The delivery of vaccines at random rates into an infected population can similarly be modeled as “noise.” Writing in Physical Review Letters, Mark Dykman of Michigan State University and Ira Schwartz and Alexandra Landsman of the Naval Research Laboratory in Washington D.C. show that even a small number of random vaccinations can lead to an exponential increase in the extinction rate of a disease.
The group adapts an established model in the field of population dynamics known as the SIS model ( and are variables that define the number of people that are susceptible to an infection and those that are already infected, respectively) and maps the problem to the variational calculus used in classical dynamics. They assume that a small percentage of incoming “susceptibles” receive the vaccination at random times.
The key finding that even weak vaccination can increase the extinction rate of an epidemic exponentially has a physical meaning: as in many dynamical systems, the right frequency of external pulses—in this case, the vaccination rate—can resonate with the system itself. – Jessica Thomas