Non-linear transmission and simple models for bovine tuberculosis

Abstract

1. A new model is presented for a possum-tuberculosis (TB) system (Trichosurus vulpecula-Mycobacterium bovis) that is both realistic and parsimonious. The model includes a phenomenological treatment of heterogeneity of risk for susceptible hosts, similar to that used in insect host-parasitoid systems. 2. Parameter values for the model reflect current knowledge and differ significantly from those in other recent models of this system. Associated with these structural and parametric changes are substantially different predictions for the dynamics and control of TB in possums. 3. The model predictions include (i.) only limited host suppression due to the disease (< 10%, cf. several earlier simple models for TB in both possums and badgers); (ii) asymptotically stable disease dynamics (cf. homogeneous-mixing models that predict either extremely weak stability such that disease fails to recover When host density is temporarily reduced, or oscillatory behaviour and potential elimination of disease following such a perturbation); (iii) TB that is harder to control than in the homogeneous-mixing model equivalents, in line with practical experience; and (iv) a threshold host density for disease elimination that differs substantially from the host equilibrium density in the presence of disease. 4. Homogeneous-mixing models are unable to reproduce this behaviour, whatever parameter values are chosen. Heterogeneous-mixing models with non-linear transmission may therefore be worth consideration in other endemic wildlife disease systems, as is now commonplace for insect-parasitoid and insect-pathogen ones.