Externalities are a basic concept in the economics of health care. Yet actual ACIP policies do not pay significant attention to externality issues. The rationale for vaccination recommendations often doesn’t consider strategies to target sub-populations, such as school children, that are most likely to generate negative externalities by spreading the disease.
A paper by Boulier, Datta and Goldfarb (“Vaccination Externalities”) uses epidemiological modeling to estimate the marginal social benefit of each vaccine. The model is based on the Susceptible-Infective-Removed (SIR) model. A population is divided into 3 groups: (S)usceptibles can catch the diseases, (I)nfected individuals can transmit it, and (R)emoved individuals are those who have recovered from a disease. Individuals who are vaccinated are placed in the R group with probability m, where is the efficacy of the vaccine.
The model is fairly complex and will not be fully discussed here, but it is important to note the three determinants of a disease’s infectiousness.
- The rate of contact among population members: When individuals have more contact with each other (e.g.: at school, sporting events), the probability of coming in contact with more infected individuals is higher.
- The transmissibility of the disease given contact
- Period of infection: With a longer infection period, it is more likely that you will come in contact with an infected individual.
The paper’s conclusions are as follows:
“Five positive and negative findings are of particular interest. The most striking positive finding is that the actual size of the vaccination externality can be large at some levels of vaccination. In particular, for some of our influenza simulations, the marginal externality can exceed one case of disease prevented among the nonvaccinated for each additional vaccination. A second striking positive finding is that the marginal externality of vaccination may rise and then fall with increases in the fraction of the population vaccinated. The exact pattern depends on the infectiousness of the disease, and the effectiveness of the vaccine. Third, the patterns of externalities we find are quite different from, and more complex than, the diagrammatic presentations found in standard microeconomics or health economics textbooks. Fourth, the marginal social benefit of vaccination need not be monotonically related to the infectiousness of a disease. Fifth, externalities need not vary monotonically with vaccine efficacy, or the infectiousness of the disease.”
Intuitively, we see that the marginal private benefit to vaccination decreases as the number of individuals vaccinated in the population increases. The marginal social benefit of vaccination, however, increases initially from zero as more people are vaccinated since increasing the number vaccinated not only prevents the individual from being infected, but also reduces the infection rate in the general population. Eventually, however, the marginal social benefit reaches a peak and the marginal social benefit declines. This occurs because after a certain point, there are very few people left who can transmit the disease (most have been vaccinated). For instance, if there are 1000 people in the population and 997 have been vaccinated, only these 3 people are transmitter, so vaccination will provide a small marginal social benefit.
- Boulier, B., Datta, T., Goldfarb, R. 2007. “Vaccination Externalities” The B.E. Journal of Economic Analysis & Policy, 7(1).