Resisting the Spread of Disease - Part 2

One of the most useful tools in analyzing the spread of disease is
a system of evolutionary equations that reflects the dynamics among
three distinct categories of a population: those susceptible (S) to
a disease, those infected (I) with it, and those recovered (R) from
it. This SIR model is applicable to a range of diseases, from
smallpox to the flu. To predict the impact of a particular disease
it is crucial to determine certain parameters associated with it,
such as the average number of people that a typical infected person
will infect. Researchers estimate these parameters by applying
statistical methods to gathered data, which aren.t complete
because, for example, some cases aren.t reported. Armed with
reliable models, mathematicians help public health officials battle
the complex, rapidly changing world of modern disease. Today.s
models are more sophisticated than those of even a few years ago.
They incorporate information such as contact periods that vary with
age (young people have contact with one another for a longer period
of time than do adults from different households), instead of
assuming equal contact periods for everyone. The capacity to treat
variability makes it possible to predict the effectiveness of
targeted vaccination strategies to combat the flu, for instance.
Some models now use graph theory and matrices to represent networks
of social interactions, which are important in understanding how
far and how fast a given disease will spread. For More Information:
Mathematical Models in Population Biology and Epidemiology, Fred
Brauer and Carlos Castillo-Chavez.