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Disease Dynamics and Vaccine Predictability

By Karthika Swamy Cohen and Lina Sorg


Infectious 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.”

Grenfell 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.
Grenfell utilized 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 shorter.

Grenfell also 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.

"Subtle 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.
Grenfell described 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.

"We should always expect that we are going to fail because of the complexities," he said, describing the difficulty in modeling such situations accurately

He then 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.”

While 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.