Thresholds and stability analysis of models for the spatial spread of a fatal disease

The metapopulation dynamics of an infectious disease: tuberculosis in possums

An SEI metapopulation model is developed for the spread of an infectious agent by migration. The model portrays two age classes on a number of patches connected by migration routes which are used as host animals mature. A feature of this model is that the basic reproduction ratio may be computed directly, using a scheme that separates topography, demography, and epidemiology. We also provide formulas for individual patch basic reproduction numbers and discuss their connection with the basic reproduction ratio for the system. The model is applied to the problem of spatial spread of bovine tuberculosis in a possum population. The temporal dynamics of infection are investigated for some generic networks of migration links, and the basic reproduction ratio is computed-its value is not greatly different from that for a homogeneous model. Three scenarios are considered for the control of bovine tuberculosis in possums where the spatial aspect is shown to be crucial for the design of disease management operations.

Models of Mycobacterium bovis in wildlife and cattle

Following the first model of wildlife tuberculosis (in European badgers) there has been a spate of papers modelling wildlife TB. These have looked at population parameters and disease dynamics in the badger and possum. Recent papers in particular have looked at various methods of controlling the wildlife vector to reduce the incidence of TB in cattle. The author examines the role of modelling to show what insights it has given us, which issues have not been addressed, and where the shortfalls lie. Particular attention will be paid to a comparison between models of badgers and possums, and between simple and more complex models, and possible areas of future research will be revealed.