Shirli Bar-David, James O. Lloyd-Smith, and Wayne M. Getz. 2006. Dynamics and management of infectious disease in colonizing populations. Ecology 87:1215–1224.

Appendix B. Model projections for disease extinction or growth over 20 years.

The simulations of the spatially-explicit model indicate that the range of transmissibility determined in empirical studies, as for BTB in fallow deer (Wahlström et al. 1998), leads to disparate outcomes for disease invasion and persistence in a colonizing population: For low transmissibility (β = 0.1), the probability of disease extinction (p_ext) over the 20-year simulation was high, though the outbreak did persist due to stochastically in some simulations (e.g., 1- p_ext >0.4 after 10 years, 1- p_ext >0.15 after 20 years) (Fig. B1).  Moderately and highly transmissible diseases exhibit infrequent extinction and faster growth: for β=1, the disease persisted for 20 years in more than 95% of simulations, with more than 50% of all females infected on average (79+32 out of 133+25 individuals [mean + SE]) (Fig. B1).

a. Proportion of outbreaks extinct: β = 0.1(-), 0.5 (..), 1 (-.)

b. Number of infected individuals (β = 0.1) and population size

c. Number of infected individuals (β = 0.5)

d. Number of infected individuals (β = 1)

FIG. B1.  Model projections for disease extinction or growth over 20 years. Proportion of simulated disease invasions that are extinct by a given time (a), and the number of infected individuals (shown with the boxes, b–d) under different disease scenarios with a range of transmission rates. The total population size (mean and standard error, shown with the line and error bars) for all scenarios is also shown in (b).  The box lines represent the lower quartile, median, and upper quartile values of 250 runs, and whiskers show the range of other results to a maximum of 1.5 interquartile range.  Results beyond the whiskers are shown by crosses (+).

LITERATURE CITED

Wahlström, H., L. Englund, T. Carpenter, U. Emanuelson, A. Engvall, and I. Vagsholm. 1998. A Reed-Frost model of the spread of tuberculosis within seven Swedish extensive farmed fallow deer herds. Preventive Veterinary Medicine 35:181–193.