Interparticle correlation in death processes with application to variability in compartmental models
Ball F., Donnelly P.
<jats:p>This paper is concerned with a pure death process, starting with <jats:italic>N</jats:italic> individuals, with death rates <jats:italic>μ <jats:sub>n</jats:sub>, n</jats:italic> = 1, 2, …, <jats:italic>N.</jats:italic> It is shown that the fates of distinct individuals are positively correlated if <jats:italic>μ <jats:sub>n</jats:sub>/n</jats:italic> decreases with <jats:italic>n,</jats:italic> and negatively correlated if <jats:italic>μ <jats:sub>n</jats:sub>/n</jats:italic> increases with <jats:italic>n.</jats:italic> The application of this result to the problem of variability in compartmental models is elaborated and in particular a conjecture of Faddy (1985) is settled. Further applications to well-known death processes are also briefly described.</jats:p>