I'm not seeing where the probabilities in the decision tree come from. Does 10% of the unvaccinated population catch flu every year, and 6% of the vaccinated? Those seem extraordinarily high figures, and I don't see them in the text. The two figures together imply an efficacy of 40%, not the 60% cited. The connection of the other probabilities to the data is also not clear.

Although the costs of the possible outcomes shown in Figure 1 were calculated under the assumption that the individual receiving the flu shout was uninsured, having an insurance policy greatly increases the expected value of receiving a flu shot, as many insurance companies will completely cover the cost of receiving a flu shot.

You're still paying for the medical care you receive on insurance. You're just paying in advance, at a rate that the insurance company calculates to cover the expected costs, plus their own profits. If the entire population suddenly goes out and gets flu shots this year, that will show up in everyone's premiums down the road. If your employer pays your insurance, you're still paying, in the form of a lower salary. The only people who don't pay medical costs are those on public benefits, whose costs are paid by those not on benefits.

ETA: This applies to nationalised health systems as well. Flu jabs are there paid for by taxes. All these different ways of paying for it may distribute the cost in different ways, but that cost is always paid. If it were not paid, there would be no vaccinations.

ETA2: Likewise sick pay. If your employer guarantees your salary while you're sick, it's at the cost of your salary when you're well. The cost is spread over the whole company, but it is paid. The cost is always paid.

I'd also like to see some sensitivity analysis, given that the $14 benefit derived from the model is a difference between much larger figures, $104 and $90.