Arni S.R. Srinivasa Rao, Chris T. Bauch
Mathematical Institute
Centre for Mathematical Biology
University of Oxford
24-29 St Giles', Oxford, OX1 3LB, U.K.
e-mail: arni@maths.ox.ac.uk
Department of Mathematics and Statistics
University of Guelph
Guelph, N1G 2W1, CANADA
e-mail: cbauch@uoguelph.ca

Abstract.Here we treat the transmission of disease through a population as a standard Galton-Watson branching process, modified to take the presence of vaccination into account. Vaccination reduces the number of secondary infections produced per infected individual. We show that introducing vaccination in a population therefore reduces the expected time to extinction of the infection. We also prove results relating the distribution of number of secondary infections with and without vaccinations.

Received: March 8, 2008

AMS Subject Classification: 60J85, 92D30

Key Words and Phrases: branching process, epidemic, vaccination, gamma function

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 44
Issue: 4