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Novel dynamics of a simple Daphnia-microparasite model with dose-dependent infection
1. | Department of Mathematics, College of Medicine, Third Military Medical University, Chongqing, 400038 |
2. | School of Mathematics and Statistical Sciences, Arizona State University, Tempe, AZ 85281 |
References:
[1] |
R. M. Anderson and R. M. May, Population biology of infectious diseases I, Nature (London), 280 (1979), 361-367.
doi: 10.1038/280361a0. |
[2] |
R. M. Anderson and R. M. May, The population dynamics of microparasites and their invertebrate hosts, Phil. Tran. R. Soc. Lond. B, 291 (1981), 451-524.
doi: 10.1098/rstb.1981.0005. |
[3] |
D. Ebert, Infectivity, multiple infections, and the genetic correlation between withinhost growth and parasite virulence: A reply to Hochberg, Evolution, 52 (1998), 1869-1871.
doi: 10.2307/2411360. |
[4] |
D. Ebert, "Ecology, Epidemiology, and Evolution of Parasitism in Daphnia," [Internet]. Bethesda (MD): National Library of Medicine (US), National Center for Biotechnology Information. Available from: http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=Books, 2005. |
[5] |
D. Ebert, M. Lipsitch and K. L. Mangin, The effect of parasites on host population density and extinction: Experimental epidemiology with Daphnia and six microparasites, Am. Nat., 156 (2000), 459-477.
doi: 10.1086/303404. |
[6] |
D. Ebert, C. D. Zschokke-Rohringer and H. J. Carius, Dose effects and density-dependent regulation of two microparasites of Daphnia magna, Oecologia, 122 (2000), 200-209.
doi: 10.1007/PL00008847. |
[7] |
J. Guckenheimer and P. Holmes, "Nonlinear Oscillation, Dynamixal Systems and Bifurcations of Vector Fields," Springer-Verlag. 1983. |
[8] |
T. W. Hwang and Y. Kuang, Deterministic extinction effect of parasites on host populations, J. Math. Biol., 46 (2003), 17-30.
doi: 10.1007/s00285-002-0165-7. |
[9] |
T. W. Hwang and Y. Kuang, Host extinction dynamics in a simple parasite-host interaction model, Math. Biosci. Eng., 2 (2005), 743-751. |
[10] |
A. Korobeinikov, Global properties of basic virus dynamics models, Bull. Math. Biol., 66 (2004), 879-883.
doi: 10.1016/j.bulm.2004.02.001. |
[11] |
W. M. Liu, S. A. Levin and Y. Iwasa, Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models, J. Math. Biol., 23 (1986), 187-204.
doi: 10.1007/BF00276956. |
[12] |
L. Perko, "Differential Equations and Dynamical Systems," Springer, New York, 1996. |
[13] |
R. R. Regoes, D. Ebert and S. Bonhoeffer, Dose-dependent infection rates of parasites produce the Allee effect in epidemiology, Proc. R. Soc. Lond. B, 269 (2002), 271-279.
doi: 10.1098/rspb.2001.1816. |
[14] |
S. Ruan and W. Wang, Dynamical behavior of an epidemic model with a nonlinear incidence rate, J. Differential Equations, 188 (2003), 135-163.
doi: 10.1016/S0022-0396(02)00089-X. |
[15] |
P. van den Driessche and J. Watmough, Reproduction numbers and subthreshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29-48.
doi: 10.1016/S0025-5564(02)00108-6. |
[16] |
H. Wang, K. Dunning, J. J. Elser and Y. Kuang, Daphnia species invasion, competitive exclusion, and chaotic coexistence, Discrete Continuous Dynam. Systems - B, 12 (2009), 481-493. |
[17] |
D. Xiao and S. Ruan, Global analysis of an epidemic model with nonmonotone incidence rate, Math. Biosci., 208 (2007), 419-429.
doi: 10.1016/j.mbs.2006.09.025. |
[18] |
Y. Yu, J.J. Nieto, A. Torres and K. Wang, A viral infection model with a nonlinear infection rate, Bound. Value Probl., (2009), doi:10.1155/2009/958016. |
show all references
References:
[1] |
R. M. Anderson and R. M. May, Population biology of infectious diseases I, Nature (London), 280 (1979), 361-367.
doi: 10.1038/280361a0. |
[2] |
R. M. Anderson and R. M. May, The population dynamics of microparasites and their invertebrate hosts, Phil. Tran. R. Soc. Lond. B, 291 (1981), 451-524.
doi: 10.1098/rstb.1981.0005. |
[3] |
D. Ebert, Infectivity, multiple infections, and the genetic correlation between withinhost growth and parasite virulence: A reply to Hochberg, Evolution, 52 (1998), 1869-1871.
doi: 10.2307/2411360. |
[4] |
D. Ebert, "Ecology, Epidemiology, and Evolution of Parasitism in Daphnia," [Internet]. Bethesda (MD): National Library of Medicine (US), National Center for Biotechnology Information. Available from: http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=Books, 2005. |
[5] |
D. Ebert, M. Lipsitch and K. L. Mangin, The effect of parasites on host population density and extinction: Experimental epidemiology with Daphnia and six microparasites, Am. Nat., 156 (2000), 459-477.
doi: 10.1086/303404. |
[6] |
D. Ebert, C. D. Zschokke-Rohringer and H. J. Carius, Dose effects and density-dependent regulation of two microparasites of Daphnia magna, Oecologia, 122 (2000), 200-209.
doi: 10.1007/PL00008847. |
[7] |
J. Guckenheimer and P. Holmes, "Nonlinear Oscillation, Dynamixal Systems and Bifurcations of Vector Fields," Springer-Verlag. 1983. |
[8] |
T. W. Hwang and Y. Kuang, Deterministic extinction effect of parasites on host populations, J. Math. Biol., 46 (2003), 17-30.
doi: 10.1007/s00285-002-0165-7. |
[9] |
T. W. Hwang and Y. Kuang, Host extinction dynamics in a simple parasite-host interaction model, Math. Biosci. Eng., 2 (2005), 743-751. |
[10] |
A. Korobeinikov, Global properties of basic virus dynamics models, Bull. Math. Biol., 66 (2004), 879-883.
doi: 10.1016/j.bulm.2004.02.001. |
[11] |
W. M. Liu, S. A. Levin and Y. Iwasa, Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models, J. Math. Biol., 23 (1986), 187-204.
doi: 10.1007/BF00276956. |
[12] |
L. Perko, "Differential Equations and Dynamical Systems," Springer, New York, 1996. |
[13] |
R. R. Regoes, D. Ebert and S. Bonhoeffer, Dose-dependent infection rates of parasites produce the Allee effect in epidemiology, Proc. R. Soc. Lond. B, 269 (2002), 271-279.
doi: 10.1098/rspb.2001.1816. |
[14] |
S. Ruan and W. Wang, Dynamical behavior of an epidemic model with a nonlinear incidence rate, J. Differential Equations, 188 (2003), 135-163.
doi: 10.1016/S0022-0396(02)00089-X. |
[15] |
P. van den Driessche and J. Watmough, Reproduction numbers and subthreshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29-48.
doi: 10.1016/S0025-5564(02)00108-6. |
[16] |
H. Wang, K. Dunning, J. J. Elser and Y. Kuang, Daphnia species invasion, competitive exclusion, and chaotic coexistence, Discrete Continuous Dynam. Systems - B, 12 (2009), 481-493. |
[17] |
D. Xiao and S. Ruan, Global analysis of an epidemic model with nonmonotone incidence rate, Math. Biosci., 208 (2007), 419-429.
doi: 10.1016/j.mbs.2006.09.025. |
[18] |
Y. Yu, J.J. Nieto, A. Torres and K. Wang, A viral infection model with a nonlinear infection rate, Bound. Value Probl., (2009), doi:10.1155/2009/958016. |
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