Herding cats is a cakewalk compared with getting people to take flu vaccine shots in the last weeks of summer—work, school, limited pharmacy hours, beach days and countless other factors conspire to interfere. As a result, vaccinations tend to trickle in over many months. Rather than resisting this tendency, some mathematicians now think that public health officials may one day embrace it. A bit of randomness in treatment schedules may actually help manage a disease outbreak.
This conclusion comes from an analysis of treatment options in infectious disease outbreaks through the lens of complexity theory, which attempts to make sense of systems that are fundamentally unpredictable. Researchers using complexity theory to study disease outbreaks have identified rare instances when the outbreak will die out suddenly. Say, for instance, health workers administer antibiotics to fight an outbreak of bacterial meningitis, causing infections to decline. A classic disease model would suggest that every infected person must be isolated and treated before the disease can die out. But complexity theory shows that occasionally, the disease will die out due to random and unpredictable factors.
Such a “random extinction event” is impossible to predict, but new research shows that judicious timing of treatments can increase the odds of one occurring. Knowing how to vary them to make random extinction events more likely could be particularly helpful in developing nations, where pharmaceutical supplies are often limited and treatments are not available year-round, but are given in bursts a certain number of times per year. This is often the case when an aid organization administers treatments remotely.
Ira Schwartz, an applied mathematician and physicist at the U.S. Naval Research Laboratory, and his colleagues utilized a computer simulation that models the general behavior of infectious diseases in a population of 8,000 people. The simulation took into account the element of randomness and compared the outcome of two different scenarios: one in which treatment is delivered at regular intervals in time and another at random intervals. They compared these two scenarios for infectious diseases such as bacterial meningitis, venereal disease and plague, which are treated largely with antibiotics.
The results show that in cases where treatment bursts could only be administered between two and eight times per year, the random schedule created an exponential decrease in the time to a random extinction event: in other words, a disease died out faster. “The research demonstrates why randomized treatment schedules work,” says Schwartz, a co-author on the paper, which was published in PLoS ONE in August.
In 2008 Schwartz co-authored another paper that used similar models to test the effect of random vaccination on incoming members of the population (infants), and showed similar decreases in disease extinction time.
In the new paper the researchers speculate that if disease treatments are delivered twice per year, six months apart, a disease may have time to regain strength between doses. In a random schedule, however, those doses might come closer together, increasing the likelihood that the second dose would attack the disease while the latter is in a weakened state. Such a one–two punch increases the possibility that a random extinction event will occur. (Although researchers can calculate the odds of such an event, they remain ultimately unpredictable.) For this reason, the researchers conclude that when resources are limited, treatment should be distributed to a larger percentage of the population in a few random, closely distributed pulses, rather than many smaller pulses distributed to fewer people.
With more research into the random interplay between treatment and disease, it is possible scientists will provide more suggestions for how to best administer treatments, particularly in locations where supplies and manpower are limited.
Charles Doering, acting director of the Center for the Study of Complex Systems at the University of Michigan, says Schwartz’s team is one of few groups exploring how randomness in treatment schedules can affect infectious disease progress. Although the researchers used well-established models of how diseases spread and survive in human populations, their mathematical techniques for taking randomness into account, developed from quantum mechanics, is difficult to apply to disease models. “You never quite know,” he says. “If you changed any of the structure of the model, maybe the conclusions would change.” But the work may inspire further investigation with larger computer simulations or laboratory experiments that test these theories on live populations of microorganisms. “This gives a starting point; a working hypothesis to investigate,” he adds.