Citation: |
[1] |
E. Allen, "Modeling With Itô Stochastic Differential Equations,'' Mathematical Modelling: Theory and Applications, 22, Springer, Dordrecht, The Netherlands, 2007. |
[2] |
E. J. Allen, L. J. S. Allen, A. Arciniega and P. Greenwood, Construction of equivalent stochastic differential equation models, Stoch. Anal. Appl., 26 (2008), 274-297. |
[3] |
L. J. S. Allen, "An Introduction to Mathematical Biology,'' Prentice Hall, Upper Saddle River, NJ, 2007. |
[4] |
L. J. S. Allen, "An Introduction to Stochastic Processes with Applications to Biology,'' 2nd edition, CRC Press, Boca Raton, FL, 2011. |
[5] |
L. J. S. Allen and N. Kirupaharan, Asymptotic dynamics of deterministic and stochastic epidemic models with multiple pathogens, Int. J. Numer. Anal. Modeling, 2 (2005), 329-344. |
[6] |
R. M. Anderson and R. M. May, The invasion, persistence and spread of infectious diseases with animal and plant communities, Phil. Trans. R. Soc. Lond. B, 314 (1986), 533-570.doi: 10.1098/rstb.1986.0072. |
[7] |
N. T. J. Bailey, "The Elements of Stochastic Processes with Applications to the Natural Sciences,'' Reprint of the 1964 original, Wiley Classics Library, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1990. |
[8] |
M. S. Bartlett, The relevance of stochastic models for large-scale epidemiological phenomena, Appl. Statist., 13 (1965), 2-8. |
[9] |
M. Begon, R. G. Bowers, N. Kadianakis and D. E. Hodgkinson, Disease and community structure: The importance of host self-regulation in a host-host-pathogen model, Am. Nat., 139 (1992), 1131-1150.doi: 10.1086/285379. |
[10] |
V. A. Bokil and M.-R. Leung, An analysis of the coexistence of three competing species with a shared pathogen, Technical Report ORST-MATH-11-02, Oregon State Univ., 2011. Citation URL: http://ir.library.oregonstate.edu/xmlui/handle/1957/13738/. |
[11] |
E. T. Borer, P. R. Hosseini, E. W. Seabloom and A. P. Dobson, Pathogen-induced reversal of native dominance in a grassland community, Proc. Natl. Acad. Sci. U. S. A., 104 (2007), 5473-5478. |
[12] |
R. G. Bowers and J. Turner, Community structure and the interplay between interspecific infection and competition, J. Theor. Biol., 187 (1997), 95-109.doi: 10.1006/jtbi.1997.0418. |
[13] |
S. K. Collinge and C. Ray, "Disease Ecology: Community Structure and Pathogen Dynamics," Oxford Univ. Press, Oxford, 2006. |
[14] |
A. Dobson, Population dynamics of pathogens with multiple host species, Am. Nat., 164 (2004), S64-S78.doi: 10.1086/424681. |
[15] |
R. Durrett, Mutual invadability implies coexistence in spatial models, Mem. Am. Math. Soc., 156 (2002), viii+118 pp. |
[16] |
R. Durrett, Special invited paper: Coexistence in stochastic spatial models, Ann. Appl. Probab., 19 (2009), 477-496.doi: 10.1214/08-AAP590. |
[17] |
R. Durrett and C. Neuhauser, Coexistence results for some competition models, Ann. Appl. Probab., 7 (1997), 10-45. |
[18] |
L. Gilbert, R. Norman, K. M. Laurenson, H. W. Reid and P. J. Hudson, Disease persistence and apparent competition in a three-host community: An empirical and analytical study of large-scale, wild populations, J. Anim. Ecol., 70 (2001), 1053-1061.doi: 10.1046/j.0021-8790.2001.00558.x. |
[19] |
D. T. Gillespie, "Markov Processes: An Introduction for Physical Scientists,'' Academic Press, Inc., Boston, MA, 1992. |
[20] |
J. V. Greenman and P. J. Hudson, Infected coexistence instability with and without density-dependent regulation, J. Theor. Biol., 185 (1997), 345-356.doi: 10.1006/jtbi.1996.0309. |
[21] |
M. Griffiths and D. Greenhalgh, The probability of extinction in a bovine respiratory syncytial virus epidemic model, Math. Biosci., 231 (2011), 144-158.doi: 10.1016/j.mbs.2011.02.011. |
[22] |
B. A. Han, "The Effects of an Emerging Pathogen on Amphibian Host Behaviors and Interactions," Ph.D thesis, Oregon State Univ., Corvallis, OR, 2009. |
[23] |
L. Han, Z. Ma and T. Shi, An SIRS epidemic model of two competitive species, Math. Comput. Model., 37 (2003), 87-108.doi: 10.1016/S0895-7177(03)80008-0. |
[24] |
L. Han and A. Pugliese, Epidemics in two competing species, Nonlinear Anal. Real World Appl., 10 (2009), 723-744.doi: 10.1016/j.nonrwa.2007.11.005. |
[25] |
T. E. Harris, "The Theory of Branching Processes,'' Die Grundlehren der Mathematischen Wissenschaften, Bd. 119, Springer-Verlag, Berlin, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1963. |
[26] |
M. J. Hatcher, J. T. A. Dick and A. M. Dunn, How parasites affect interactions between competitors and predators, Ecol. Lett., 9 (2006), 1253-1271.doi: 10.1111/j.1461-0248.2006.00964.x. |
[27] |
D. J. Higham, Modeling and simulating chemical reactions, SIAM Rev., 50 (2008), 347-368.doi: 10.1137/060666457. |
[28] |
R. D. Holt and A. P. Dobson, Chapter 2: Extending the principles of community ecology to address the epidemiology of host-pathogen systems, in "Disease Ecology: Community Structure and Pathogen Dynamics" (eds. S. K. Collinge and C. Ray), Oxford Univ. Press, Oxford, (2006), 2-27. |
[29] |
R. D. Holt and J. Pickering, Infectious disease and species coexistence: A model of Lotka-Volterra form, Am. Nat., 126 (1985), 196-211.doi: 10.1086/284409. |
[30] |
P. Hudson and J. Greenman, Competition mediated by parasites: Biological and theoretical progress, Trends Ecol. Evol., 13 (1998), 387-390. |
[31] |
P. Jagers, "Branching Processes with Biological Applications,'' Wiley Series in Probability and Mathematical Statistics Applied Probability and Statistics, Wiley-Interscience [John Wiley & Sons], London-New York-Sydney, 1975. |
[32] |
S. T. Karlin and H. M. Taylor, "A First Course in Stochastic Processes,'' 2nd edition, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1975. |
[33] |
J. M. Kiesecker and A. R. Blaustein, Pathogen reverses competition between larval amphibians, Ecology, 80 (1999), 2442-2448. |
[34] |
P. Kloeden and E. Platen, "Numerical Solution of Stochastic Differential Equations,'' Applications of Mathematics (New York), 23, Springer-Verlag, Berlin, 1992. |
[35] |
N. Lanchier and C. Neuhauser, A spatially explicit model for competition among specialists and generalists in a heterogeneous environment, Ann. Appl. Probab., 16 (2006), 1385-1410.doi: 10.1214/105051606000000394. |
[36] |
N. Lanchier and C. Neuhauser, Stochastic spatial models of host-pathogen and host-mutualist interactions. I, Ann. Appl. Probab., 16 (2006), 448-474.doi: 10.1214/105051605000000782. |
[37] |
C. A. Manore, "Non-Spatial and Spatial Models for Multi-Host Pathogen Spread in Competing Species: Applications to Barley Yellow Dwarf Virus and Rinderpest," Ph.D thesis, Oregon State Univ., Corvallis, OR, 2012. |
[38] |
R. M. May and W. J. Leonard, Nonlinear aspects of competition between three species, Special issue on mathematics and the social and biological sciences, SIAM J. Appl. Math., 29 (1975), 243-253.doi: 10.1137/0129022. |
[39] |
H. McCallum, N. Barlow and J. Hone, How should pathogen transmission be modelled?, Trends Ecol. Evol., 16 (2001), 295-300.doi: 10.1016/S0169-5347(01)02144-9. |
[40] |
R. K. McCormack, "Multi-Host Multi-Patch Mathematical Epidemic Models for Disease Emergence with Applications to Hantavirus in Wild Rodents," Ph.D thesis, Texas Tech Univ., Lubbock, TX, 2006. |
[41] |
R. K. McCormack and L. J. S. Allen, Stochastic SIS and SIR multihost epidemic models, in "Differential & Difference Eqns. Appl.," Hindawi Publ. Corp., New York, (2006), 775-785. |
[42] |
R. K. McCormack and L. J. S. Allen, Disease emergence in multi-host epidemic models, Math. Med. Biol., 24 (2007), 17-34.doi: 10.1093/imammb/dql021. |
[43] |
C. J. Mode, "Multitype Branching Processes. Theory and Applications,'' Modern Analytic and Computational Methods in Science and Mathematics, No. 34 , American Elsevier Publishing Co., Inc., New York, 1971. |
[44] |
S. M. Moore, C. A. Manore, V. A. Bokil, E. T. Borer and P. R. Hosseini, Spatiotemporal model of barley and cereal yellow dwarf virus transmission dynamics with seasonality and plant competition, Bull. Math. Biol., 73 (2011), 2707-2730. |
[45] |
C. Neuhauser and S. W. Pacala, An explicitly spatial version of the Lotka-Volterra model with interspecific competition, Ann. Appl. Probab., 9 (1999), 1226-1259. |
[46] |
R. Norman, R. G. Bowers, M. Begon and P. J. Hudson, Persistence of tick-borne virus in the presence of multiple host species: Tick reservoirs and parasite mediated competition, J. Theor. Biol., 200 (1999), 111-118.doi: 10.1006/jtbi.1999.0982. |
[47] |
J. M. Ortega, "Matrix Theory. A Second Course," The University Series in Mathematics, Plenum Press, New York, 1987. |
[48] |
S. Pénisson, "Conditional Limit Theorems for Multitype Branching Processes and Illustration in Epidemiological Risk Analysis," Ph.D thesis, Institut für Mathematik der Unversität Potsdam, Germany, 2010. |
[49] |
R. A. Saenz and H. W. Hethcote, Competing species models with an infectious disease, Math. Biosci. Eng., 3 (2006), 219-235. |
[50] |
D. M. Tompkins, R. A. H. Draycott and P. J. Hudson, Field evidence for apparent competition mediated via the shared parasites of two gamebird species, Ecol. Lett., 3 (2000), 10-14. |
[51] |
D. M. Tompkins, A. R. White and M. Boots, Ecological replacement of native red squirrels by invasive greys driven by disease, Ecol. Lett., 6 (2003), 189-196. |
[52] |
P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29-48. |
[53] |
P. van den Driessche and M. L. Zeeman, Disease induced oscillations between two competing species, SIAM J. Appl. Dyn. Sys., 3 (2004), 601-619. |
[54] |
E. Venturino, The effects of diseases on competing species, Math. Biosci., 174 (2001), 111-131.doi: 10.1016/S0025-5564(01)00081-5. |
[55] |
P. Whittle, The outcome of a stochastic epidemic: A note on Bailey's paper, Biometrika, 42 (1955), 116-122.doi: 10.2307/2333427. |
[56] |
E. C. Zeeman and M. L. Zeeman, From local to global behavior in competitive Lotka-Volterra systems, Trans. Am. Math. Soc., 355 (2003), 713-734.doi: 10.1090/S0002-9947-02-03103-3. |