Chris T. Bauch of McMaster University in Ontario and his colleagues set up a mathematical model to investigate possible reactions to a smallpox vaccination program using game theory (which predicts behavior in settings where the benefits of a strategy depend on decisions made by others) and the epidemiological dynamics of how smallpox spreads. In terms of vaccination policy, an individual is trying to minimize his risk of getting sick, either from the vaccination itself or from a bioterrorist attack. If the majority of the population is already immune to the disease, a particular individual has less to gain by volunteering for vaccination because his chances of being exposed to the disease are lowered.
According to the report, relying on voluntary vaccinations would result in a 54 percent compared to optimal immunity for the "best guess" scenario using estimated values for parameters such as vaccinator response time, the rate of vaccinations and the number of individuals attacked, according to the report. When the researchers varied the parameters across their potential ranges, they determined an average increased mortality of 22 percent. The authors note that public health officials should consider appealing to people's altruistic streaks, because "our results illustrate how the conflict between group interest and self-interest typically causes large differences between vaccine coverage levels that are best for the group and uptake levels that might actually be achieved under a voluntary vaccination program."