Abstract
This paper is concerned with a Sevast’yanov age-dependent branching process, describing outbreaks of an infectious disease with incubation period. The main goal was to define the optimal proportion of susceptible individuals that has to be vaccinated in order to eliminate the disease. To this end we study the properties of the time to extinction of an infection according to the proportion of immune individuals in the population. The results lead us to suggest a vaccination policy based on the mean of the infection survival time. Finally, we provide a simulation-based method to determine the optimal vaccination level, and as an illustration analyze the data of outbreaks of avian influenza spreading in Vietnam at the end of 2006.
Mathematics Subject Classification (2000): 60J80, 92D30
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Acknowledgements
M. González and R. Martínez was supported by the Ministerio de Ciencia e Innovación and the FEDER through the Plan Nacional de Investigación Científica, Desarrollo e Innovación Tecnológica, grants MTM2006-08891 and MTM2009-13248. M. Slavtchova-Bojkova was supported by the NFSI, grant VU-MI-105/2005, Bulgaria, and by an action of the program ECO-NET’2006 financed by the French government. She is also especially grateful to the University of Extremadura, Consejeróa de Infraestructura y Desarrollo Tecnológico de la Junta de Extremadura, and the FEDER (grant TEM07034) for the excellent research facilities during the period of preparation of this paper.
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González, M., Martínez, R., Slavtchova-Bojkova, M. (2010). Time to extinction of infectious diseases through age-dependent branching models. 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_17
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DOI: https://doi.org/10.1007/978-3-642-11156-3_17
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