Saturday, March 24, 2007

Nash strategy and public health

A recent article (subscription may be required) in the Economist talks about semi-rational public behavior for vaccine for seasonal (not pandemic) flu. Those choosing the vaccine are those most at risk - mostly the elderly and to a lesser extent those (like me) on a short vector. Which makes sense. This is an example of what I might describe as a Nash behaviour, in which people who can't or won't negotiate will make purely selfish (motivated by personal cost/benefit) decisions.

But the classic vector for flu is to be brought into the home by kids, where the adults then catch it and subsequently spread it in their workplaces.  The Nash vaccination behaviour is calculated to result in 100 times more flu infections than what is called a utilitarian strategy, in which the immunization of at least 77% of kids would roughly eliminate the disease for lack of a vector with which to maintain itself. "When a critical proportion of a group is immune to a disease, too few individuals are susceptible for that disease to be passed from one to another".

This is where the article stops. Going a further step, I wonder at the net national financial impact of Nash vs utilitarian strategy for flu vaccination. What would be the effect of 100x fewer flu infections on productivity, GDP, trade balance, and eventually exchange rate? Qualitatively, would there not be an increase in productivity, causing a small increase in GDP (decrease in health and drug industries, increase in others), and disproportionate increase in trade balance? What would it do to an B$836.1 US trade imbalance?

I'm reminded of a story in Britain a few years ago, about parents who were opting out of universal vaccination for some diseases (smallpox and red measles come to faulty mind) because there was no practical incidence any longer. In essence, a selfish (in the Nash sense, not a value judgment) decision to benefit from the vaccination of others and counting on not enough folks opting out to create a new propagation vector. Not to pick on Britain - I'm sure this happens elsewhere as well, but I encountered the story while living in Britain.

The very odd thought occurs to me that if a group makes a public decision to eradicate a disease by semi-requiring global immunization, but only 70% immunization is required to achieve the goal, who should make the decision about which 70%? Should those excluded be the higher risk, or the more nervous/selfish?
If individuals, how do we incent (reward) private decisions for public goods such as disease prevention and national productivity?

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