Mathematical modeling of viral zoonoses in wildlife

Natural Resource Modeling

Volumn 25, Issue 1, 2012, Pages 5-51

  Allen, L J S ^a   Brown, V L ^b   Jonsson, C B ^c   Klein, S L ^d   Laverty, S M ^e   Magwedere, K ^f   Owen, J C ^g   van den Driessche, P ^h  

^a TEXAS TECH UNIVERSITY   (United States)

^b UNIVERSITY OF MICHIGAN   (United States)

^c UNIVERSITY OF LOUISVILLE   (United States)

^d JOHNS HOPKINS BLOOMBERG SCHOOL OF PUBLIC HEALTH   (United States)

^e UNIVERSITY OF UTAH   (United States)

^f Directorate of Veterinary Services   (Namibia)

^g MICHIGAN STATE UNIVERSITY   (United States)

^h UNIVERSITY OF VICTORIA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ANIMALS;

AGRICULTURAL PRODUCTIONS; HEALTH CONCERNS; INFECTIOUS DISEASE;

AGRICULTURE;

EID: 84855222325     PISSN: 08908575     EISSN: 19397445     Source Type: Journal    
DOI: 10.1111/j.1939-7445.2011.00104.x     Document Type: Review

References (180)

1. G. Abramson, V.M. Kenkre, T.L. Yates, and R.R. Parmenter 2003], Traveling Waves of Infection in the Hantavirus Epidemics, Bull. Math. Biol. 65, 519-534.
2. A.S. Ackleh and L.J.S. Allen 2003], Competitive Exclusion and Coexistence for Pathogens in an Epidemic Model with Variable Population Size, J. Math. Biol. 47, 153-168.
3. A.S. Ackleh and L.J.S. Allen 2005], Competitive Exclusion in SIS and SIR Epidemic Models with Total Cross Immunity and Density-Dependent Host Mortality, Discrete Cont. Dyn. Sys.-Ser. B 178-188.
4. F.R. Adler, C.A. Clay, and E.M. Lehmer 2008], The Role of Heterogeneity in the Persistence and Prevalence of Sin Nombre Virus in Deer Mice, Am. Nat. 172(6), 855-867.
5. F.R. Adler and J.M. Losada 2002], Super- and Coinfection: Filling the Range, (U. Dieckmann, J.A.J. Metz, M.W. Sabelis, and K. Sigmund, eds.) Adaptive Dynamics of Infectious Diseases: In Pursuit of Virulence Management, Cambridge University Press, Cambridge, UK, pp. 138-149.
6. F.R. Adler, J.M. Pearce-Duvet, and M.D. Dearing 2008], How Host Population Dynamics Translate into Time-Lagged Prevalence: An Investigation of Sin Nombre Virus in Deer Mice, Bull. Math. Biol. 70(1), 236-252.
7. L.J.S. Allen 2008], An Introduction to Stochastic Epidemic Models, (F. Brauer, P. van den Driessche, and J. Wu, eds.) Mathematical Epidemiology, Lecture Notes in Mathematics, Springer-Verlag, Berlin, Heidelberg, pp. 81-130.
8. L.J.S. Allen 2010], An Introduction to Stochastic Processes with Applications to Biology, 2nd Ed., CRC Press, Chapman & Hall, Boca Raton, FL.
9. L.J.S. Allen and P.J. Cormier 1996], Environmentally Driven Epizootics, Math. Biosci. 131, 51-80.
10. L.J.S. Allen, D.A. Flores, R.K. Ratnayake, and J.R. Herbold 2002], Discrete-time Deterministic and Stochastic Models for the Spread of Rabies, Appl. Math. Comp. 132, 271-292.
11. L.J.S. Allen, M. Langlais, and C. J. Phillips 2003], The Dynamics of Two Viral Infections in a Single Host Population with Applications to Hantavirus, Math. Biosci. 186, 191-217.
12. L.J.S. Allen, R.K. McCormack, and C.B. Jonsson 2006], Mathematical Models for Hantavirus Infection in Rodents, Bull. Math. Biol. 68, 511-524.
13. L.J.S. Allen and P. van den Driessche 2008]. The Basic Reproduction Number in Some Discrete-Time Epidemic models, J. Differ. Eqns. Appl. 14, 1127-1147.
14. L.J.S. Allen, C.L. Wesley, R.D. Owen, D.G. Goodin, D. Koch, C.B. Jonsson, Y.-K. Chu, S. Hutchinson, and R. Paige 2009], A Habitat-Based Model for the Spread of Hantavirus between Reservoir and Spillover Species, J. Theor. Biol. 260, 510-522.
15. S. Altizer, A. Dobson, P. Hosseini, P. Hudson, M. Pascual, and P. Rohani 2006], Seasonality and the Dynamics of Infectious Diseases, Ecol. Lett. 467-484.
16. R.M. Anderson and R.M. May 1979a], Population Biology of Infectious Diseases: Part Nature 280, 361-367.
17. R.M. Anderson and R.M. May 1979b], Population Biology of Infectious Diseases: Part II, Nature 280, 455-461.
18. R.M. Anderson and R.M. May 1986], The Invasion, Persistence and Spread of Infectious Diseases with Animal and Plant Communities, Phil. Trans. Roy. Soc. Lond. B 314, 533-570.
19. R.M. Anderson and R.M. May 1992], Infectious Diseases of Humans: Dynamics and Control, Oxford University Press, Oxford.
20. H. Andersson and T. Britton 2000], Stochastic Epidemic Models and Their Statistical Analysis, Springer Lecture Notes in Statistics 151, Springer-Verlag, New York.
21. J. Arino, R. Jordan, and P. van den Driessche 2007], Quarantine in a Multi-Species Epidemic Model with Spatial Dynamics, Math. Biosci. 206, 46-60.
22. A. Asachenkov, G. Marchuk, R. Mohler, and S. Zuev 1994], Disease Dynamics, Birkhäuser, Boston.
23. 0 for Vector-Borne Diseases with a Periodic Vector Population, Bull. Math. Biol. 69, 1067-1091.
24. N. Bacaer and S. Guernaoui 2006], The Epidemic Threshold of Vector-Borne Diseases with Seasonality. The Case of Cutaneous Leishmaniasis in Chichaoua, Morocco, J. Math. Biol. 53, 421-436.
25. N.T.J. Bailey 1990], The Elements of Stochastic Processes with Applications to the Natural Sciences, John Wiley & Sons, New York.
26. C. Banerjee, L.J.S. Allen, and J. Salazar-Bravo 2008], Models for an Arenavirus Infection in a Rodent Population: Consequences of Horizontal, Vertical and Sexual Transmission, Math. Biosci. Eng. 617-645.
27. M.S. Bartlett 1957], Measles Periodicity and Community Size, J. R. Stat. Soc. Ser. A 120, 48-71.
28. R.G. Bengis, F.A. Leighton, J.R. Fischer, M. Artois, T. Mörner, and C.M. Tate 2004], The Role of Wildlife in Emerging and Re-Emerging Zoonoses, Rev. Sci. Tech. Off. Int. Epiz. 23(2), 497-511.
29. F. Brauer 1990], Models for the Spread of Universally Fatal Diseases, J. Math. Biol. 28, 451-462.
30. F. Brauer 1991], Models for the Spread of Universally Fatal Diseases, II, in (S. Busenberg and M. Martelli, eds.) Differential Equation Models in Biology, Epidemiology and Ecology, Springer-Verlag, New York, pp. 57-69.
31. F. Brauer 2008], Compartmental Models in Epidemiology, (F. Brauer, P. van den Driessche, and J. Wu, eds.) Mathematical Epidemiology, Lecture Notes in Mathematics, Springer-Verlag, Berlin, Heidelberg, pp. 19-79.
32. F. Brauer, P. van den Driessche, and J. Wu (Eds.) [2008], Mathematical Epidemiology, Lecture Notes in Mathematics, Springer-Verlag, Berlin, Heidelberg.
33. R. Breban, J.M. Drake, and P. Rohani 2010], A General Multi-Strain Model with Environmental Transmission: Invasion Conditions for the Disease-Free and Endemic States, J. Theor. Biol. 264, 729-736.
34. H.J. Bremermann and H.R. Thieme 1989], A Competitive Exclusion Principle for Pathogen Virulence, J. Math. Biol. 27, 179-190.
35. J.D. Broadfoot, R.C. Rosette, and D.T. O'Leary 2001], Raccoon and Skunk Population Models for Urban Disease Control Planning in Ontario, Canada, Ecol. Appl. 11, 295-303.
36. J.J. Bull, L.A. Meyers, and M. Lachman 2005], Quasispecies made Simple, PLOS Comp. Biol. 450-460.
37. S.N. Busenberg and K.L. Cooke 1993], Vertically Transmitted Diseases: Models and Dynamics, Springer-Verlag, New York.
38. C. Castillo-Chavez and J.X. Velasco-Hernandez 1998], On the Relationship Between Evolution of Virulence and Host Demography, J. Theor. Biol. 192, 437-444.
39. H.L. Caswell 2001], Matrix Population Models, Sinauer Assoc. Inc., Sunderland, MA.
40. H. Chen, Y. Li, Z. Li, J. Shi, K. Shinya, G. Deng, Q. Qi, G. Tian, S. Fan, H. Zhao, Y. Sun, and Y. Kawaoka 2006], Properties and Dissemination of H5N1 Viruses Isolated During an Influenza Outbreak in Migratory Waterfowl in Western China, J. Virol. 80, 5976-5983.
41. J.E. Childs, A.T. Curns, M.E. Dey, L.A. Real, L. Feinstein, and O.N. Bjornstad 2000], Predicting the Local Dynamics of Epizootic Rabies among Raccoons in the United States, Proc. Nat. Acad. Sci. 97, 13666-13671.
42. J.E. Childs, J.S. Mackenzie, and J.A. Richt (Eds.) [2007], Wildlife and Emerging Zoonotic Diseases: The Biology, Circumstances and Consequences of Cross-Species Transmission, Springer, Berlin, Heidelberg, New York.
43. B.B. Chomel, A. Belotto, and F.-X. Meslin 2007], Wildlife, Exotic Pets, and Emerging Zoonoses, Emerg. Inf. Dis. 13, 6-11.
44. D.H. Chung, Y. Sun, W.B. Parker, J.B. Arterburn, A. Bartolucci and C.B. Jonsson 2007], Ribavirin Reveals a Lethal Threshold of Allowable Mutation Frequency for Hantaan Virus, J. Virol. 81, 11722-11729.
45. A.C. Clements and D.U. Pfeiffer 2010], Emerging Viral Zoonoses: Frameworks for Spatial and Spatiotemporal Risk Assessment and Resource Planning, Vet. J. 182, 21-30.
46. M.J. Coyne, G. Smith, and F.E. McAllister 1989], Mathematic Model for the Population Biology of Rabies in Raccoons in the Mid-Atlantic States, Am. J. Vet. Res. 59, 2148-2154.
47. P.W. Daniels, K. Halpin, A. Hyatt, and D. Middleton 2007], Infection and Disease in Reservoir and Spillover Hosts: Determinants of Pathogen Emergence, (J.E. Childs, J.S. Mckenzie, and J.A. Richt, eds.) Wildlife and Emerging Zoonotic Diseases: The Biology Circumstances and Consequences of Cross-Species Transmission, Springer, Berlin, Heidelberg, New York, pp. 113-131.
48. T. Day 2002], On the Evolution of Virulence and the Relationship Between Various Measures of Mortality, Proc. R. Soc. Lond. B 269, 1317-1323.
49. T. Day and J.G. Burns 2003], A Consideration of Patterns of Virulence Arising from Host-Parasite Coevolution, Evolution 57, 671-676.
50. P. Daszak, A.A. Cunningham, and A.D. Hyatt 2000], Emerging Infectious Diseases of Wildlife-Threats to Biodiversity and Human Health, Science 287, 443-449.
51. S. Davis, E. Calvet, and H. Leirs 2005], Fluctuating Rodent Populations and Risk to Humans from Rodent-Borne Zoonoses, Vector-Borne Zoon. Dis. 305-314.
52. P. De Leenheer and S.S. Pilyugin 2008], Multistrain Virus Dynamics with Mutations: A Global Analysis, Math. Med. Biol. 25, 285-322.
53. P. De Leenheer and H.L. Smith 2003], Virus Dynamics: Global Analysis, SIAM J. Appl. Math. 63, 1313-1327.
54. U. Dieckmann, J.A.J. Metz, M.W. Sabelis, and K. Sigmund (Eds.) [2002], Adaptive Dynamics of Infectious Diseases: In Pursuit of Virulence Management, Cambridge University Press, Cambridge, UK.
55. O. Diekmann and J.A.P. Heesterbeek 2000], Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation, Wiley, New York.
56. 0 in Models for Infectious Diseases in Heterogeneous Population, J. Math. Biol. 28, 365-382.
57. W. Ding, L.J. Gross, K. Langston, S. Lenhart, and L.A. Real 2007], Rabies in Raccoons: Optimal Control for a Discrete Time Model on a Spatial Grid, J. Biol. Dyn. 379-393.
58. L.J. Dizney and L.A. Ruedas 2009], Increased Host Species Diversity and Decreased Prevalence of Sin Nombre Virus, Emerg. Infect. Dis. 15, 1012-1018.
59. A. Dobson 2004], Population Dynamics of Pathogens with Multiple Host Species, Am. Nat. 164, S64-S78.
60. M. Eigen 1971], Self-Organization of Matter and the Evolution of Biological Macromolecules, Naturwissenschaften 58, 465-523.
61. S. Eikenberry, S. Hews, J.D. Magy, and Y. Kuang 2009], The Dynamics of a Delay Model of Hepatitis B Virus Infection with Logistic Hepatocyte Growth, Math. Biosci. Eng. 283-299.
62. L. Esteva and C. Vargas 2003], Coexistence of Different Serotypes of Dengue Virus, J. Math. Biol. 46, 31-47.
63. Z. Feng and J.X. Velasco-Hernandez 1997], Competitive Exclusion in a Vector-Host Model for the Dengue Fever, J. Math. Biol. 35, 523-544.
64. F. Fenner and K. Myers 1978], Myxoma Virus and Myxomatosis in Retrospect: The First Quarter Century of a New Disease, in (E. Kurstak and K. Maramorosch, eds.) Viruses and Environment, Academic Press, New York, pp. 539-570.
65. F. Fenner and F.N. Ratcliffe 1965], Myxomatosis, Cambridge University Press, Cambridge, UK.
66. A. Fenton 2008], Worms and Germs: The Population Dynamic Consequences of Microparasite-Macroparasite Co Infection, Parasitology 135, 1545-1560.
67. A. Fenton, T. Lamb, and A.L. Graham 2008], Optimality Analysis of Th1/Th2 Immune Responses During Microparasite-Macroparasite Co-infection, with Epidemiological Feedbacks, Parasitology 135, 841-853.
68. J.E. Foley, P. Foley, and N.C. Pederson 1999], The Persistence of a SIS Disease in a Metapopulation, J. Appl. Ecol. 36, 555-563.
69. E. Fromont, M. Artois, M. Langlais, F. Courchamp, and D. Pontier 1997], Modeling the Feline Leukemia Virus (FeLV) in Natural Populations of Cats (Felis catus), Theor. Pop. Biol. 52, 60-70.
70. A.P. Galvani and R.M. May 2005], Epidemiology: Dimensions of Superspreading, Nature 438, 293-295.
71. G.E. Glass, J.E. Cheek, J.A. Patz, T.M. Shields, T.J. Doyle, D.A. Thoroughman, D.K. Hunt, R.E. Enscore, K.L. Gage, C. Irland, C.J. Peters, and R. Bryan 2000], Using Remotely Sensed Data to Identify Areas at Risk for Hantavirus Pulmonary Syndrome, Ecol. Inf. Dis. 238-247.
72. G.E. Glass, W. Livingston, J.N. Mills, W.G. Hlady, J.B. Fine, W. Biggler, T. Coke, D. Frazier, S. Atherley, P.E. Rollin, T.G. Ksiazek, C. J. Peters, and J.E. Childs 1998], Black Creek Canal Virus Infection in Sigmodon Hispidus in Southern Florida, Am. J. Trop. Med. Hyg. 59, 699-703.
73. R. Glavits, E. Ferenczi, E. Ivanics, T. Bakonyi, T. Mato, P. Zarka, and V. Palya 2005], Co-Occurrence of West Nile Fever and Circovirus Infection in a Goose Flock in Hungary, Avian Pathol. 34, 408-414.
74. D.G. Goodin, D.E. Koch, R.D. Owen, Y.-K. Chu, J.M.S. Hutchinson, and C.B. Jonsson 2006], Land Cover Associated with Hantavirus Presence in Paraguay, Global Ecol. Biogeog. 15, 519-527.
75. S.A. Gourley, Y. Kuang, and J.D. Nagy 2008], Dynamics of a Delay Differential Equation Model of Hepatitis B Virus Infection, J. Biol. Dyn. 140-153.
76. J.D. Graci, K. Too, E.D. Smidansky, J.P. Edathil, E.W. Barr, D.A. Harki, J.E. Galarraga, J.M. Bollinger, Jr, B.R. Peterson, D. Loakes, D.M. Brown, and C.E. Cameron 2008], Lethal Mutagenesis of Picornaviruses with N-T-Modified Purine Nucleoside Analogues, Antimicrob. Agents Chemother. 52, 971-979.
77. A. Grand-Pérez, S. Sierra, M.G. Castro, E. Domingo, and P.R. Lowenstein 2002], Molecular Indetermination in the Transition to Error Catastrophe: Systematic Elimination of Lymphocytic Choriomeningitis Virus through Mutagenesis does not Correlate Linearly with Large Increases in Mutant Spectrum Complexity, Proc. Nat. Acad. Sci. 99, 12938-12943.
78. B.T. Grenfell, B.T and A.P. Dobson (Eds.) [1995], Ecology of Disease in Natural Populations. Cambridge University Press, Cambridge, UK.
79. B.T. Grenfell, O.G. Pybus, J.R. Gog, J.L.N. Wood, J.M. Daly, J.A. Mumford, and E.C. Holmes 2004], Unifying the Epidemiological and Evolutionary Dynamics of Pathogens, Science 303, 327-332.
80. I. Gudelj, K.A.J. White, and N.F. Britton 2004], The Effects of Spatial Movement and Group Interactions on Disease Dynamics of Social Animals, Bull. Math. Biol. 66, 91-108.
81. L. Han, Z. Ma, and H.W. Hethcote 2001], Four Predator Prey Models with Infectious Diseases, Math. Comp. Model. 34, 849-856.
82. D.M. Hawley and S.M. Altizer 2011], Disease Ecology Meets Ecological Immunology: Understanding the Links Between Organismal Immunity and Infection Dynamics in Natural Populations, Funct. Ecol. 25, 48-60.
83. S.M. Hazel, M. Bennett, J. Chantrey, K. Bown, R. Cavanagh, T.R. Jones, D. Baxby, and M. Begon 2000], A Longitudinal Study of An Endemic Disease in Its Wildlife Reservoir: Cowpox and Wild Rodents, Epidemiol. Infect. 124, 551-562.
84. T. Hemachudha and C.E. Rupprecht 2005], Rabies, (K.L. Roos ed.) Principles of Neurologic Infectious Diseases, McGraw Hill Co., Medical Pub. Div., New York, pp. 151-176.
85. H.W. Hethcote 2000], The Mathematics of Infectious Diseases, SIAM Review 42, 599-653.
86. H.W. Hethcote, W. Wang, and Y. Li 2005], Species Coexistence and Periodicity on Host-Host-Pathogen Models, J. Math. Biol. 51, 629-660.
87. J.A. Heesterbeek and M.G. Roberts 2007], The Type-Reproduction Number T in Models for Infectious Disease Control, Math. Biosci. 206, 3-10.
88. G. Hess 1996], Disease in Metapopulation Models: Implications for Conservation, Ecology 77, 1617-1632.
89. G.R. Hess, S.E. Randolph, P. Arneberg, C. Chemini, C. Furlanello, J. Harwood, M.G. Roberts, and J. Swinton 2002], Spatial Aspects of Disease Dynamics, (P.J. Hudson, A. Rizzoli, B.T. Grenfell, H. Heesterbeek, and A.P. Dobson, eds.) The Ecology of Wildlife Disease, Oxford University Press, Oxford, pp. 102-118.
90. F.M. Hilker and K. Schmitz 2008], Disease Induced Stabilization of Predator-Prey Oscillations, J. Theor. Biol. 255, 299-306.
91. M.E. Hochberg and R.D. Holt 1990], The Coexistence of Competing Parasites The Role of Cross-Species Infection, Am. Nat. 136, 517-541.
92. E.C. Holmes 2010], The RNA Virus Quasispecies: Fact or Fiction? J. Mol. Biol. 400, 271-273.
93. P.J. Hudson, A. Rizzoli, B.T. Grenfell, H. Heesterbeek, and A.P. Dobson (Eds.), [2002], The Ecology of Wildlife Diseases, Oxford University Press, Oxford.
94. M.J. Keeling and P. Rohani 2008], Modeling Infectious Diseases in Humans and Animals, Princeton University Press, Princeton and Oxford.
95. F. Keesing, L.K. Belden, P. Daszak, A. Dobson, C.D. Harvell, R.D. Holt, P. Hudson, A. Jolles, K.E. Jones, and C.E. Mitchell 2010], Impacts of Biodiversity on the Emergence and Transmission of Infectious Diseases, Nature 468, 647-652.
96. F. Keesing, R.D. Holt, and R.S. Ostfeld 2006], Effects of Species Diversity on Disease Risk, Ecol. Lett. 485-499.
97. A.M. Kilpatrick, A.A. Chmura, D.W. Gibbons, R.C. Fleischer, P.P. Marra, and P. Daszak 2006], Predicting the Global Spread of H5N1 Avian Influenza, Proc. Natl. Acad. Sci. 103, 19368-19373.
98. A.M. Kilpatrick, S.L. LaDeau, and P.P. Marra 2007], Ecology of West Nile Virus Transmission and its Impact on Birds in the Western Hemisphere, Auk. 124, 1121-1136.
99. S.L. Klein and C.H. Calisher 2007], Emergence and persistence of hantaviruses, Wildlife and Emerging Diseases: The Biology, Circumstances and Consequences of Cross-Species Transmission, pp. 217-252, J.E. Childs, J.S. Mackenzie, and J.A. Richt (Eds.) Springer, Berlin, Heidelberg, New York.
100. S.L. Klein, M.C. Zink, and G.E. Glass 2004], Seoul Virus Infection Increases Aggressive Behaviour in Male Norway Rats, Anim. Behav. 67, 421-429.
101. K. Koelle, P. Khatri, M. Kamradt, and T.B. Kepler 2010], A Two-Tiered Model for Simulating the Ecological and Evolutionary Dynamics of Rapidly Evolving Viruses, with an Application to Influenza, J. R. Soc. Interface 1257-1274.
102. A.S. Lauring and R. Andino 2010], Quasispecies Theory and the Behavior of RNA Viruses, PLOS Pathogens 1-8.
103. S.M. Laverty and F.R. Adler 2009], The Role of Age Structure in the Persistence of a Chronic Pathogen in a Fluctuating Population, J. Biol. Dyn. 224-234.
104. H.Y. Lee, D.J. Topham, S.Y. Park, J. Hollenbaugh, J. Treanor, T.R. Mosmann, X. Ji, B. Ward, H. Miao, J. Holde Wiltse, A.S. Perelson, M. Zand, and J. Wu 2009], Simulation and Prediction of the Adaptive Immune Response to Influenza A Virus Infection, J. Virol. 83, 7151-7165.
105. S. Levin and D. Pimentel 1981 Selection of Intermediate Rates of Increase in Parasite-Host Systems, Am. Nat. 117, 308-315.
106. M. Lewis, J. Renclawowicz, and P. van den Driessche 2006], Traveling Waves and Spread Rates for a West Nile Virus Model, Bull. Math. Biol. 3-23.
107. 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 2005], Should we Expect Population Thresholds for Wildlife Disease? Trends Ecol. Evol. 20, 511-519.
108. J.O. Lloyd-Smith, D. George, K.M. Pepin, V.E. Pitzer, J.R.C. Pulliam, A.P. Dobson, P.J. Hudson, and B.T. Grenfell 2009], Epidemic Dynamics at the Human-Animal Interface, Science 326, 1362-1367.
109. J.O. Lloyd-Smith, S.J. Schreiber, P.E. Kopp, and W.M. Getz 2005], Superspreading and the Effect of Individual Variation on Disease Emergence, Nature 438, 355-359.
110. N.A. Maidana and H.M. Yang 2009], Spatial Spreading of West Nile Virus Described by Traveling Waves, J. Theor. Biol. 258, 403-417.
111. G.I. Marchuk 1997], Mathematical Modelling of Immune Response in Infectious Diseases, Kluwer Academic Publishers, Dordrecht, The Netherlands.
112. A. Más, C. López-Galíndez, I. Cacho, J. Gómez, and M.A. Martínez 2010], Unfinished Stories on Viral Quasispecies and Darwinian Views of Evolution, J. Mol. Biol. 397, 865-877.
113. R.M. May and M.A. Nowak 1994], Superinfection, Metapopulation Dynamics and the Evolution of Virulence, J. Theor. Biol. 170, 95-114.
114. R.M. May and M.A. Nowak 1995], Coinfection and the Evolution of Parasite Virulence, Proc. R. Soc. Lond. B 261, 209-215.
115. D. Mayberry, A. Woolnough, L. Twigg, G. Martin, T. Lowe, and S. McLeod 2010], Preliminary Investigations for Measuring Animal Contact Rates, Final Report, Department of Agriculture, Fisheries and Forestry, Wildlife Exotic Disease Preparedness Program, Canberra, Western Australia.
116. H. McCallum, N. Barlow, and J. Hone 2001], How Should Pathogen Transmission be Modelled? Trends Ecol. & Evol. 16, 295-300.
117. R.K. McCormack and L.J.S. Allen 2007], Disease Emergence in Multi-Host Epidemic Models, Math. Med. Biol. 24, 17-34.
118. N. Mideo, S. Alizon, and T. Day [2008], Linking Within- and Between-Host Dynamics in the Evolutionary Epidemiology of Infectious Diseases, Trends Ecol. & Evol. 23, 511-517.
119. J. Mosquera and F.R. Adler 1998], Evolution of Virulence: A Unified Framework for Coinfection and Superinfection, J. Theor. Biol. 195, 293-313.
120. R.M. Nisbet and W.S.C. Gurney 1982], Modelling Fluctuating Populations, John Wiley & Sons, Chichester, New York.
121. K. Murphy, P. Travers, and M. Walport 2008], Janeway's Immunobiology, 7th Ed. Garland Science, New York.
122. J.D. Murray 1993], Mathematical Biology, 2nd Ed., Springer, Berlin.
123. J.D. Murray and W.L. Seward 1992], On the Spatial Spread of Rabies Among Foxes with Immunity, J. Theor. Biol. 156, 327-348.
124. J.D. Murray, E.A. Stanley, and D.L. Brown 1986], On the Spatial Spread of Rabies Among Foxes, Proc. Roy. Soc. Lond. B 229, 111-150.
125. M.A. Nowak and R.M. May 1994], Superinfection and the Evolution of Parasite Virulence, Proc. R. Soc. Lond. B 255, 81-89.
126. M.A. Nowak and R.M. May 2000], Virus Dynamics, Oxford University Press, New York.
127. M.A. Nowak and K. Sigmund 2002], Super- and Coinfection: The Two Extremes, in (U. Dieckmann, J.A.J. Metz, M.W. Sabelis, and K. Sigmund, eds.) Adaptive Dynamics of Infectious Diseases: In Pursuit of Virulence Management. Cambridge University Press, Cambridge, UK, pp. 124-137.
128. J.C. Owen and F.R. Moore 2006], Seasonal Differences in Immunological Condition of Three Species of Thrushes, Condor 108, 390-399.
129. J.C. Owen and F.R. Moore 2008], Swainson's Thrushes in Migratory Disposition Exhibit Reduced Immune Function, J. Ethol. 26, 383-388.
130. J.C. Owen, F.R. Moore, N. Panella, E. Edwards, R. Bru, M. Hughes, and N. Komar 2006], Migrating Birds as Dispersal Vehicles of West Nile Virus, EcoHealth 79-85.
131. C.R. Parrish, E.C. Holmes, D.M. Morens, E. Park, D.S. Burk, and C.H. Calisher 2008], Cross-Species Virus Transmission and the Emergence of New Epidemic Diseases, Micro. Mol. Biol. Rev. 72, 457-470.
132. A.B. Pedersen and T.J. Davies 2009], Cross-Species Pathogen Transmission and Disease Emergence in Primates, EcoHealth 496-508.
133. A.B. Pedersen and A. Fenton 2007], Emphasizing the Ecology in Parasite Community Ecology, Trends Ecol. Evol. 22, 133-139.
134. N.C. Pedersen, G. Theilen, M.A. Keane, L. Fairbanks, T. Mason, B. Orser, C.H. Chen, and C. Allison 1977 Studies of Naturally Transmitted Feline Leukemia Virus Infection, Am. J. Vet. Res. 38, 1523-1531.
135. A.S. Perelson 2002], Modelling Viral and Immune System Dynamics, Nat. Rev. 28-36.
136. A.S. Perelson and P.W. Nelson 1999], Mathematical Analysis of HIV-1 Dynamics In Vivo, SIAM Rev. 41, 3-44.
137. A. Pretorius, M.J. Oelofsen, M.S. Smith, and E. van der Ryst 1997], Rift Valley Fever Virus: A Seroepidemiologic Study of Small Terrestrial Vertebrates in South Africa, Am. J Trop. Med. Hyg. 57, 693-698.
138. M.A. Previtali, E.M. Lehmer, J.M.C. Pearce-Duvet, J.D. Jones, C.A. Clay, B.A. Wood, P.W. Ely, S.M. Laverty, and M.D. Dearing 2010], Investigating the Roles of Human Disturbance, Precipitation, and a Pathogen on the Survival and Reproductive Probabilities of Deer Mice (Peromyscus maniculatus), Ecology 91, 582-592.
139. A. Pugliese 1990], Population Models for Diseases with No Recovery, J. Math. Biol. 28, 65-82.
140. A. Pugliese 1991], An S→E→I Epidemic Model with Varying Population Size, Differential Equation Models in Biology, Epidemiology and Ecology, pp. 121-138, S. Busenberg and M. Martelli (Eds.) Springer-Verlag, New York.
141. A. Pugliese 2002], On the Evolutionary Coexistence of Parasite strains, Math. Biosci. 177-178, 355-375.
142. A. Pugliese and A. Gandolfi 2008], A Simple Model of Pathogen Immune Dynamics Including Specific and Non-Specific Immunity, Math. Biosci. 214, 73-80.
143. J.R.C. Pulliam 2008], Viral Host Jumps: Moving Toward a Predictive Framework, EcoHealth 80-91.
144. M.G. Roberts and J.A.P. Heesterbeek 2003], A New Method to Estimate the Effort Required to Control an Infectious Disease, Proc. Roy. Soc. Lond. B 270, 1359-1364.
145. B. Roche, C. Lebarbenchon, M. Gauthier-Clerc, C.-M. Chang, F. Thomas, F. Renaud, S. van der Werf, and J.-F. Guégan 2009], Water-Borne Transmission Drives Avian Influenza Dynamics in Wild Birds: The Case of the 2005--2006 Epidemics in the Camargue Area, Inf. Gen. Evol. 800-805.
146. S. Ruan and J. Wu 2009], Chapter 15: Modeling Spatial Spread of Communicable Diseases Involving Animal Hosts, (S. Cantrell, C. Cosner, and S. Ruan, eds.) Spatial Ecology, CRC Press/Chapman & Hall, Boca Raton, FL, pp. 293-316.
147. F. Sauvage, M. Langlais, and D. Pontier 2007], Predicting the Emergence of Human Hantavirus Disease Using a Combination of Viral Dynamics and Rodent Demographic Patterns, Epidemiol. Infect. 135, 46-56.
148. F. Sauvage, M. Langlais, N.G. Yoccoz, and D. Pontier 2003], Modelling Hantavirus in Fluctuating Populations of Bank Voles: The Role of Indirect Transmission on Virus Persistence, J. Anim. Ecol. 72, 1-13.
149. K.A. Schmidt and R.S. Ostfeld 2001], Biodiversity and the Dilution Effect in Disease Ecology, Ecology 82, 609-619.
150. G. Schönrich, A. Rang, N. Lütteke, M.J. Rafferty, N. Charbonnel, and R.G. Ulrich 2008], Hantavirus Induced Immunity in Rodent Reservoirs and Humans, Immun. Rev. 225, 163-189.
151. G.B. Sharp, Y. Kawaoka, D.J. Jones, W.J. Bean, S.P. Pryor, V. Hinshaw, and R.G. Webster 1997], Coinfection of Wild Ducks by Influenza A Viruses: Distribution Patterns and Biological Significance, J. Virol. 71, 6128.
152. G.C. Smith and C.L. Cheeseman 2002], Mathematical Model for the Control of Diseases in Wildlife Populations: Culling, Vaccination, and Fertility Control, Ecol. Modelling 150, 45-53.
153. D.E. Stallknecht 2007], Impediments to Wildlife Disease Surveilance, Research, and Diagnostics, Curr. Top. Microbiol. Immunol. 315, 445-461.
154. E.K. Steinberg and P. Kareiva 1997], Chapter 14: Challenges and Opportunities for Empirical Evaluation of "Spatial Theory", Spatial Ecology, The Role of Space in Population Dynamics and Interspecific Interactions, pp. 318-332, D. Tilman and P. Kareiva (Eds.) Princeton Univ. Press, Princeton, N.J.
155. D.L. Suarez, D.A. Senne, J. Banks, I.H. Brown, S.C. Essen, C.-W. Lee, R.J. Manvell, C. Mathieu-Benson, V. Moreno, J.C. Pedersen, B. Panigrahy, H. Rojas, E. Spackman, and D.J. Alexander 2004], Recombination Resulting in Virulence Shift in Avian Influenza Outbreak, Chile, Emerg. Inf. Dis. 20, 693-699.
156. J.P. Swaddle and S.E. Calos 2008], Increased Avian Diversity is Associated with Lower Incidence of Human West Nile Virus Infection: Observation of the Dilution Effect, PLoS ONE 3(6), e2488, 1-8.
157. J. Swinton, J. Harwood, B.T. Grenfell, and C.A. Gilligan 1998], Persistence Thresholds for Phocine Distemper Virus Infection in Harbour Sea Phoca Vitulina Metapopulations, J. Anim. Ecol. 67, 54-68.
158. Ch. Suppo, J.M. Nauln, M. Langlais, and M. Artois 2000], A Modelling Approach to Vaccination and Contraception Programmes for Rabies Control in Fox Populations, Proc. Roy. Soc. Lond. B 267, 1575-1582.
159. L.H. Taylor, S.M. Latham, and W.E. Woolhouse 2001], Risk Factors for Human Disease Emergence, Philos. Trans. Roy. Soc. Lond. B 356, 983-989.
160. S. Telfer, R. Birtles, M. Bennett, X. Lambin, S. Paterson, and M. Begon 2008], Parasite Interactions in Natural Populations: Insights from Longitudinal Data, Parasitology 135, 767-781.
161. S. Telfer, X. Lambin, R. Birtles, P. Beldomenico, S. Burthe, S. Paterson, and M. Begon 2010], Species Interactions in a Parasite Community Drie Infection Risk in a Wildlife Population, Science 330, 243-246.
162. H.R. Thieme 1992], Epidemic and Demographic Interaction in the Spread of Potentially Fatal Diseases in Growing Populations, Math. Biosci. 111, 99-130.
163. D. Tilman and P. Kareiva (Eds.), [1997], Spatial Ecology, The Role of Space in Population Dynamics and Interspecific Interactions, Princeton Univ. Press, Princeton, N.J.
164. H.C. Tuckwell and E. Le Corfec 1998], A Stochastic Model for Early HIV-1 Population Dynamics, J. Theor. Biol. 195, 451-463.
165. P. van den Driessche and J. Watmough 2002], Reproduction Numbers and Subthreshold Endemic Equilibria for Compartment Models of Disease Transmission, Math. Biosci. 180, 29-48.
166. P. van den Driessche and J. Watmough 2008], Further Notes on the Basic Reproduction Number, (F. Brauer, P. van den Driessche, and J. Wu, eds.) Mathematical Epidemiology, Lecture Notes in Mathematics, Springer-Verlag, Berlin, Heidelberg, pp. 159-178.
167. P. van den Driessche and M.L. Zeeman 2004], Disease Induced Oscillations between Two Competing Species, SIAM J. Appl. Dyn. Syst. 601-619.
168. J.A. van Gils, V.J. Munster, R. Radersma, D. Liefhebber, R.A. Fouchier, and M. Klaassen 2007], Hampered Foraging and Migratory Performance in Swans Infected with Low Pathogenic Avian Influenza A Virus, PLoS ONE 2(1) e184, 1-6.
169. W. Wang and X.-Q. Zhao 2008], Threshold Dynamics for Compartmental Epidemic Models in Periodic Environments, J. Dyn. Diff. Eqns. 20, 699-717.
170. E.J. Watts, S.C.F. Palmer, A.S. Bowman, R.J. Irvine, A. Smith, and J.M.J. Travis 2009], The Effect of Host Movement on Viral Transmission Dynamics in a Vector-Borne Disease System, Parasitology 136, 1221-1234.
171. C.L. Wesley, L.J.S. Allen, and M. Langlais 2010], Models for the Spread and Persistence of Hantavirus Infection in Rodents with Direct and Indirect Transmission, Math. Biosci. Eng. 195-211.
172. T.P. Weber and N.I. Stilianakis 2007], Ecological Immunology of Avian Influenza in Migratory Birds, Emerg. Inf. Dis. 13, 1139-1143.
173. D. Wodarz 2007], Killer Cell Dynamics: Mathematical and Computational Approaches to Immunology, Interdisciplinary Applied Mathematics, 32, Springer, New York.
174. C. Wolf, M. Langlais, F. Sauvage, and D. Pontier 2006], A Multi-patch Epidemic Model with Periodic Demography, Direct and Indirect Transmission and Variable Maturation Rate, Math. Pop. Studies 13, 153-177.
175. N.D. Wolfe, P. Daszak, A.M. Kilpatrick, and D.S. Burke 2005], Bushmeat Hunting, Deforestation, and Prediction of Zoonotic Disease Emergence, Emerg. Inf. Dis. 11, 1822-1827.
176. M.J. Wonham, M.A. Lewis, J. Renclawowicz, and P. van den Driessche 2006], Transmission Assumptions Generate Conflicting Predictions in Host-Vector Models: A Case Study in West Nile Virus, Ecol. Lett. 706-725.
177. M.E.J. Woolhouse, C. Dye, J.-F. Etard, T. Smith, J.D. Charlwood, G.P. Garnett, P. Hagan, J.L. Hii, P.D. Ndhlovu, R.J. Quinnell, C.H. Watts, S.K. Chandiwana, and R.M. Anderson 1997], Heterogeneities in the Transmission of Infectious Agents: Implications for the Design Of Control Programs, Proc. Nat. Acad. Sci. 94, 338-342.
178. M.E.J. Woolhouse, L.H. Taylor, and D.T. Haydon 2001], Population Biology of Multi-Host Pathogens, Science 292, 1109-1112.
179. Y. Yuan and L.J.S. Allen 2011], Stochastic Models for Virus and Immune System Dynamics, Math. Biosci., in press.
180. J. Zhou and H.W. Hethcote 1994], Population Size Dependent Incidence in Models for Diseases Without Immunity, J. Math. Biol. 32, 809-834.