Swine Flu, Vaccines, and Mathematical Models

The recent swine flu outbreak in Mexico reminds me that, although lately I’ve been working on other things, I should also continue my work in health policy research and related areas.

Here we consider the problem:  in a flu pandemic, what strategies can we use to conserve scarce vaccine?

Let’s assume, for example, that during the first 3 months of a flu pandemic, a country has 1 million doses of flu vaccine.  How can this quantity, which is not sufficient to immunize the entire at-risk population, be used as effectively as possible?

First we need to decide what “as effectively as possible” means.  Is the objective to minimize total mortality, to minimize mortality and morbidity, to maximize what are called QALY’s (quality-adjusted years of life), or to reduce negative economic impact?  All of these are defensible criteria.  This requires some careful analytical modeling and work.

As just one example related to this, should scarce vaccines be direct more towards children, young adults, or older adults?  Older adults are a likely target, as they have the highest mortality rates in a flu pandemic.  However they are, unfortunately, least likely to exhibit a positive immune response to flu vaccines.

Conversely, children respond well to the vaccines; and by potentially saving a child’s life, one theoretically gains  many years of productive life. Further, while this may require further epidemiological study, children, who attend school along with dozens or hundreds of other children, are probably disproportionately both at risk for flu and involved in transmission once they catch it.   However school-age children also tend to have fewer complications and lower mortality rates with flu.

In the end, an optimal allocation of flu vaccine may require a fairly complex analysis and/or computer simulation.  Various parameters that feed these analyses would need to be quantified beforehand.  For this we would have two choices:  (1) either estimate the parameters based on a combination of guesswork and literature review, or (2) to conduct small experimental studies aimed to supply more realistic values.

The choice between (1) and (2) could itself be made by performing mathematical sensitivity analyses within the simulation models; highly sensitive parameters — those for which small differences have a large effect on results — would be worth investing more money to quanity precisely.

In general, it should be noted that everything discussed here — simulations, literature reviews, mathematical analyses, etc. — are extremely inexpensive compared to the costs of large-scale population immunizations.  Half a million dollars, say, buys an immense amount of mathematical research.  And it could easily save tens or even hundreds of millions of dollars by preventing disease or streamlining immunization efforts.

Predicting Individual Response to Vaccine

Another productive area of mathematical modeling here would be to try to predict individual  response to vaccines.  For a given flu vaccine, only a certain proportion of people develop the intended antibodies.  For a particular population and vaccine, for example, this rate may be only 70%.  It would be worthwhile to know in advance whether a given person is among the 70% that respond to a vaccine or the 30% that do not.  If someone won’t probably won’t respond, spare the vaccine dose and give it to someone who will.

Such analyses can be performed using routine predictive statistical methods, like logistic regression, or perhaps more modern techniques.  Possible predictor variables might include:  subject age, sex, immunization history, flu history, ethnicity, overall health, weight.

Other predictive variables might be measured via blood tests or even DNA testing.  The choice concerning how heroically to collect predictive variables would depend on factors unique to the pandemic, such as the virulence of the strain, and the amount of existing vaccine.  In theory, if a flu strain is dangerous enough, and if vaccine is scarce enough, literally every available dose must be directed to someone it can potentially benefit.  In that case even as expensive (currently) a procedure as micro-array DNA screening could be utilized.

Other benefits from mathematical modeling and prediction in a pandemic might come by analyzing cross-reactivity of previously-developed vaccines for the current flu strain.  In the past vaccines have been developed for perhaps dozens of flu strains.  In theory, each of these vaccines is unique.  The usual assumption is that a vaccine for one flu strain offers little or no protection for a new strain.
However, that is not always the case.

The only way to be sure would be to test old vaccines against the new flu strain.  In theory, this could be done using human subjects in only a few days, at the outset of a pandemic.  All that is required is to administer an old flu vaccine to a subject, wait a few days, and then see if their blood contains antibodies effective against the new strain.

Perhaps this is a long-shot, but we might get lucky, and would lose nothing by trying.

An even more elaborate strategy would involve trying to predict cross-reactivity of previous flu vaccines to the new strain in a particular patient.  That is, by considering demographic, biological, or genetic variables of a given subject, we might identify those will exhibit favorable crossreactivity.

In addition, we could probably make some good guesses about crossreactivity simply by comparing the genetic composition of the new strain to previous ones, and applying mathematical or artificial intelligence models.

More broadly, there’s a lot more we can do at the behavioral level to prevent or limit a flu pandemic.  Public information aimed at teaching people how to prevent spread of flu is effective and cost-effective.  The pharmaceutical company GSK, for example,  has produced some excellent web-based presentations that teach people about flu prevention.  People need to learn, for example how to wash their hands correctly (30 seconds; warm water; wash both sides and between fingers).

Personally, I would like to see studies done on the potential preventive effects of wearing surgical masks on airplanes or subways.  Or perhaps, in the case of airlines, does anybody know what’s going on with the air recirculation system?  Is it filtered, and, if so, can the filters trap virus-bearing dust particles?  Airlines might be reluctant to address this issue.  Pictures of mask-wearing passengers isn’t exactly good advertising.  But on the other hand, people now are already avoiding air travel because of flu fears.  If the airlines could show that masks significantly reduce risk of contagion it might actually be good for them.