Should I Vaccinate? A Mathematical Model.

Economists have long preoccupied themselves with trying to make rational decisions, especially when facing risk or uncertainty. From allocating your money between different asset classes, to choosing whether or not to be vaccinated — such rational choice models can help you decide whether or not the risks of a decision are worth the expected payoffs.

In 2005, long before COVID-19, researchers from the City University of London’s economics department published a paper on how rational individuals can decide on whether to be vaccinated. I thought it would be interesting to see how that might help us make some rational decisions about whether or not to take a COVID-19 vaccine.

But before we proceed — two things should be noted. Firstly, this model is a selfish one. It does not consider how the calculus would change if the majority behaved cooperatively, making it safer for everyone in the group. So if you care about people other than yourself, this model does not account for that. Secondly, this model is highly dependent on the reliability of your input calculations. Calculate the inputs wrongly, and you are likely to produce irrational outcomes. As with all models: garbage in, garbage out.

So assuming you are both (i) incredibly selfish, and (ii) incredibly good at accurately calculating probabilities and outcomes, here’s what you should do:

Step 1: Relative Risks

Calculate your expected risks (probability) of:

• being infected (ρ), and
• having adverse reactions from the vaccine you intend to take (φ)

Step 2: Estimated Losses

Calculate your expected losses:

• Due to vaccine side effects (S): Like nearly everything in life, taking a vaccine comes with risks such as adverse side effects. The losses from adverse side effects can be calculated by estimating your expected income losses and attendant costs arising from negative side effects of the vaccine.
• Due to infection from not being vaccinated (I): Not getting vaccinated is not risk-free either. You can calculate the estimated losses you are likely to suffer by estimating your expected income losses and attendant costs arising from infection.

Step 3: Vaccine Efficacy

Calculate the expected:

• efficacy rate of the vaccine you intend to take (e): This is readily available from the manufacturers’ data from their clinical trials.

Step 4: Should I Vaccinate?

Put the input variables you calculated above into the simplified decision rule below (relax, its just multiplying fractions):

This decision rule expresses four key ideas:

1. It is only rational to vaccinate when you expect the relative risk of infection to risk of side effects (left hand side) to be greater than the threshold probability level of expected losses (right hand side).
2. The higher the expected losses from adverse side effects (S), the higher is the threshold probability on the right hand side of the model. A larger risk of adverse events means more expected income losses arising from vaccine side effects, reducing your willingness to vaccinate.
3. The higher the expected losses from infection (I), the lower the threshold level of probability above which individual decides to get vaccinated.
4. The vaccine efficacy (e) has an inverse relationship with the threshold probability (right hand side). The higher the vaccine efficacy, the lower the possibility of infection, and therefore the larger the propensity to accept vaccination; and vice versa.

However you feel about the vaccine, this model provides a handy way to think rationally about balancing both the risks and benefits of being vaccinated. It also encourages us to identify our key assumptions more clearly, even if you arrive at a different conclusion from everyone else.

If you found this helpful, feel free to share it with anyone you know who may be undecided about getting vaccinated.