  Analytical stability calculation is done to prove stability properties for
systems with parameters that do not have explicit values. For systems with
three components, the usual method of finding the characteristic polynomial as
the determinant of J-lambda I and applying the Routh-Hurwitz conditions is
reasonably efficient. For larger systems of four to six components, the method
is impractical, as the calculations become too messy. In epidemiological
models, there is often a very small parameter that appears as the ratio of a
disease-based time scale to a demographic time scale; this allows efficient use
of asymptotic approximation to simplify the calculations at little cost. Here
we describe the tools and an example of efficient stability analysis, followed
by a set of guidelines that are generally useful in applying the method.
