The metapopulation dynamics of an infectious disease
by
Mick Roberts
AgResearch

When considering the dynamics of an infectious disease in a homogeneously mixing population, the principal quantity of interest is the basic reproduction ratio, R₀. This is the threshold quantity that determines if the infection can persist. It has been observed that control operations directed against bovine tuberculosis in New Zealand possum populations have sometimes failed to eradicate the disease, despite achieving R₀ < 1, and immigration of possums from neighbouring habitat patches has been suggested as an explanation. In response, an SEI metapopulation model for the spread of an infectious agent by migration has been developed. A feature of the model is that R₀ may be computed directly, using a scheme that separates topography, demography and epidemiology. The scheme is formalised on three generic topographic structures: the loop, chain and spider. Formulae have also been derived for individual patch basic reproduction numbers, and their connection with R₀ for the system explored.

Date received: October 8, 2001