  Epidemic models with inhomogeneous populations have been used to study major
outbreaks and recently Britton and Lindenstrand \cite{BL} described the case
when latency and infectivity have independent gamma distributions. They found
that variability in these random variables had opposite effects on the epidemic
growth rate. That rate increased with greater variability in latency but
decreased with greater variability in infectivity. Here we extend their result
by using the McKay bivariate gamma distribution for the joint distribution of
latency and infectivity, recovering the above effects of variability but
allowing possible correlation. We use methods of stochastic rate processes to
obtain explicit solutions for the growth of the epidemic and the evolution of
the inhomogeneity and information entropy. We obtain a closed analytic solution
to the evolution of the distribution of the number of uninfected individuals as
the epidemic proceeds, and a concomitant expression for the decay of entropy.
The family of McKay bivariate gamma distributions has a tractable information
geometry which provides a framework in which the evolution of distributions can
be studied as the outbreak grows, with a natural distance structure for
quantitative tracking of progress.
