Mathematical models for wildlife disease management
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Endemic diseases in wildlife present both intra- and inter-species management problems with risk to conservation of endangered species and spillover of virulent disease to other wildlife, farmed and domestic populations. Mathematical models have been developed to aid understanding of the transmission and persistence of such endemic disease. We review such models with an emphasis on models of tuberculosis. The understanding gained from previous model studies is used to formulate a new mathematical model for the wild boar reservoir of tuberculosis in central Spain where the disease persists at high prevalence and impacts other wild and domestic species. This model is used to investigate the efficacy of hunting and vaccination as management techniques to control tuberculosis in wild boar. Insight from the specific wild boar TB model generates a general result for compensatory population growth following culling of a population harbouring endemic disease. We show that compensatory growth due to a reduction in disease-induced mortality following culling could be a new mechanism for producing the ‘Hydra’ effect. We extend the wild boar TB model to reflect the situation in Asturias where wolf predation may influence the disease dynamics leading to lower prevalence of tuberculosis in wild boar. In conclusion we review how our findings can provide insight for disease management and control, and consider how the model could be extended to investigate emerging diseases for which wild boar may also be a reservoir.