The flu and game theory

The current swine flu scare is a reminder that the flu is a fierce disease. New strains can develop quickly and disarm populations. One only has to remember the 1918-1919 Spanish flu which caused anywhere from 20 million to 40 million deaths.

Combating the flu is no small feat. It requires anticipating new strains, developing vaccines, and delivering medicine to masses. And ultimately the success depends on coordination of real people, which means global governments, hospitals, and individuals. Accordingly, there are many strategic issues in fighting the flu that can be better understood using the framework of game theory. Here are three strategic questions:

1. Is the swine flu panic good?

A casual observer might be cynical about the media attention. The death toll so far does not seem to warrant the extensive coverage. Is the fear meant to promote ratings and profits? Is it meant to help the government extend its power?

Perhaps the answer is something more beneficial. Jake at EconomPicData offers an interesting alternative on the swine flu scare using game theory. His matrix suggests that “induce panic” is a dominant strategy (I’ve recreating the text in a slightly more readable table):

link to original

Jake’s analysis makes a good point, but there are a few problems. One is the government plays this game repeatedly with the public over many issues. Calling too many false alarms will damage its reputation and limit its effectiveness.

Second, the entry labeled “nothing happens” for a false scare is not accurate. There is much cost to creating a false panic. Hospital emergency rooms are being flooded, schools are closing temporarily, and governments are banning imports of pork products without solid evidence. In a drastic measure, Egypt killed almost 300,000 pigs without conclusive evidence that the pigs were infected with the virus.

The appropriate answer, therefore, is to walk the middle line. Just as excessive punishment does not deter crime appropriately, excessive fear does not prepare populations cost effectively. The punishment must fit the crime, and the fear induced should fit the facts.

2. When a vaccine is developed, who needs to take it?

There is little question why the elderly and the sick are advised to get flu shots. They account for 90 percent of deaths from the flu, and so the benefit of the vaccination appears to outweigh whatever risks there are.

But what about the healthy and young? The flu is not as likely to affect them, and there are costs and risks to the vaccination. What is the right answer?

From a social perspective, it is beneficial for the healthy to get vaccinated, as explained by Robert Bazell in Slate:

That is the major reason you should get a flu shot. Even if spending a week violently sick and bedridden doesn’t worry you, by immunizing yourself you vastly lessen the chances you will spread the virus to some child or older person (family member, friend, or stranger) who might die from it.

In medicine, this concept is called “herd immunity”-that is, if enough members of a group of animals (including humans) are immunized against a disease, the entire group is more likely to escape infection.

The problem with herd immunity, however, is deciding who has to get the shots. Individually healthy people would prefer not to go through the effort of getting the shot and “free ride” on those who do. The situation is akin to the prisoner’s dilemma, which may explain the low vaccination rate in the U.S.

(Two ways to tackle this problem would be to make vaccinations mandatory and subsidizee flu shots to minimize the cost barrier).

3. Going forward, what’s the best way to select the flu vaccine?

Selecting the flu vaccine is an amazingly complex problem, and the mathematics are stunning. Consider the following simplified and slightly unrealistic math problem (obtained from these lecture slide ppt)

Suppose there are two expected strains of flu and two vaccines that can combat them. The distribution of strains is unknown and one can only guess how effective the vaccines can be.

It is believed that vaccine 1 will have an 85 percent chance of working against strain 1 but only a 70 percent chance against strain 2. Similarly, vaccine 2 has a 60 percent chance against strain 1 but a 90 percent change against strain 2. Here is the matrix to summarize the odds:

Suppose each person can only get one vaccine due to cost considerations. Clearly neither vaccine is effective against both strains. Is there a combination that can maximize the population immunity?

The answer is yes, and the solution is entirely similar to an earlier post about optimizing serves in tennis. If the strains are equally likely to occur, for instance, then give vaccine 1 to 2/3 of the population and vaccine 2 to 1/3 of the population to yield a 76.7 percent immunity rate. (The problem can also be solved for other distribution of strains, per the minimax theorem)

In practice, there are many more issues to be modeled. But even then, game theory and probability are used in both coordinating the supply chain (ppt) as well as selecting the flu vaccine the W.H.O. recommends.