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Virus dynamics model with intracellular delays and immune response
Aggregation and environmental transmission in chronic wasting disease
1. | Department of Mathematics, Christopher Newport University, 1 Avenue of the Arts, Newport News, VA 23606, United States |
2. | Department of Mathematics, The University of Texas-Pan American, 1201 W. University Drive, Edinburg, TX 78539, United States |
3. | Department of Mathematics, Univeristy of Ottawa, 585 King Edward, Ottawa, ON K1N 6N5, Canada |
References:
[1] |
A. Aguzzi, M. Heikenwalder and M. Polymenidou, Insights into prion strains and neurotoxicity, Nature Reviews Molecular Cell Biology, 8 (2007), 552-561.
doi: 10.1038/nrm2204. |
[2] |
E. Almberg, P. Cross, C. Johnson, D. Heisey and B. Richards, Modeling routes of Chronic Wasting Disease transmission: Environmental prion persistence promotes deer population decline and extinction, PLoS One, 6 (2011), e19896.
doi: 10.1371/journal.pone.0019896. |
[3] |
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, 129 (2002), 147-153.
doi: 10.1017/S0950268802007148. |
[4] |
R. Breban, Role of environmental persistence in pathogen transmission: A mathematical modeling approach, J. Math. Biol., 66 (2013), 535-546.
doi: 10.1007/s00285-012-0520-2. |
[5] |
C. Castillo-Chavez and B. Song, Dynamical models of tuberculosis and their applications, Mathematical Biosciences and Engineering, 1 (2004), 361-404.
doi: 10.3934/mbe.2004.1.361. |
[6] |
J. Collinge and A. R. Clarke, A general model of prion strains and their pathogenicity, Science, 318 (2007), 930-936.
doi: 10.1126/science.1138718. |
[7] |
M. M. Conner, M. R. Ebinger, J. A. Blanchong and P. C. Cross, Infectios disease in cervids of North America, Ann. N.Y. Acad. Sci., 1134 (2008), 146-172.
doi: 10.1196/annals.1439.005. |
[8] |
M. M. Conner, M. W. Miller, M. R. Ebinger and K. P. Burnham, A meta-BACI approach for evaluating management intervention on chronic wasting disease in mule deer, Ecological Applications, 17 (2007), 140-153.
doi: 10.1890/1051-0761(2007)017[0140:AMAFEM]2.0.CO;2. |
[9] |
O. Diekmann and J. A. M. Heesterbeek, Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation, John Wiley & Sons, 2000. |
[10] |
K. Dietz, Overall population patterns in the transmission cycle of infectious disease agents, Population Biology of Infectious Diseases, ed. R.M. Anderson and R.M. May, Dahlem Konferenzen, Springer-Verlag, 25 (1982), 87-102.
doi: 10.1007/978-3-642-68635-1_6. |
[11] |
G. L. Dusek, R. J. MacKie, J. D. Herriges and B. B. Compton, Population ecology of white-tailed deer along the Lower Yellowstone River, Wildlife Monographs, 104 (1989), 3-68. |
[12] |
H. R. Fryer and A. R. McLean, There is no safe dose of prions, PLoS ONE, 6 (2011), e23664.
doi: 10.1371/journal.pone.0023664. |
[13] |
J. E. Gross and M. W. Miller, Chronic wasting disease in mule deer: Disease dynamics and control, The Journal of Wildlife Management, 65 (2001), 205-215.
doi: 10.2307/3802899. |
[14] |
T. Habib, E. Merrill, M. J. Pybus and D. Coltman, Modelling landscape effects on density-contact rate relationships in eastern Alberta: Inplications for chronic wasting disease, Ecological Modelling, 222 (2011), 2722-2732.
doi: 10.1016/j.ecolmodel.2011.05.007. |
[15] |
J. O. Lloyd-Smith, P. C. Cross, C. J. Briggs, M. Daugherty, W. M. Getz, J. Latto, M. S. Sanchez, A. B. Smith and A. Swei, Should we expect population thresholds for wildlife disease?, Trends in Ecology & Evolution, 20 (2005), 511-519.
doi: 10.1016/j.tree.2005.07.004. |
[16] |
C. K. Mathiason, S. A. Hays, J. Powers, J. Hayes-Klug and J. Langenberg, et al, Infectious prions in pre-clinical deer and transmission of chronic wasting disease solely by environmental exposure, PLoS ONE, 4 (2009), e5916.
doi: 10.1371/journal.pone.0005916. |
[17] |
R. M. May, Host-parasitoid systems in patchy environments: A phenomenological model, Journal of Animal Ecology, 47 (1978), 833-844.
doi: 10.2307/3674. |
[18] |
M. W. Miller, N. T. Hobbs and S. J. Tavener, Dynamics of prion disease transmission in mule deer, Ecological Applications, 16 (2006), 2208-2214.
doi: {10.1890/1051-0761(2006)016[2208:DOPDTI]2.0.CO;2}. |
[19] |
M. W. Miller, E. S. Williams, N. T. Hobbs and L. L. Wolfe, Environmental sources of prion transmission in mule deer, Emerg. Infect. Dis., 10 (2004), 1003-1006.
doi: 10.3201/eid1006.040010. |
[20] |
P. R. Moorcroft and M. A. Lewis, Mechanistic Home Range Analysis, Princeton University Press, 2006. |
[21] |
E. M. Schauber and A. Woolf, Chronic wasting disease in deer and elk: A critique of current models and their application, Wildlife Society Bulletin, 31 (2003), 610-616. |
[22] |
H. R. Thieme, Mathematics in Population Biology, Princeton Series in Theoretical and Computational Biology, Princeton University Press, 2003. |
[23] |
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, 46 (2009), 457-466.
doi: 10.1111/j.1365-2664.2008.01576.x. |
[24] |
E. S. Williams and M. W. Miller, Chronic wasting disease in deer and elk in North America, Revue Scientifique et technique de l'Office International des Epizzoties, 21 (2002), 305-316. |
show all references
References:
[1] |
A. Aguzzi, M. Heikenwalder and M. Polymenidou, Insights into prion strains and neurotoxicity, Nature Reviews Molecular Cell Biology, 8 (2007), 552-561.
doi: 10.1038/nrm2204. |
[2] |
E. Almberg, P. Cross, C. Johnson, D. Heisey and B. Richards, Modeling routes of Chronic Wasting Disease transmission: Environmental prion persistence promotes deer population decline and extinction, PLoS One, 6 (2011), e19896.
doi: 10.1371/journal.pone.0019896. |
[3] |
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, 129 (2002), 147-153.
doi: 10.1017/S0950268802007148. |
[4] |
R. Breban, Role of environmental persistence in pathogen transmission: A mathematical modeling approach, J. Math. Biol., 66 (2013), 535-546.
doi: 10.1007/s00285-012-0520-2. |
[5] |
C. Castillo-Chavez and B. Song, Dynamical models of tuberculosis and their applications, Mathematical Biosciences and Engineering, 1 (2004), 361-404.
doi: 10.3934/mbe.2004.1.361. |
[6] |
J. Collinge and A. R. Clarke, A general model of prion strains and their pathogenicity, Science, 318 (2007), 930-936.
doi: 10.1126/science.1138718. |
[7] |
M. M. Conner, M. R. Ebinger, J. A. Blanchong and P. C. Cross, Infectios disease in cervids of North America, Ann. N.Y. Acad. Sci., 1134 (2008), 146-172.
doi: 10.1196/annals.1439.005. |
[8] |
M. M. Conner, M. W. Miller, M. R. Ebinger and K. P. Burnham, A meta-BACI approach for evaluating management intervention on chronic wasting disease in mule deer, Ecological Applications, 17 (2007), 140-153.
doi: 10.1890/1051-0761(2007)017[0140:AMAFEM]2.0.CO;2. |
[9] |
O. Diekmann and J. A. M. Heesterbeek, Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation, John Wiley & Sons, 2000. |
[10] |
K. Dietz, Overall population patterns in the transmission cycle of infectious disease agents, Population Biology of Infectious Diseases, ed. R.M. Anderson and R.M. May, Dahlem Konferenzen, Springer-Verlag, 25 (1982), 87-102.
doi: 10.1007/978-3-642-68635-1_6. |
[11] |
G. L. Dusek, R. J. MacKie, J. D. Herriges and B. B. Compton, Population ecology of white-tailed deer along the Lower Yellowstone River, Wildlife Monographs, 104 (1989), 3-68. |
[12] |
H. R. Fryer and A. R. McLean, There is no safe dose of prions, PLoS ONE, 6 (2011), e23664.
doi: 10.1371/journal.pone.0023664. |
[13] |
J. E. Gross and M. W. Miller, Chronic wasting disease in mule deer: Disease dynamics and control, The Journal of Wildlife Management, 65 (2001), 205-215.
doi: 10.2307/3802899. |
[14] |
T. Habib, E. Merrill, M. J. Pybus and D. Coltman, Modelling landscape effects on density-contact rate relationships in eastern Alberta: Inplications for chronic wasting disease, Ecological Modelling, 222 (2011), 2722-2732.
doi: 10.1016/j.ecolmodel.2011.05.007. |
[15] |
J. O. Lloyd-Smith, P. C. Cross, C. J. Briggs, M. Daugherty, W. M. Getz, J. Latto, M. S. Sanchez, A. B. Smith and A. Swei, Should we expect population thresholds for wildlife disease?, Trends in Ecology & Evolution, 20 (2005), 511-519.
doi: 10.1016/j.tree.2005.07.004. |
[16] |
C. K. Mathiason, S. A. Hays, J. Powers, J. Hayes-Klug and J. Langenberg, et al, Infectious prions in pre-clinical deer and transmission of chronic wasting disease solely by environmental exposure, PLoS ONE, 4 (2009), e5916.
doi: 10.1371/journal.pone.0005916. |
[17] |
R. M. May, Host-parasitoid systems in patchy environments: A phenomenological model, Journal of Animal Ecology, 47 (1978), 833-844.
doi: 10.2307/3674. |
[18] |
M. W. Miller, N. T. Hobbs and S. J. Tavener, Dynamics of prion disease transmission in mule deer, Ecological Applications, 16 (2006), 2208-2214.
doi: {10.1890/1051-0761(2006)016[2208:DOPDTI]2.0.CO;2}. |
[19] |
M. W. Miller, E. S. Williams, N. T. Hobbs and L. L. Wolfe, Environmental sources of prion transmission in mule deer, Emerg. Infect. Dis., 10 (2004), 1003-1006.
doi: 10.3201/eid1006.040010. |
[20] |
P. R. Moorcroft and M. A. Lewis, Mechanistic Home Range Analysis, Princeton University Press, 2006. |
[21] |
E. M. Schauber and A. Woolf, Chronic wasting disease in deer and elk: A critique of current models and their application, Wildlife Society Bulletin, 31 (2003), 610-616. |
[22] |
H. R. Thieme, Mathematics in Population Biology, Princeton Series in Theoretical and Computational Biology, Princeton University Press, 2003. |
[23] |
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, 46 (2009), 457-466.
doi: 10.1111/j.1365-2664.2008.01576.x. |
[24] |
E. S. Williams and M. W. Miller, Chronic wasting disease in deer and elk in North America, Revue Scientifique et technique de l'Office International des Epizzoties, 21 (2002), 305-316. |
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