The effects of stochasticity and seasonality on model dynamics: Bovine tuberculosis in badgers

1. Field measurement of bovine tuberculosis in badgers (Meles meles) suggests that disease prevalence varies between years in an apparently cyclic fashion. Here, the ability of the simple compartment model of the disease presented by Bentil & Murray (1993) to reproduce this behaviour is investigated. The model predicts that, for realistic parameter values, the disease prevalence will stabilize at a fixed equilibrium, although the transient motion towards this equilibrium may involve damped cycles. 2. The model is extended to include the effects of seasonality and stochasticity, both of which have been shown to reduce stability in similar models parameterized for childhood diseases in humans. However, these changes are found not to sustain the transient cycles. 3. It is argued that, by analogy with models of childhood diseases, the addition of age-structure to the model is unlikely to increase its propensity to exhibit cycles. 4. Finally, it is suggested that one of the fundamental assumptions underlying compartment models makes them unsuitable for representing this problem, which must be addressed using spatially explicit models.