By Karthika Swamy Cohen and Lina Sorg
diseases are particularly amenable to mathematical modeling. Models can display
how such diseases progress, connect the projected progression to data, and
ultimately predict the outcome of epidemics. Establishing parameters for
infectious diseases generate effective public health interventions, including
the development of vaccinations. Bryan Grenfell of Princeton University talked
about this and more in his joint Annual and Life Sciences meeting plenary,
“Spatio-temporal Dynamics of Childhood Infectious Disease: Predictability and
the Impact of Vaccination.”
centered his discussion primarily around measles, a highly-transmissible,
aerosol-transmitted acute viral infection. Measles has a high morbidity rate
and is quite immunosuppressive. After infection however, those affected have
lifelong immunity. The first vaccination was created in 1963.
SIR model depicting the current dynamics of measles in Niger. Image credit: Bryan Grenfell plenary presentation at AN16/LS16.
a simple SIR model
and inferred epidemic parameters from time series to fit his
model. In developed countries, measles frequently appears because of the
aggregation of children in school; Grenfell demonstrated dips on a graph that
represent school breaks and holidays, when the disease is less prevalent, and
drew a comparison between the U.S. and the U.K., where summer breaks are
discussed the limits on disease predictability before vaccination and even
today, when apprehension about vaccines limits their effectiveness. Vaccine
hesitancy is a significant problem in predicting disease spread, he said.
Vaccination is a herd immunity,” he said. When sufficient numbers of people in a community are immunized against an infectious disease, most members in the population are protected from the disease.
changes make big differences to the dynamics," Grenfell observed. He
demonstrated this by explaining the application of his model to several examples:
the current dynamics of measles in Niger, an Amish population in Ohio, and a
major outbreak in Greenland in 1951.
In the case
of the Amish population, when two individuals from the Philippines brought the
virus, there was very high initial transmission since people in the community
tend not to get vaccinated. On the other hand, infection also dropped because
the community was fairly isolated. In the case
in Greenland, when a young sailor brought measles to a local dance, 204 people
were infected due to the extreme transmissibility in that situation.
Comparison of measles outbreaks between the U.S. and U.K. Image credit: Bryan Grenfell plenary presentation at AN16/LS16.
how behavior changes can affect the effectiveness of vaccines both at an
individual and population level. In the absence of behavior changes, there is only
one source of nonlinearity, which makes the problem much less complicated.
always expect that we are going to fail because of the complexities," he
said, describing the difficulty in modeling such situations accurately
moved on to the study of vaccination at the individual level. This necessitates
the study of the biology of the bug and how it drives seasonal variations in
transitions. “We can't just look at the population level, we need to drill down
to the individual host level,” he explained. “Individual level dynamics ratify
up to the population level.”
Grenfell’s model offered evidence for future simplicity in epidemiological
dynamics, some questions require researchers to cross scales between ecological
and molecular levels, and between natural and social science. Ultimately,
however, Grenfell supported the merits of prediction whenever possible. “We should always
try, if the data is up to it, to predict epidemics,” he said.
||Karthika Swamy Cohen is the managing editor of SIAM News.
||Lina Sorg is the associate editor ofSIAM News.