THE existing formula is simple. When vaccinating against influenza, inoculate those most susceptible to the disease's wrath. Such vulnerable types include the elderly (who are the most likely to die if infected) and infants (whose immune systems are not fully developed). This seems a reasonable policy, and it is the one that has long been promulgated by America's Centres for Disease Control (CDC). Only recently has it been extended to include children up to the age of 18, on the basis that they are more likely than other people to catch flu in the first place, through enforced socialising at school—even though they are at little risk of dying from it.

According to Jan Medlock of Clemson University in South Carolina, and Alison Galvani of Yale, however, vaccinating those most at risk of bad effects is not the right way to deal with the disease. In a report published this week in Science, they argue that even with the extension of vaccination to school-age children, the existing policy of protecting the individual is still playing down the real public-health value of vaccines—namely that they create a so-called herd immunity which helps to break the disease's chain of transmission.

They argue that it would be better to concentrate on vaccinating those most likely to spread the virus—both schoolchildren and people between the ages of 30 and 40, who are likely to be the parents of those children, and who are, at the moment, at the bottom of the vaccination priority list. That, at least, is the outcome of their mathematical model of how influenza spreads. Indeed, it is almost all of the outcomes. For in order to obtain a robust result, Drs Medlock and Galvani considered two different sorts of epidemic and five different definitions of an optimal conclusion.

As model epidemics they chose those of 1918 (the famous “Spanish” flu that is reckoned to have killed 50m-100m) and 1957 (less lethal, but still pretty nasty). As definitions of a good outcome they started with two simple measures: the number of infections averted, and the number of deaths averted. They then went on to look at more sophisticated measures: the number of years of life saved (taking into account the ages of those who would otherwise have died), the “contingent valuation” of those lives and the economic cost of vaccinating.

Contingent valuation is based on surveys of the “disutility” of death at different ages. This provides a crude way to balance what has already been invested in a life against what might come of it. Measuring economic costs weighs the expense of both vaccination and illness against the net present value of the future earnings of someone who would otherwise die from the disease.

Yet no matter which outcome was looked at, nor which pattern of epidemic was chosen, the result was the same. The best approach to influenza is to vaccinate young people and their parents, not infants and the elderly. Moreover, it is a cheaper and more efficient option. Around 85m doses of vaccine are distributed in the United States in normal years. Dr Medlock and Dr Galvani reckon that if their approach were followed, that might be cut to just over 60m.

As luck would have it, though, the new advice agrees more closely with the recommendations of the CDC's advisory committee on immunisation practices about the best approach to the epidemic of N1H1 swine flu that is now circulating. For reasons still unknown, elderly people are not as susceptible to this strain as they are to others, and what deaths there have been have tended to occur among the young—particularly young adults. The strategy of “vaccinate those at risk” thus coincides with “vaccinate the spreaders”. A fortunate coincidence, perhaps.