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Dynamics of a predator-prey system with prey subject to Allee effects and disease
A continuous phenotype space model of RNA virus evolution within a host
1. | Centre de Recerca Matemàtica, Campus de Bellaterra, Edifici C, 08193 Bellaterra, Barcelona |
2. | Department of Neuroscience, Columbia University, 40 Haven Avenue, New York, NY 10032, United States |
References:
[1] |
R. M. Anderson and R. M. May, The population dynamics of microparasites and their invertebrate hosts, Philos. Trans. R. Soc. Lond. Ser. B, 291 (1981), 451-524.
doi: 10.1098/rstb.1981.0005. |
[2] |
V. Andreasen, Dynamics of annual influenza A epidemics with immuno-selection, J. Math. Biol., 46 (2003), 504-536.
doi: 10.1007/s00285-002-0186-2. |
[3] |
V. Andreasen, S. Levin and J. Lin, A model of influenza A drift evolution, Z. Angew. Math. Mech., 76 (1996), 421-424. |
[4] |
M. F. Boni, J. R. Gog, V. Andreasen and M. W. Feldman, Epidemic dynamics and antigenic evolution in a single season of influenza A, Proc. R. Soc. B, 273 (2006), 1307-1316.
doi: 10.1098/rspb.2006.3466. |
[5] |
V. Calvez, A. Korobeinikov and P. K. Maini, Cluster formation for multi-strain infections with cross-immunity, J. Theor. Biol., 233 (2005), 75-83.
doi: 10.1016/j.jtbi.2004.09.016. |
[6] |
J. R. Gog and B. T. Grenfell, Dynamics and selection of many-strain pathogens, Proc. Natl Acad. Sci. USA, 99 (2002), 17209-17214.
doi: 10.1073/pnas.252512799. |
[7] |
Y. Haraguchi and A. Sasaki, Evolutionary pattern of intra-host pathogen antigenic drift: Effect of crossreactivity in immune response, Phil. Trans. R. Soc. B, 352 (1997), 11-20.
doi: 10.1098/rstb.1997.0002. |
[8] |
T. Inoue, T. Kajiwara and T. Sasaki, Global stability of models of humoral immunity against multiple viral strains, Journal of Biological Dynamics, 4 (2010), 282-295.
doi: 10.1080/17513750903180275. |
[9] |
S. Iwami, T. Miura, S. Nakaoka and Y. Takeuchi, Immune impairment in HIV infection: Existence of risky and immunodeficiency thresholds, J. Theor. Biol., 260 (2009), 490-501.
doi: 10.1016/j.jtbi.2009.06.023. |
[10] |
Y. Iwasa, F. Michor and M. A. Nowak, Virus evolution within patients increases pathogenicity, J. Theor. Biol., 232 (2005), 17-26.
doi: 10.1016/j.jtbi.2004.07.016. |
[11] |
A. N. Kolmogorov, I. G. Petrovskii and N. S. Piskunov, A study of the equation of diffusion with increase in the quantity of matter, and its application to a biological problem. Byul. Moskovskogo Gos. Univ., 1 (1937), 1-25. also in Selected Works of A.N. Kolmogorov: Mathematics and Mechanics, Kluwer, Dordrecht, (1991), 1-25. |
[12] |
A. Korobeinikov, Global asymptotic properties of virus dynamics models with dose dependent parasite reproduction and virulence, and nonlinear incidence rate, Math. Med. Biol., 26 (2009), 225-239.
doi: 10.1093/imammb/dqp009. |
[13] |
A. Korobeinikov, Stability of ecosystem: Global properties of a general prey-predator model, Math. Med. Biol., 26 (2009), 309-321.
doi: 10.1093/imammb/dqp009. |
[14] |
J. Lin, V. Andreasen, R. Casagrandi and S. A. Levin, Traveling waves in a model of influenza A drift, J. Theor. Biol., 222 (2003), 437-445.
doi: 10.1016/S0022-5193(03)00056-0. |
[15] |
L. M. Mansky and H. M. Temin, Lower in vivo mutation rate of human immunodeficiency virus type 1 than that predicted from the fidelity of purified reverse transcriptase, Journal of Virology, 69 (1995), 5087-5094. |
[16] |
M. A. Nowak, R. M. Anderson, A. R. McLean, T. F. W. Wolfs, J. Goudsmit and R. M. May, Antigenic diversity threshold and the development of AIDS, Science, 254 (1991), 963-969.
doi: 10.1126/science.1683006. |
[17] |
M. A. Nowak and R. M. May, Virus Dynamics, Oxford University Press, 2000. |
[18] |
A. Rambaut, D. Posada, K. A. Crandall and E. C. Holmes, The causes and consequences of HIV evolution, Nature Reviews, 5 (2004), 52-61. http://tree.bio.ed.ac.uk/downloadPaper.php?id=242.
doi: 10.1038/nrg1246. |
[19] |
J. Saldaña, S. F. Elena and R. V. Solé, Coinfection and superinfection in RNA virus populations: A selection-mutation model, Math. Biosci., 183 (2003), 135-160.
doi: 10.1016/S0025-5564(03)00038-5. |
[20] |
A. Sasaki, Evolution of antigenic drift/switching: Continuously evading pathogens, J. Theor. Biol., 168 (1994), 291-308.
doi: 10.1006/jtbi.1994.1110. |
[21] |
A. Sasaki and Y. Haraguchi, Antigenic drift of viruses within a host: A finite site model with demographic stochasticity, J. Mol. Evol., 51 (2000), 245-255. |
[22] |
M. O. Souza and J. P. Zubelli, Global stability for a class of virus models with cytotoxic T lymphocyte immune response and antigenic variation, Bull. Math. Biol., 73 (2011), 609-625.
doi: 10.1007/s11538-010-9543-2. |
[23] |
M. A. Stafford et al., Modeling plasma virus concentration during primary HIV infection, J. Theor. Biol., 203 (2000), 285-301.
doi: 10.1006/jtbi.2000.1076. |
[24] |
L. S. Tsimring, H. Levine and D. A. Kessler, RNA virus evolution via a fitness-space model, Phys. Rev. Lett. 76 (1996), 4440-4443.
doi: 10.1103/PhysRevLett.76.4440. |
[25] |
C. Vargas-De-León and A. Korobeinikov, Global stability of a population dynamics model with inhibition and negative feedback, Math. Med. Biol., 30 (2013), 65-72.
doi: 10.1093/imammb/dqr027. |
[26] |
D. Wodarz, J. P. Christensen and A. R. Thomsen, The importance of lytic and nonlytic immune responses in viral infections, TRENDS in Immunology, 23 (2002), 194-200.
doi: 10.1016/S1471-4906(02)02189-0. |
[27] |
D. Wodarz, P. Klenerman and M. A. Nowak, Dynamics of cytotoxic T-lymphocyte exhaustion, Proc. R. Soc. Lond. B 265 (1998), 191-203.
doi: 10.1098/rspb.1998.0282. |
show all references
References:
[1] |
R. M. Anderson and R. M. May, The population dynamics of microparasites and their invertebrate hosts, Philos. Trans. R. Soc. Lond. Ser. B, 291 (1981), 451-524.
doi: 10.1098/rstb.1981.0005. |
[2] |
V. Andreasen, Dynamics of annual influenza A epidemics with immuno-selection, J. Math. Biol., 46 (2003), 504-536.
doi: 10.1007/s00285-002-0186-2. |
[3] |
V. Andreasen, S. Levin and J. Lin, A model of influenza A drift evolution, Z. Angew. Math. Mech., 76 (1996), 421-424. |
[4] |
M. F. Boni, J. R. Gog, V. Andreasen and M. W. Feldman, Epidemic dynamics and antigenic evolution in a single season of influenza A, Proc. R. Soc. B, 273 (2006), 1307-1316.
doi: 10.1098/rspb.2006.3466. |
[5] |
V. Calvez, A. Korobeinikov and P. K. Maini, Cluster formation for multi-strain infections with cross-immunity, J. Theor. Biol., 233 (2005), 75-83.
doi: 10.1016/j.jtbi.2004.09.016. |
[6] |
J. R. Gog and B. T. Grenfell, Dynamics and selection of many-strain pathogens, Proc. Natl Acad. Sci. USA, 99 (2002), 17209-17214.
doi: 10.1073/pnas.252512799. |
[7] |
Y. Haraguchi and A. Sasaki, Evolutionary pattern of intra-host pathogen antigenic drift: Effect of crossreactivity in immune response, Phil. Trans. R. Soc. B, 352 (1997), 11-20.
doi: 10.1098/rstb.1997.0002. |
[8] |
T. Inoue, T. Kajiwara and T. Sasaki, Global stability of models of humoral immunity against multiple viral strains, Journal of Biological Dynamics, 4 (2010), 282-295.
doi: 10.1080/17513750903180275. |
[9] |
S. Iwami, T. Miura, S. Nakaoka and Y. Takeuchi, Immune impairment in HIV infection: Existence of risky and immunodeficiency thresholds, J. Theor. Biol., 260 (2009), 490-501.
doi: 10.1016/j.jtbi.2009.06.023. |
[10] |
Y. Iwasa, F. Michor and M. A. Nowak, Virus evolution within patients increases pathogenicity, J. Theor. Biol., 232 (2005), 17-26.
doi: 10.1016/j.jtbi.2004.07.016. |
[11] |
A. N. Kolmogorov, I. G. Petrovskii and N. S. Piskunov, A study of the equation of diffusion with increase in the quantity of matter, and its application to a biological problem. Byul. Moskovskogo Gos. Univ., 1 (1937), 1-25. also in Selected Works of A.N. Kolmogorov: Mathematics and Mechanics, Kluwer, Dordrecht, (1991), 1-25. |
[12] |
A. Korobeinikov, Global asymptotic properties of virus dynamics models with dose dependent parasite reproduction and virulence, and nonlinear incidence rate, Math. Med. Biol., 26 (2009), 225-239.
doi: 10.1093/imammb/dqp009. |
[13] |
A. Korobeinikov, Stability of ecosystem: Global properties of a general prey-predator model, Math. Med. Biol., 26 (2009), 309-321.
doi: 10.1093/imammb/dqp009. |
[14] |
J. Lin, V. Andreasen, R. Casagrandi and S. A. Levin, Traveling waves in a model of influenza A drift, J. Theor. Biol., 222 (2003), 437-445.
doi: 10.1016/S0022-5193(03)00056-0. |
[15] |
L. M. Mansky and H. M. Temin, Lower in vivo mutation rate of human immunodeficiency virus type 1 than that predicted from the fidelity of purified reverse transcriptase, Journal of Virology, 69 (1995), 5087-5094. |
[16] |
M. A. Nowak, R. M. Anderson, A. R. McLean, T. F. W. Wolfs, J. Goudsmit and R. M. May, Antigenic diversity threshold and the development of AIDS, Science, 254 (1991), 963-969.
doi: 10.1126/science.1683006. |
[17] |
M. A. Nowak and R. M. May, Virus Dynamics, Oxford University Press, 2000. |
[18] |
A. Rambaut, D. Posada, K. A. Crandall and E. C. Holmes, The causes and consequences of HIV evolution, Nature Reviews, 5 (2004), 52-61. http://tree.bio.ed.ac.uk/downloadPaper.php?id=242.
doi: 10.1038/nrg1246. |
[19] |
J. Saldaña, S. F. Elena and R. V. Solé, Coinfection and superinfection in RNA virus populations: A selection-mutation model, Math. Biosci., 183 (2003), 135-160.
doi: 10.1016/S0025-5564(03)00038-5. |
[20] |
A. Sasaki, Evolution of antigenic drift/switching: Continuously evading pathogens, J. Theor. Biol., 168 (1994), 291-308.
doi: 10.1006/jtbi.1994.1110. |
[21] |
A. Sasaki and Y. Haraguchi, Antigenic drift of viruses within a host: A finite site model with demographic stochasticity, J. Mol. Evol., 51 (2000), 245-255. |
[22] |
M. O. Souza and J. P. Zubelli, Global stability for a class of virus models with cytotoxic T lymphocyte immune response and antigenic variation, Bull. Math. Biol., 73 (2011), 609-625.
doi: 10.1007/s11538-010-9543-2. |
[23] |
M. A. Stafford et al., Modeling plasma virus concentration during primary HIV infection, J. Theor. Biol., 203 (2000), 285-301.
doi: 10.1006/jtbi.2000.1076. |
[24] |
L. S. Tsimring, H. Levine and D. A. Kessler, RNA virus evolution via a fitness-space model, Phys. Rev. Lett. 76 (1996), 4440-4443.
doi: 10.1103/PhysRevLett.76.4440. |
[25] |
C. Vargas-De-León and A. Korobeinikov, Global stability of a population dynamics model with inhibition and negative feedback, Math. Med. Biol., 30 (2013), 65-72.
doi: 10.1093/imammb/dqr027. |
[26] |
D. Wodarz, J. P. Christensen and A. R. Thomsen, The importance of lytic and nonlytic immune responses in viral infections, TRENDS in Immunology, 23 (2002), 194-200.
doi: 10.1016/S1471-4906(02)02189-0. |
[27] |
D. Wodarz, P. Klenerman and M. A. Nowak, Dynamics of cytotoxic T-lymphocyte exhaustion, Proc. R. Soc. Lond. B 265 (1998), 191-203.
doi: 10.1098/rspb.1998.0282. |
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