Domestic dog demography. To calculate vaccination coverage and the decline in herd immunity due to population turnover and waning of vaccine-induced immunity, it was necessary to estimate the size of the domestic dog populations (N) and their rates of growth (r dogs ). We projected human population sizes in both districts using 2002 national census data [39, 40] , and we calculated human:dog ratios from household questionnaires conducted in 1994, 2003, and 2008 in Serengeti district and in 1994 and 2004 in Ngorongoro district. We then estimated dog populations from the projected human population sizes and the human:dog ratios and calculated the rate of increase of the dog population in each district (r dogs ¼ log(N t /N 0 )/t) ( Table 3 ).