New Mathematical Model Explains Changing Patterns in Epidemics
Jan. 27, 2000
Sources: Benjamin Bolker, (352) 392-1107, bolker@ufl.edu
David Earn, (011) 905 525-9140, earn@math.mcmaster.ca
GAINESVILLE, Fla. --- A simple, new mathematical model enables scientists to predict epidemics of infectious diseases such as measles.
A team of researchers from the University of Florida, University of Cambridge in England and McMaster University in Hamilton, Ontario, Canada, developed the model and applied it to measles epidemics. Their research will appear in Friday's issue of the journal Science.
Analysis of the new model led to an important prediction that has not been made previously: Increases or decreases in birth rates or vaccination rates should cause dramatic changes in patterns of epidemics. The group then tested their prediction by examining historical records of births, vaccination and cases of measles.
The team's research has implications for predicting the outcome of vaccination programs and how diseases might be eradicated through such programs. The findings:
- enable researchers to predict how epidemic patterns will be affected if birth or vaccination rates change;
- show that external factors have an important impact on ecological and epidemiological systems.
"This may be one more tool in trying to predict the dynamics of disease," said Benjamin Bolker, an assistant professor of zoology at UF.
In developing the model, Bolker, David Earn, a professor of applied mathematics at McMaster University, and colleagues Pejman Rohani and Bryan Grenfell, both of the department of zoology at Cambridge, studied historical data on the outbreaks of measles in London and Liverpool in England, and New York and Baltimore.
Patterns of measles epidemics in those cities range from similar outbreaks every year, to large or small outbreaks in alternate years, to very irregular outbreaks of varying size. In each city, numerous transitions between these various epidemic patterns have occurred. The team's research uncovers what caused the transitions, namely changes in birth rates and changes in vaccination rates.
"The model we have developed is simpler than others that are currently being studied. Our approach will make it easier to address other problems in epidemiology and ecology," Earn said.
While their current paper focuses on pattern changes in epidemics of measles, Earn and Bolker said the same mathematical approach can be applied to studies of other diseases, including chicken pox, rubella, polio and whooping cough. The model also could apply to many ecological systems, Earn and Bolker said. For example, it could help predict the development of insect infestations, Bolker said.
"The possibility for prediction extends beyond diseases to other predator-prey cycles," Bolker said.
In October, the same team of researchers published a paper in Science that reported on radically different effects of immunization programs on measles and whooping cough epidemics.
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