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Branching process approximation to the initial stages of an epidemic
process has been used since the 1950's as a technique for providing
stochastic counterparts to deterministic epidemic threshold theorems.
One way of describing the approximation is to construct both
branching and epidemic processes on the same probability space, in
such a way that their paths coincide for as long as possible. In
this paper, it is shown, in the context of a Markovian model of parasitic
infection, that coincidence...
Stein's method is used to prove approximations in total variation to the
distributions of integer valued random variables by (possibly signed)
compound Poisson measures. For sums of independent random variables,
the results obtained are very explicit, and improve upon earlier
work of Kruopis (1983) and Čekanavičius (1997);
coupling methods are used to derive concrete expressions for the error
bounds. An example is given to illustrate the potential for application
to sums of dependent random variables.
...
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