that is a basically irrelevant $3 million for the generators.

Now, of course, you can assume that the vaccine will take, say a year to distribute, and the numbers come down considerably – by a factor of maybe 25. I think I’m not going to hope for that and maybe a six-month rollout is what is going to happen. So my back of envelope calculation leads to about three or four thousand freezers needed, which seems far more doable.

Well, no this isn’t actually the right simplification and my mistake  shows the trouble with back of envelope calculations. leave out something and they go all cattywampus. In this case, I think we also have to have enough vaccine stations to mitigate the number of people who can reasonably wait in line or in their cars. If we don’t, the lines for vaccines will make the lines we saw for testing look like a walk in the park. Oh, and yes we also need to have at least one vaccine station in each town of say more than 10,000 people and less than 25,000 people. (There are 1,572 towns with a population of between 10,000 and 25,000 in the United States.) Anyway, looking at this table: https://www.statista.com/statistics/241695/number-of-us-cities-towns-villages-by-population-size/ and assuming we want a minimum of one vaccine station for each town and say at least one per 25,000 people, I get that even for a slower roll-out, we may need at least 10,000 -80C freezers – and maybe more. 

(Of course, all this may not be necessary. The Moderna mRNA vaccine looks like it can be shipped and stored in ordinary freezer trucks. Other vaccine candidates seem to have even less severe storage requirements.)