Ecological Archives A025-033-A4

Suzanne M. O'Regan, Krisztian Magori, J. Tomlin Pulliam, Marcus A. Zokan, Rajreni B. Kaul, Heather D. Barton, and John M. Drake. 2015. Multi-scale model of epidemic fade-out: Will local extirpation events inhibit the spread of white-nose syndrome? Ecological Applications 25:621–633. http://dx.doi.org/10.1890/14-0417.1

Appendix D. Aspects neglected by the modeling approach.

One aspect neglected by our modeling approach is regional stochasticity. In general, random demographic fluctuations may prevent the epidemic from taking off within a county, or if the epidemic does take off, may lead to its early curtailment or increase its duration through introduction of fresh susceptibles to a patch. Alternatively, a regional epidemic may be greater than predicted by the deterministic theory. We used the deterministic projection of the time to epidemic burnout of a county as an approximation because from the stochastic threshold theorem (Daley et al. 2001, Allen 2003), which states that there is a critical probability for which a major outbreak can occur, the probability of a major epidemic within a county with SIR dynamics is high (> 0.6 or (1-1/R0)). Within each county, we assumed a single hibernaculum initially becomes infected. Mean final sizes calculated from stochastic SIR models are larger, or closer to that predicted by the deterministic model, for populations with a large number of susceptibles relative to the number of infectives (Allen 2003). Therefore, the deterministic projection is a reasonable approximation for the average epidemic duration within a county under parameters appropriate to White-Nose Syndrome.

A further approximation made by our model is that projections are based on yearly time steps, thereby integrating over the within-year seasonality of hibernacula occupation. However, it is not expected that this approximation has introduced any errors appreciably greater than occurs inevitably due to the fact that county-level incidence data is normally obtained in the spring each year (U.S. Fish and Wildlife Service 2011) and that researchers typically visit hibernacula only on an annual basis. Indeed, the temporal scale we have chosen is therefore probably the most appropriate for a macroscopic spatial analysis of the spread of WNS. Of course, it would be appropriate to include within-year seasonality of congregation at summer and winter roosting sites and segregation based on sex during the summer months to accurately represent spread on a microscopic spatial scale. We believe that such an analysis is not possible with existing data.

A possibly more important consideration is that our analysis assumes disease-induced mortality to extirpate the infection from hibernacula and does not allow for disease recovery or resistance. Although there are reports that bats can recover from White-Nose Syndrome (Meteyer et al. 2011, Dobony et al. 2011), it is unknown if recovered bats have any immunity (and if they do whether it is temporary or permanent and partial or full). Furthermore, only a small number of bats in the wild are known to have recovered from the infection (Dobony et al. 2011). P. destructans is virulent in bats and typically causes a moribund state in Little Brown bats in around 11 weeks (Warnecke et al. 2012). Because of the widespread reports of mass mortality in hibernacula (Frick et al. 2010; Turner et al. 2011, U.S. Fish and Wildlife Service, 2012), it is reasonable to investigate the assumption that disease-induced-mortality extirpates the infection from hibernacula using a dynamical model. Recovery may be incorporated into models if there is evidence of large numbers of bats recovering from the infection. Qualitatively, our expectation is that immunity or resistance will allow more slow-burning epidemics to continue propagating, exacerbating the deleterious effects of the disease, at least until hibernacula are repopulated by resistant individuals.

Literature cited

Allen, L. J. S. 2003. An introduction to stochastic processes with applications to biology. Pearson/Prentice Hall.

Daley, D. J., and J. M. Gani. 2001. Epidemic Modelling: An Introduction. Cambridge University Press.

Dobony, C. A., A. C. Hicks, K. E. Langwig, R. I. von Linden, J. C. Okoniewski, and R. E. Rainbolt. 2011. Little Brown Myotis Persist Despite Exposure to White-Nose Syndrome. Journal of Fish and Wildlife Management 2(2):190–195. doi:10.3996/022011-JFWM-014