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

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Workshop on Branching Processes and Their Applications

Part of the book series: Lecture Notes in Statistics ((LNSP,volume 197))

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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.

Mathematics Subject Classification (2000): 60J80; 92D30

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Acknowledgements

The author wishes to thank Andrew Barbour for fruitful discussions. The author also gratefully acknowledge the referee for comments and suggestions that greatly improved the presentation. This work was supported by the Schweizerischer Nationalfonds (SNF), project no. 107726.

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Authors and Affiliations

  1. Institute of Mathematics, University of Zurich, Winterthurerstrasse 190, 8057, Zurich, Switzerland

    Dominik Heinzmann

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  1. Dominik Heinzmann
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Correspondence to Dominik Heinzmann .

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Editors and Affiliations

  1. Fac. Ciencias, Universidad de Extremadura, Avenida Elvas s/n, Badajoz, 06071, Spain

    Miguel González Velasco

  2. Fac. Ciencias, Universidad de Extremadura, Avenida Elvas s/n, Badajoz, 06071, Spain

    Inés M. Puerto

  3. Universidad de Extremadura, Avda. Virgen del Puerto, Plasencia, 10600, Spain

    Rodrigo Martínez

  4. Fac. Ciencias, Universidad de Extremadura, Avenida Elvas s/n, Badajoz, 06071, Spain

    Manuel Molina

  5. Fac. Ciencias, Universidad de Extremadura, Avenida Elvas s/n, Badajoz, 06071, Spain

    Manuel Mota

  6. Facultad de Veterinaria, Universidad de Extradura, Avda Universidad s/n, Caceres, 10071, Spain

    Alfonso Ramos

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Heinzmann, D. (2010). Time to extinction in a two-host interaction model for the macroparasite Echinococcus granulosus . In: González Velasco, M., Puerto, I., Martínez, R., Molina, M., Mota, M., Ramos, A. (eds) Workshop on Branching Processes and Their Applications. Lecture Notes in Statistics(), vol 197. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11156-3_18

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