The dynamics and control of bovine tuberculosis in possums

A model for the dynamics of an infectious disease in a wild animal population is analysed. The model incorporates susceptible, infected but not infectious, and infectious classes, with no recovery from disease, density-dependent regulation of host birth and death rates, and pseudo-vertical transmission. The existence and local stability of equilibrium levels are determined. Expressions for the intensity of three alternative control measures- the culling, sterilization, and vaccination of host animals- required to eradicate the disease are obtained. Finally, the model is applied to possible control measures against bovine tuberculosis infection in possums in New Zealand