Interventions in GARCE Branching Processes with Application to Ebola Virus Data

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Abstract

In hindsight, even a cursory look may have revealed substantial growth of the 2014 Ebola infection and death cases in West Africa before drastic interventions showed an effect in late 2014. Yet a timely assessment as to whether an intervention has a sufficient impact to stabilize and eventually end an outbreak is equally important as early detection and accurate prediction of the magnitude of the outbreak several months before it spins out of control. To this aim, we consider an intervention effect in the GARCE branching process model, proposed by Hueter, that was successful to early detect the magnitude of the outbreak when data became available in early 2014. This model provides a novel and simple approach to branching processes that allows for time-varying random environments and instances of peak growth and near extinction-type rates as seen in Ebola viruses, tuberculosis infections, and infectious diseases. We present results on the survival and extinction behaviours, characterization of the phase transition between the subcritical and supercritical phases, and a sufficient condition for escape from supercriticality upon a level shift intervention. Intervention analysis of the Ebola outbreak data are presented and findings on the outbreak’s estimated phase and intervention effect are discussed.

Keywords

Ebola virus disease outbreak Interventions Branching processes in random environment Extinction GARCE Level shift Phase transition 

Mathematics Subject Classification (2010)

60J80 62M10 60G10 60F05 60J85 

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Notes

Acknowledgements

I am grateful to a referee and the Editors for helpful suggestions.

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Department of StatisticsColumbia UniversityNew YorkUSA

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