About this Journal Submit a Manuscript Table of Contents
ISRN Biomathematics
Volume 2012 (2012), Article ID 802450, 18 pages
http://dx.doi.org/10.5402/2012/802450
Research Article

Modeling Gender-Structured Wildlife Diseases with Harvesting: Chronic Wasting Disease as an Example

1Department of Mathematics, The University of Ottawa, Ottawa, ON, Canada K1N 6N5
2Department of Mathematics and Faculty of Medicine, The University of Ottawa, Ottawa, ON, Canada K1N 6N5

Received 29 May 2012; Accepted 18 July 2012

Academic Editors: D. Bhattacharyya and G. Bocharov

Copyright © 2012 Mo'tassem Al-Arydah et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. E. S. Williams and S. Young, “Chronic wasting disease of captive mule deer: a spongiform encephalopathy,” Journal of wildlife diseases, vol. 16, no. 1, pp. 89–98, 1980. View at Scopus
  2. S. Gilch, N. Chitoor, Y. Taguchi, M. Stuart, J. E. Jewell, and H. M. Schätzl, “Chronic wasting disease,” Topics in Current Chemistry, vol. 305, pp. 51–77, 2011. View at Publisher · View at Google Scholar · View at Scopus
  3. C. J. Sigurdson, “A prion disease of cervids: chronic wasting disease,” Veterinary Research, vol. 39, no. 4, article no. 41, 2008. View at Publisher · View at Google Scholar · View at Scopus
  4. D. O. Joly, M. D. Samuel, J. A. Langenberg et al., “Spatial epidemiology of chronic wasting disease in Wisconsin white-tailed deer,” Journal of Wildlife Diseases, vol. 42, no. 3, pp. 578–588, 2006. View at Scopus
  5. C. Mathiason, A. Nalls, K. Anderson, J. Hayes-Klug, N. Haley, and E. Hoover, “Mother to offspring transmission of chronic wasting disease,” in Proceedings of the Meeting Report International Prion Congress: from Agent to Disease (PRION'10), vol. 4, no. 3, p. 158, 2010.
  6. M. W. Miller, N. T. Hobbs, and S. J. Tavener, “Dynamics of prion disease transmission in mule deer,” Ecological Applications, vol. 16, no. 6, pp. 2208–2214, 2006. View at Publisher · View at Google Scholar · View at Scopus
  7. M. W. Miller, E. S. Williams, N. T. Hobbs, and L. L. Wolfe, “Environmental sources of prion transmission in mule deer,” Emerging Infectious Diseases, vol. 10, no. 6, pp. 1003–1006, 2004. View at Scopus
  8. Government of Alberta, Agriculture and Rural Development, “Chronic Wasting Disease (CWD) of Elk and Deer,” 2010, http://www.agric.gov.ab.ca/app21/rtw/index.jsp.
  9. Chronic Wasting Disease Alliance, 2010, http://www.cwd-info.org/.
  10. University of Alberta, “Border Deer Study: about CWD,” 2010, http://ursus.biology.ualberta.ca/overview.htm.
  11. S. Kahn, C. Dubé, L. Bates, and A. Balachandran, “Chronic wasting disease in Canada: part 1,” Canadian Veterinary Journal, vol. 45, no. 5, pp. 397–404, 2004. View at Scopus
  12. E. S. Almberg, P. C. Cross, C. J. Johnson, D. M. Heisey, and B. J. Richards, “Modeling routes of chronic wasting disease transmission: environmental prion persistence promotes deer population decline and extinction,” PLoS One, vol. 6, no. 5, Article ID e19896, 2011. View at Publisher · View at Google Scholar · View at Scopus
  13. M. W. Miller, E. S. Williams, C. W. McCarty et al., “Epizootiology of chronic wasting disease in free-ranging cervids in Colorado and Wyoming,” Journal of Wildlife Diseases, vol. 36, no. 4, pp. 676–690, 2000. View at Scopus
  14. G. Wasserberg, E. E. Osnas, R. E. Rolley, and M. D. Samuel, “Host culling as an adaptive management tool for chronic wasting disease in white-tailed deer: a modelling study,” Journal of Applied Ecology, vol. 46, no. 2, pp. 457–466, 2009. View at Publisher · View at Google Scholar · View at Scopus
  15. A. Sharp and J. Pastor, “Stable limit cycles and the paradox of enrichment in a model of chronic wasting disease,” Ecological Applications, vol. 21, no. 4, pp. 1024–1030, 2011. View at Publisher · View at Google Scholar · View at Scopus
  16. G. Giordano and F. Lutscher, “Predation and harvesting of an age-and sex-structured population,” Journal of Biological Dynamics, vol. 5, no. 6, pp. 600–618, 2011. View at Publisher · View at Google Scholar
  17. M. Kot, Elements of Mathematical Ecology, Cambridge University Press, 2001.
  18. J.-M. Gaillard, M. Festa-Bianchet, and N. G. Yoccoz, “Population dynamics of large herbivores: variable recruitment with constant adult survival,” Trends in Ecology and Evolution, vol. 13, no. 2, pp. 58–63, 1998. View at Publisher · View at Google Scholar · View at Scopus
  19. C. Castillo-Chavez and W. Huang, “The logistic equation revisited: the two-sex case,” Mathematical Biosciences, vol. 128, no. 1-2, pp. 299–316, 1995. View at Publisher · View at Google Scholar · View at Scopus
  20. M. R. Miller, A. White, K. Wilson, and M. Boots, “The population dynamical implications of male-biased parasitism in different mating systems,” PLoS One, vol. 2, no. 7, article no. e624, 2007. View at Publisher · View at Google Scholar · View at Scopus
  21. J. M. Heffernan, R. J. Smith, and L. M. Wahl, “Perspectives on the basic reproductive ratio,” Journal of the Royal Society Interface, vol. 2, no. 4, pp. 281–293, 2005. View at Publisher · View at Google Scholar · View at Scopus
  22. J. Li, D. Blakeley, and R. J. Smith?, “The Failure of R0,” Computational and Mathematical Methods in Medicine, vol. 2011, Article ID 527610, 17 pages, 2011. View at Publisher · View at Google Scholar
  23. J. Carr, Applications of Centre Manifold Theory, Springer, New York, NY, USA, 1981.
  24. C. Castillo-Chavez and B. Song, “Dynamical models of tuberculosis and their applications,” Mathematical Biosciences and Engineering, vol. 1, no. 2, pp. 361–404, 2004.
  25. O. Diekmann, J. A. Heesterbeek, and J. A. Metz, “On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations,” Journal of Mathematical Biology, vol. 28, no. 4, pp. 365–382, 1990. View at Scopus
  26. P. van den Driessche and J. Watmough, “Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,” Mathematical Biosciences, vol. 180, pp. 29–48, 2002. View at Publisher · View at Google Scholar · View at Scopus
  27. M. J. Pybus, “Alberta's Chronic Wasting Disease Management Programs in 2006 and upcoming surveillance,” 2010, http://www.srd.alberta.ca/FishWildlife/WildlifeDiseases/ChronicWastingDisease/documents/Alberta2006CWDManagementAndUpcomingSurveillance.pdf.
  28. J. E. Gross and M. W. Miller, “Chronic wasting disease in mule deer: disease dynamics and control,” Journal of Wildlife Management, vol. 65, no. 2, pp. 205–215, 2001. View at Scopus
  29. J. Binfet and D. W. Lutz, “Deer and Elk population status and harvest structure in Western North America: a summary of state and provincial status surveys,” in Proceedings of the Western States and Provinces Deer and Elk Workshop, vol. 5, pp. 48–68, 2003, http://www.muledeerworkinggroup.com/Docs/Proceedings/.
  30. A. N. Hamir, J. A. Richt, J. M. Miller et al., “Experimental transmission of Cchronic Wasting Disease (CWD) of Elk (Cervus elaphus nelsoni), white-tailed Deer (Odocoileus vivginianus), and Mule Deer (Odocoileus hemionus) to white-tailed Deer by intracerebral route,” Veterinary Pathology, vol. 45, no. 3, pp. 297–306, 2008. View at Publisher · View at Google Scholar · View at Scopus
  31. C. W. Clark and D. E. Tait, “Sex-selective harvesting of wildlife populations,” Ecological Modelling, vol. 14, no. 3-4, pp. 251–260, 1982. View at Scopus
  32. M. M. Conner, J. E. Gross, P. C. Cross, M. R. Ebinger, R. R. Gillies, and M. D. Samuel, “Scale-dependent approaches to modeling spatial epidemiology of chronic wasting disease,” Special Report, 2007, http://www.cwd-info.org/index.php/fuseaction/resources.newresearch.
  33. S. M. Blower and H. Dowlatabadi, “Sensitivity and uncertainty analysis of complex models of disease transmission: an HIV model, as an example,” International Statistics Review, vol. 62, no. 2, pp. 229–243, 1994. View at Publisher · View at Google Scholar
  34. J. M. Gaillard, M. Festa-Bianchet, and N. G. Yoccoz, “Population dynamics of large herbivores: variable recruitment with constant adult survival,” Trends in Ecology and Evolution, vol. 13, no. 2, pp. 58–63, 1998. View at Publisher · View at Google Scholar · View at Scopus
  35. J. O. Lloyd-Smith, P. C. Cross, C. J. Briggs et al., “Should we expect population thresholds for wildlife disease?” Trends in Ecology and Evolution, vol. 20, no. 9, pp. 511–519, 2005. View at Publisher · View at Google Scholar · View at Scopus
  36. M. M. Conner, M. R. Ebinger, J. A. Blanchong, and P. C. Cross, “Infectious disease in cervids of North America,” Annals of the New York Academy of Sciences, vol. 1134, pp. 146–172, 2008. View at Publisher · View at Google Scholar · View at Scopus
  37. M. Begon, M. Bennett, R. G. Bowers, N. P. French, S. M. Hazel, and J. Turner, “A clarification of transmission terms in host-microparasite models: numbers, densities and areas,” Epidemiology and Infection, vol. 129, no. 1, pp. 147–153, 2002. View at Publisher · View at Google Scholar · View at Scopus
  38. T. J. Habib, E. H. Merrill, M. J. Pybus, and D. W. Coltman, “Modelling landscape effects on density-contact rate relationships of deer in eastern Alberta: implications for chronic wasting disease,” Ecological Modelling, vol. 222, no. 15, pp. 2722–2732, 2011. View at Publisher · View at Google Scholar · View at Scopus