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A division-dependent compartmental model for computing cell numbers in CFSE-based lymphocyte proliferation assays
Bacteriophage-resistant and bacteriophage-sensitive bacteria in a chemostat
1. | School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, United States |
2. | School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287-1804, United States |
References:
[1] |
E. Beretta and Y. Kuang, Modeling and analysis of a marine bacteriophage infection,, Mathematical Biosciences, 149 (1998), 57.
doi: 10.1016/S0025-5564(97)10015-3. |
[2] |
E. Beretta, H. Sakakibara and Y. Takeuchi, Analysis of a chemostat model for bacteria and bacteriophage,, Vietnam Journal of Mathematics, 30 (2002), 459.
|
[3] |
E. Beretta, H. Sakakibara and Y. Takeuchi, Stability analysis of time delayed chemostat models for bacteria and virulent phage,, Dynamical Systems and their Applications in Biology, 36 (2003), 45.
|
[4] |
E. Beretta, F. Solimano and Y. Tang, Analysis of a chemostat model for bacteria and virulent bacteriophage,, Discrete and Continuous Dynamical Systems B, 2 (2002), 495.
|
[5] |
B. Bohannan and R. Lenski, Effect of resource enrichment on a chemostat community of bacteria and bacteriophage,, Ecology, 78 (1997), 2303. Google Scholar |
[6] |
B. Bohannan and R. Lenski, Linking genetic change to community evolution: insights from studies of bacteria and bacteriophage,, Ecology Letters, 3 (2000), 362. Google Scholar |
[7] |
A. Campbell, Conditions for existence of bacteriophages,, Evolution, 15 (1961), 153.
doi: 10.2307/2406076. |
[8] |
L. Chao, B. Levin and F. Stewart, A complex community in a simple habitat: an experimental study with bacteria and phage,, Ecology, 58 (1977), 369.
doi: 10.2307/1935611. |
[9] |
E. Ellis and M. Delbrück, The growth of bacteriophage,, The Journal of General Physiology, 22 (1939), 365.
doi: 10.1085/jgp.22.3.365. |
[10] |
G. Folland, "Real Analysis: Modern Techniques and Their Applications,'' $2^{nd}$ edition,, Wiley, (1999).
|
[11] |
J. Hale and J. Kato, Phase space for retarded equations with infinite delay,, Funkcialaj Ekvacioj, 21 (1978), 11.
|
[12] |
J. Hale and S. Verduyn Lunel, "Introduction to Functional Differential Equations,", Springer-Verlag, (1993).
|
[13] |
Y. Hino, S. Murakami and T. Naito, "Functional Differential Equations with Infinite Delay,", Springer-Verlag, (1991).
|
[14] |
Y. Kuang, "Delay Differential Equations with Applications in Population Dynamics,", Academic Press, (1993).
|
[15] |
R. Lenski and B. Levin, Constraints on the coevolution of bacteria and virulent phage: A model, some experiments, and predictions for natural communities,, American Naturalist, 125 (1985), 585.
doi: 10.1086/284364. |
[16] |
B. Levin, F. Stewart and L. Chao, Resource-limited growth, competition, and predation: a model, and experimental studies with bacteria and bacteriophage,, American Naturalist, 111 (1977), 3. Google Scholar |
[17] |
K. Northcott, M. Imran and G. Wolkowicz, Composition in the presence of a virus in an aquatic system: an SIS model in a chemostat,, Journal of Mathematics Biology, 64 (2012), 1043.
doi: 10.1007/s00285-011-0439-z. |
[18] |
W. Ruess and W. Summers, Linearized stability for abstract differential equations with delay,, Journal of Mathematical Analysis and Applications, 198 (1996), 310.
doi: 10.1006/jmaa.1996.0085. |
[19] |
S. Schrag and J. Mittler, Host-parasite coexistence: The role of spatial refuges in stabilizing bacteria-phage interactions,, American Naturalist, 148 (1996), 348.
doi: 10.1086/285929. |
[20] |
H. Smith, "An introduction to Delay Differential Equations with Applications to the Life Sciences,", Springer-Verlag, (2010).
|
[21] |
H. Smith and H. Thieme, "Dynamical Systems and Population Persistence,", American Mathematical Society, (2010).
|
[22] |
H. Smith and H. Thieme, Persistence of bacteria and phages in a chemostat,, Journal of Mathematical Biology, 64 (2012), 951.
doi: 10.1007/s00285-011-0434-4. |
[23] |
H. Smith and P. Waltman, Perturbation of a globally stable steady state,, Proceeding of the American Mathematical Society, 127 (1999), 447.
doi: 10.1090/S0002-9939-99-04768-1. |
[24] |
H. Smith and P. Waltman, "The Theory of the Chemostat: Dynamics of Microbial Competition,", Cambridge University Press, (1995).
|
[25] |
H. Smith and X. Q. Zhao, Robust persistence for semidynamical systems,, Nonlinear Analysis Theory Methods Applications, 47 (2001), 6169.
doi: 10.1016/S0362-546X(01)00678-2. |
[26] |
H. Thieme, Convergence results and a poincaré-bendixson trichotomy for asymptotically autonomous differential equations,, Journal of Mathematical Biology, 30 (1992), 755.
|
[27] |
H. Thieme, "Mathematics in Population Biology,", Princeton University Press, (2003).
|
[28] |
J. Weitz, H. Hartman and S. Levin, Coevolutionary arms race between bacteria and bacteriophage,, Proceedings of the National Academy of Sciences of the United States of America, 102 (2005), 9535.
doi: 10.1073/pnas.0504062102. |
show all references
References:
[1] |
E. Beretta and Y. Kuang, Modeling and analysis of a marine bacteriophage infection,, Mathematical Biosciences, 149 (1998), 57.
doi: 10.1016/S0025-5564(97)10015-3. |
[2] |
E. Beretta, H. Sakakibara and Y. Takeuchi, Analysis of a chemostat model for bacteria and bacteriophage,, Vietnam Journal of Mathematics, 30 (2002), 459.
|
[3] |
E. Beretta, H. Sakakibara and Y. Takeuchi, Stability analysis of time delayed chemostat models for bacteria and virulent phage,, Dynamical Systems and their Applications in Biology, 36 (2003), 45.
|
[4] |
E. Beretta, F. Solimano and Y. Tang, Analysis of a chemostat model for bacteria and virulent bacteriophage,, Discrete and Continuous Dynamical Systems B, 2 (2002), 495.
|
[5] |
B. Bohannan and R. Lenski, Effect of resource enrichment on a chemostat community of bacteria and bacteriophage,, Ecology, 78 (1997), 2303. Google Scholar |
[6] |
B. Bohannan and R. Lenski, Linking genetic change to community evolution: insights from studies of bacteria and bacteriophage,, Ecology Letters, 3 (2000), 362. Google Scholar |
[7] |
A. Campbell, Conditions for existence of bacteriophages,, Evolution, 15 (1961), 153.
doi: 10.2307/2406076. |
[8] |
L. Chao, B. Levin and F. Stewart, A complex community in a simple habitat: an experimental study with bacteria and phage,, Ecology, 58 (1977), 369.
doi: 10.2307/1935611. |
[9] |
E. Ellis and M. Delbrück, The growth of bacteriophage,, The Journal of General Physiology, 22 (1939), 365.
doi: 10.1085/jgp.22.3.365. |
[10] |
G. Folland, "Real Analysis: Modern Techniques and Their Applications,'' $2^{nd}$ edition,, Wiley, (1999).
|
[11] |
J. Hale and J. Kato, Phase space for retarded equations with infinite delay,, Funkcialaj Ekvacioj, 21 (1978), 11.
|
[12] |
J. Hale and S. Verduyn Lunel, "Introduction to Functional Differential Equations,", Springer-Verlag, (1993).
|
[13] |
Y. Hino, S. Murakami and T. Naito, "Functional Differential Equations with Infinite Delay,", Springer-Verlag, (1991).
|
[14] |
Y. Kuang, "Delay Differential Equations with Applications in Population Dynamics,", Academic Press, (1993).
|
[15] |
R. Lenski and B. Levin, Constraints on the coevolution of bacteria and virulent phage: A model, some experiments, and predictions for natural communities,, American Naturalist, 125 (1985), 585.
doi: 10.1086/284364. |
[16] |
B. Levin, F. Stewart and L. Chao, Resource-limited growth, competition, and predation: a model, and experimental studies with bacteria and bacteriophage,, American Naturalist, 111 (1977), 3. Google Scholar |
[17] |
K. Northcott, M. Imran and G. Wolkowicz, Composition in the presence of a virus in an aquatic system: an SIS model in a chemostat,, Journal of Mathematics Biology, 64 (2012), 1043.
doi: 10.1007/s00285-011-0439-z. |
[18] |
W. Ruess and W. Summers, Linearized stability for abstract differential equations with delay,, Journal of Mathematical Analysis and Applications, 198 (1996), 310.
doi: 10.1006/jmaa.1996.0085. |
[19] |
S. Schrag and J. Mittler, Host-parasite coexistence: The role of spatial refuges in stabilizing bacteria-phage interactions,, American Naturalist, 148 (1996), 348.
doi: 10.1086/285929. |
[20] |
H. Smith, "An introduction to Delay Differential Equations with Applications to the Life Sciences,", Springer-Verlag, (2010).
|
[21] |
H. Smith and H. Thieme, "Dynamical Systems and Population Persistence,", American Mathematical Society, (2010).
|
[22] |
H. Smith and H. Thieme, Persistence of bacteria and phages in a chemostat,, Journal of Mathematical Biology, 64 (2012), 951.
doi: 10.1007/s00285-011-0434-4. |
[23] |
H. Smith and P. Waltman, Perturbation of a globally stable steady state,, Proceeding of the American Mathematical Society, 127 (1999), 447.
doi: 10.1090/S0002-9939-99-04768-1. |
[24] |
H. Smith and P. Waltman, "The Theory of the Chemostat: Dynamics of Microbial Competition,", Cambridge University Press, (1995).
|
[25] |
H. Smith and X. Q. Zhao, Robust persistence for semidynamical systems,, Nonlinear Analysis Theory Methods Applications, 47 (2001), 6169.
doi: 10.1016/S0362-546X(01)00678-2. |
[26] |
H. Thieme, Convergence results and a poincaré-bendixson trichotomy for asymptotically autonomous differential equations,, Journal of Mathematical Biology, 30 (1992), 755.
|
[27] |
H. Thieme, "Mathematics in Population Biology,", Princeton University Press, (2003).
|
[28] |
J. Weitz, H. Hartman and S. Levin, Coevolutionary arms race between bacteria and bacteriophage,, Proceedings of the National Academy of Sciences of the United States of America, 102 (2005), 9535.
doi: 10.1073/pnas.0504062102. |
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