# Time to extinction in a two-host interaction model for the macroparasite Echinococcus granulosus

Heinzmann, D (2010). Time to extinction in a two-host interaction model for the macroparasite Echinococcus granulosus. In: González Velasco, M; Puerto, I M; Molina, M; Mota, M; Ramos, A. Workshop on Branching Processes and Their Applications. Berlin Heidelberg: Springer-Verlag, 257-266.

## Abstract

An approximation is derived for the time to extinction in a sub-critical epidemic two-host interaction process for the macroparasite Echinococcus granulosus.
The argument is based on coupling the epidemic model with a two-type branching process, and then to approximate the time to extinction for the branching process.
It is shown that the approximate time is proportional to the logarithm of a weighted sum of the initially infectives in the host populations plus a Gumbel random variable.
The accuracy of the approximation is illustrated.

## Abstract

An approximation is derived for the time to extinction in a sub-critical epidemic two-host interaction process for the macroparasite Echinococcus granulosus.
The argument is based on coupling the epidemic model with a two-type branching process, and then to approximate the time to extinction for the branching process.
It is shown that the approximate time is proportional to the logarithm of a weighted sum of the initially infectives in the host populations plus a Gumbel random variable.
The accuracy of the approximation is illustrated.