IJPAM: Volume 44, No. 4 (2008)
Centre for Mathematical Biology
University of Oxford
24-29 St Giles', Oxford, OX1 3LB, U.K.
Department of Mathematics and Statistics
University of Guelph
Guelph, N1G 2W1, CANADA
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