posted on Nov. 17: New mathematical model explains changing patterns of epidemics

A simple, new mathematical model enables scientists to
predict epidemics of infectious diseases such as measles.

A team of researchers from McMaster University, Cambridge University and the University of Florida developed the model and applied it to measles epidemics. Their research is reported in the Jan. 28 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 group's 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.

“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,” says David Earn, professor of applied mathematics at McMaster.

In developing the model, Earn and fellow colleagues Pejman Rohani and
Bryan Grenfell, both of the Department of Zoology at the University of
Cambridge, and Benjamin Bolker of the University of Florida, studied
historical data on the outbreaks of measles in London and Liverpool in
England, and New York and Baltimore in the United States.

Patterns of measles epidemics in these 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.

While their current paper focuses on pattern changes in epidemics of measles, Earn says the same mathematical approach can be applied to studies of other diseases (such as chicken pox, rubella, polio and whooping cough) and many ecological systems. For all these systems, the group's findings indicate that external factors may explain complex changes in patterns of abundance of species.

Earn began his research in epidemiology while he was a Wellcome Trust
post-doctoral fellow at Cambridge University. He joined McMaster in October 1999. His work is focused on the development and analysis of mathematical models of biological systems.

In October 1999, the same team published a paper in Sciencewhich reported on radically different effects of immunization programs on measles and whooping cough epidemics.