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Bacteria--phagocyte dynamics, axiomatic modelling and mass-action kinetics
1. | Department of Computer Science and Applied Mathematics, The Weizmann Institute, Rehovot, 76100, Israel |
2. | The Estrin Family Chair of Computer Science and Applied Mathematics, Department of Computer Science and Applied Mathematics, The Weizmann Institute, Rehovot, 76100, Israel |
References:
[1] |
C. A. Janeway and R. Medzhitov, Innate immune recognition,, Annual Review of Immunology, 20 (2002), 197.
doi: 10.1146/annurev.immunol.20.083001.084359. |
[2] |
O. Soehnlein and L. Lindbom, Phagocyte partnership during the onset and resolution of inflammation,, Nature Reviews Immunology, 10 (2010), 427.
doi: 10.1038/nri2779. |
[3] |
C. Nathan, Neutrophils and immunity: Challenges and opportunities,, Nature Reviews Immunology, 6 (2006), 173.
doi: 10.1038/nri1785. |
[4] |
A. F. M. Marée, M. Komba, C. Dyck, M. Labecki, D. T. Finegood and L. Edelstein-Keshet, Quantifying macrophage defects in type 1 diabetes,, Journal of theoretical biology, 233 (2005), 533.
doi: 10.1016/j.jtbi.2004.10.030. |
[5] |
A. F. M. Maree, M. Komba, D. T. Finegood and L. Edelstein-Keshet, A quantitative comparison of rates of phagocytosis and digestion of apoptotic cells by macrophages from normal (BALB/c) and diabetes-prone (NOD) mice,, Journal of Applied Physiology, 104 (2008), 157.
doi: 10.1152/japplphysiol.00514.2007. |
[6] |
R. Malka, E. Shochat and V. Rom-Kedar, Bistability and bacterial infections,, PLoS ONE, 5 (2010).
doi: 10.1371/journal.pone.0010010. |
[7] |
Z. Rahman, L. Esparza-Guerra, H. Y. Yap, G. Fraschini, G. Bodey and G. Hortobagyi, Chemotherapy-induced neutropenia and fever in patients with metastatic breast carcinoma receiving salvage chemotherapy,, Cancer, 79 (1997), 1150.
doi: 10.1002/(SICI)1097-0142(19970315)79:6<1150::AID-CNCR13>3.0.CO;2-Z. |
[8] |
G. P. Bodey, M. Buckley, Y. S. Sathe and E. J. Freireich, Quantitative relationships between circulating leukocytes and infection in patients with acute leukemia,, Annals of Internal Medicine, 64 (1966), 328. Google Scholar |
[9] |
J. M. van den Berg, E. van Koppen, A. Åhlin, B. H. Belohradsky, E. Bernatowska, L. Corbeel, T. Español, A. Fischer, M. Kurenko-Deptuch, R. Mouy, T. Petropoulou, J. Roesler, R. Seger, M. J. Stasia, N. H. Valerius, R. S. Weening, B. Wolach, D. Roos and T. W. Kuijpers, Chronic granulomatous disease: The european experience,, PLoS ONE, 4 (2009).
doi: 10.1371/journal.pone.0005234. |
[10] |
A. Reynolds, J. Rubin, G. Clermont, J. Day, Y. Vodovotz and B. G. Ermentrout, A reduced mathematical model of acute inflammation response: I. derivation of model and analysis of anti-inflammation,, Journal of Theoretical Biology, 242 (2006), 220.
doi: 10.1016/j.jtbi.2006.02.016. |
[11] |
M. C. Herald, General model of inflammation,, Bulletin of Mathematical Biology, 72 (2010), 765.
doi: 10.1007/s11538-009-9468-9. |
[12] |
E. M. C. D'Agata, M. Dupont-Rouzeyrol, P. Magal, D. Olivier and S. Ruan, The impact of different antibiotic regimens on the emergence of antibiotic-resistant bacteria,, PLoS ONE, 3 (2008). Google Scholar |
[13] |
Y. Li, A. Karlin, D. J. Loike and C. S. Silverstein, A critical concentration of neutrophils is required for effective bacterial killing in suspension,, Proceedings of the National Academy of Sciences, 99 (2002), 8289.
doi: 10.1073/pnas.122244799. |
[14] |
Y. Li, A. Karlin, D. J. Loike and C. S. Silverstein, Determination of the critical concentration of neutrophils required to block bacterial growth in tissues,, The Journal of Experimental Medicine, 200 (2004), 613.
doi: 10.1084/jem.20040725. |
[15] |
E. Shochat and V. Rom-Kedar, Novel strategies for g-csf treatment of high-risk severe neutropenia suggested by mathematical modeling,, Clinical Cancer Research, 14 (2008), 6354.
doi: 10.1158/1078-0432.CCR-08-0807. |
[16] |
R. Arditi and L. R. Ginzburg, Coupling in predator-prey dynamics: Ratio-dependence,, Journal of Theoretical Biology, 139 (1989), 311.
doi: 10.1016/S0022-5193(89)80211-5. |
[17] |
A. D. Bazykin, F. S. Berezovskaya, G. A. Denisov and Y. A. Kuznetzov, The influence of predator saturation effect and competition among predators on predator-prey system dynamics,, Ecological Modelling, 14 (1981), 39.
doi: 10.1016/0304-3800(81)90013-2. |
[18] |
S. Ruan and D. Xiao, Global analysis in a predator-prey system with nonmonotonic functional response,, SIAM Journal of Applied Mathematics, 16 (2001), 1445.
|
[19] |
L. Edelstein-Keshet, J. Watmough and D. Grunbaum, Do travelling band solutions describe cohesive swarms? An investigation for migratory locusts,, Journal of Mathematical Biology, 36 (1998), 515.
doi: 10.1007/s002850050112. |
[20] |
Y. Mori, A. Jilkine and L. Edelstein-Keshet, Wave-pinning and cell polarity from a bistable reaction-diffusion system,, Biophysical Journal, 94 (2008), 3684.
doi: 10.1529/biophysj.107.120824. |
[21] |
M. Golubitsky, I. Stewart, P. L. Buono and J. J. Collins, A modular network for legged locomotion,, Physica D, 115 (1998), 56.
doi: 10.1016/S0167-2789(97)00222-4. |
[22] |
M. W. Hirsch and H. Smith, Monotone dynamical systems,, in, (2005), 239.
|
[23] |
D. Angeli and E. D. Sontag, Monotone control systems,, IEEE Transactions on Automatic Control, 48 (2003), 1684.
doi: 10.1109/TAC.2003.817920. |
[24] |
J. R. Pomerening, E. D. Sontag and J. E. Ferrell, Building a cell cycle oscillator: Hysteresis and bistability in the activation of cdc2,, Nature Cell Biology, 5 (2003), 346.
doi: 10.1038/ncb954. |
[25] |
D. Angeli, J. E. Ferrell and E. D. Sontag, Detection of multistability, bifurcations, and hysteresis in a large class of biological positive-feedback systems,, Proceedings of the National Academy of Sciences, 101 (2004), 1822.
doi: 10.1073/pnas.0308265100. |
[26] |
E. D. Sontag, Monotone and near-monotone biochemical networks,, Systems and Synthetic Biology, 1 (2007), 59.
doi: 10.1007/s11693-007-9005-9. |
[27] |
V. S. Afraimovich, V. P. Zhigulin and M. I. Rabinovich, On the origin of reproducible sequential activity in neural circuits,, Chaos, 14 (2004), 1123.
doi: 10.1063/1.1819625. |
[28] |
T. Gross and U. Feudel, Generalized models as a universal approach to the analysis of nonlinear dynamical systems,, Phys. Rev. E, 73 (2006).
doi: 10.1103/PhysRevE.73.016205. |
[29] |
E. Shochat, V. Rom-Kedar and L. A. Segel, G-CSF control of neutrophil dynamics in the blood,, Bull. Math. Biology, 69 (2007), 2299.
doi: 10.1007/s11538-007-9221-1. |
[30] |
M. Chromek, Z. Slamova, P. Bergman, L. Kovacs, L. Podracka, I. Ehren, T. Hokfelt, G. H. Gudmundsson, R. L. Gallo, B. Agerberth and A. Brauner, The antimicrobial peptide cathelicidin protects the urinary tract against invasive bacterial infection,, Nature Medicine, 12 (2006), 636.
doi: 10.1038/nm1407. |
[31] |
M. H. Zwietering, I. Jongenburger, F. M. Rombouts and K. VAN 'T Riet, Modeling of the bacterial growth curve,, Application of Environmental Microbiology, 56 (1990), 1875. Google Scholar |
[32] |
P. C. J. Leijh, M. T. van den Barselaar, T. L. van Zwet, I. Dubbeldeman-Rempt and R. van Furth, Kinetics of phagocytosis of Staphylococcus aureus and Escherichia coli by human granulocytes,, Immunology, 37 (1979), 453. Google Scholar |
[33] |
C. C. Clawson and J. E. Repine, Quantitation of maximal bactericidal capability in human neutrophils,, Journal of Laboratory and Clinical Medicine, 88 (1976), 316. Google Scholar |
[34] |
M. C. Hammer, A. L. Baltch, N. T. Sutphen, R. P. Smith and J. V. Conroy, Pseudomonas aeruginosa: Quantitation of maximum phagocytic and bactericidal capabilities of normal human granulocytes,, Journal of Laboratory and Clinical Medicine, 98 (1981), 938. Google Scholar |
[35] |
P. K. Peterson, J. Verhoef, D. Schmeling and P. G. Quie, Kinetics of phagocytosis and bacterial killing by human polymorphonuclear leukocytes and monocytes,, Journal of Infectious Diseases, 136 (1977), 502.
doi: 10.1093/infdis/136.4.502. |
[36] |
A. Katok and B. Hasselblatt, "Introduction to the Modern Theory of Dynamical Systems,", Cambridge University Press, (1995).
|
[37] |
K. P. Hadeler and P. Van den Driessche, Backward bifurcation in epidemic control,, Mathematical Biosciences, 146 (1997), 15.
doi: 10.1016/S0025-5564(97)00027-8. |
[38] |
J. Dushoff, W. Huang and C. Castillo-Chavez, Backwards bifurcations and catastrophe in simple models of fatal diseases,, Journal of Mathematical Biology, 36 (1998), 227.
doi: 10.1007/s002850050099. |
[39] |
F. Brauer, Backward bifurcations in simple vaccination models,, Journal of Mathematical Analysis and Applications, 298 (2004), 418.
doi: 10.1016/j.jmaa.2004.05.045. |
[40] |
S. Budhu, J. D. Loike, A. Pandolfi, S. Han, G. Catalano, A. Constantinescu, R. Clynes and S. C. Silverstein, CD8+ T cell concentration determines their efficiency in killing cognate antigen-expressing syngeneic mammalian cells in vitro and in mouse tissues,, The Journal of Experimental Medicine, 207 (2010), 223.
doi: 10.1084/jem.20091279. |
[41] |
D. L. DeAngelis, R. A. Goldstein and R. V. O'Neill, A model for tropic interaction,, Ecology, 56 (1975), 881.
doi: 10.2307/1936298. |
[42] |
A. D. Bazykin, "Nonlinear Dynamics of Interacting Populations,", World Scientific Pub Co Inc, (1998).
|
[43] |
R. Lindqvist, Estimation of Staphylococcus aureus growth parameters from turbidity data: Characterization of strain variation and comparison of methods,, Applied and Environmental Microbiology, 72 (2006), 4862.
doi: 10.1128/AEM.00251-06. |
[44] |
R. J. Carroll, D. Ruppert, L. A. Stefanski and C. M. Crainiceanu, "Measurement Error in Nonlinear Models: A Modern Perspective,", Chapman and Hall/CRC, (2006). Google Scholar |
[45] |
W. Press, S. Teukolsky, W. Vetterling and B. Flannery, "Numerical Recipes in C,", Cambridge University Press, (1992).
|
[46] |
J. C. Lagarias, J. A. Reeds, M. H. Wright and P. E. Wright, Convergence properties of the nelder-mead simplex method in low dimensions,, SIAM Journal of Optimization, 9 (1999), 112.
doi: 10.1137/S1052623496303470. |
[47] |
B. Efron, R. Tibshirani and R. J. Tibshirani, "An Introduction to the Bootstrap,", Chapman & Hall/CRC, (1993).
|
[48] |
M. A. Nowak and R. M. May, "Virus Dynamics,", Oxford University Press, (2000).
|
[49] |
A. A. Berryman, The orgins and evolution of predator-prey theory,, Ecology, 73 (1992), 1530.
doi: 10.2307/1940005. |
[50] |
V. Lee, C. K. Li, M. M. K. Shing, K. W. Chik, K. Li, K. S. Tsang, D. C. Zhao, D. H. Lai, A. Wong and P. M. P. Yuen, Single vs twice daily g-csf dose for peripheral blood stem cells harvest in normal donors and children with non-malignant diseases,, Bone Marrow Transplantation, 25 (2000), 931.
doi: 10.1038/sj.bmt.1702338. |
[51] |
J. Crawford, D. C. Dale and G. H. Lyman, Chemotherapy-induced neutropenia: Risks, consequences, and new directions for its management,, Cancer, 100 (2004), 228.
doi: 10.1002/cncr.11882. |
[52] |
C. Cheretakis, R. Leung, C. X. Sun, Y. Dror and M. Glogauer, Timing of neutrophil tissue repopulation predicts restoration of innate immune protection in a murine bone marrow transplantation model,, Blood, 108 (2006), 2821.
doi: 10.1182/blood-2006-04-018184. |
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K. Todar, Growth of Bacterial Populations,, in, (2008), 5. Google Scholar |
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M. L. Cohen, M. T. Murphy, G. W. Counts, C. D. Buckner, R. A. Clift and J. D. Meyers, Prediction by surveillance cultures of bacteremia among neutropenic patients treated in a protective environment,, Journal of Infectious Diseases, 147 (1983), 789.
doi: 10.1093/infdis/147.5.789. |
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P. A. Abrams, The fallacies of "ratio-dependent" predation,, Ecology, 75 (1994), 1842.
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[56] |
A. A. Berryman, A. P. Gutierrez and R. Arditi, Credible, parsimonious and useful predator-prey models: A reply to Abrams, Gleeson, and Sarnelle,, Ecology, 76 (1995), 1980.
doi: 10.2307/1940728. |
[57] |
P. A. Abrams and L. R. Ginzburg, The nature of predation: Prey dependent, ratio dependent or neither?,, Trends in Ecology & Evolution, 15 (2000), 337.
doi: 10.1016/S0169-5347(00)01908-X. |
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J. Sotomayor, Generic bifurcations of dynamical systems,, In, (1971).
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J. Guckenheimer and P. Holmes, "Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields,", Springer, (1983).
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show all references
References:
[1] |
C. A. Janeway and R. Medzhitov, Innate immune recognition,, Annual Review of Immunology, 20 (2002), 197.
doi: 10.1146/annurev.immunol.20.083001.084359. |
[2] |
O. Soehnlein and L. Lindbom, Phagocyte partnership during the onset and resolution of inflammation,, Nature Reviews Immunology, 10 (2010), 427.
doi: 10.1038/nri2779. |
[3] |
C. Nathan, Neutrophils and immunity: Challenges and opportunities,, Nature Reviews Immunology, 6 (2006), 173.
doi: 10.1038/nri1785. |
[4] |
A. F. M. Marée, M. Komba, C. Dyck, M. Labecki, D. T. Finegood and L. Edelstein-Keshet, Quantifying macrophage defects in type 1 diabetes,, Journal of theoretical biology, 233 (2005), 533.
doi: 10.1016/j.jtbi.2004.10.030. |
[5] |
A. F. M. Maree, M. Komba, D. T. Finegood and L. Edelstein-Keshet, A quantitative comparison of rates of phagocytosis and digestion of apoptotic cells by macrophages from normal (BALB/c) and diabetes-prone (NOD) mice,, Journal of Applied Physiology, 104 (2008), 157.
doi: 10.1152/japplphysiol.00514.2007. |
[6] |
R. Malka, E. Shochat and V. Rom-Kedar, Bistability and bacterial infections,, PLoS ONE, 5 (2010).
doi: 10.1371/journal.pone.0010010. |
[7] |
Z. Rahman, L. Esparza-Guerra, H. Y. Yap, G. Fraschini, G. Bodey and G. Hortobagyi, Chemotherapy-induced neutropenia and fever in patients with metastatic breast carcinoma receiving salvage chemotherapy,, Cancer, 79 (1997), 1150.
doi: 10.1002/(SICI)1097-0142(19970315)79:6<1150::AID-CNCR13>3.0.CO;2-Z. |
[8] |
G. P. Bodey, M. Buckley, Y. S. Sathe and E. J. Freireich, Quantitative relationships between circulating leukocytes and infection in patients with acute leukemia,, Annals of Internal Medicine, 64 (1966), 328. Google Scholar |
[9] |
J. M. van den Berg, E. van Koppen, A. Åhlin, B. H. Belohradsky, E. Bernatowska, L. Corbeel, T. Español, A. Fischer, M. Kurenko-Deptuch, R. Mouy, T. Petropoulou, J. Roesler, R. Seger, M. J. Stasia, N. H. Valerius, R. S. Weening, B. Wolach, D. Roos and T. W. Kuijpers, Chronic granulomatous disease: The european experience,, PLoS ONE, 4 (2009).
doi: 10.1371/journal.pone.0005234. |
[10] |
A. Reynolds, J. Rubin, G. Clermont, J. Day, Y. Vodovotz and B. G. Ermentrout, A reduced mathematical model of acute inflammation response: I. derivation of model and analysis of anti-inflammation,, Journal of Theoretical Biology, 242 (2006), 220.
doi: 10.1016/j.jtbi.2006.02.016. |
[11] |
M. C. Herald, General model of inflammation,, Bulletin of Mathematical Biology, 72 (2010), 765.
doi: 10.1007/s11538-009-9468-9. |
[12] |
E. M. C. D'Agata, M. Dupont-Rouzeyrol, P. Magal, D. Olivier and S. Ruan, The impact of different antibiotic regimens on the emergence of antibiotic-resistant bacteria,, PLoS ONE, 3 (2008). Google Scholar |
[13] |
Y. Li, A. Karlin, D. J. Loike and C. S. Silverstein, A critical concentration of neutrophils is required for effective bacterial killing in suspension,, Proceedings of the National Academy of Sciences, 99 (2002), 8289.
doi: 10.1073/pnas.122244799. |
[14] |
Y. Li, A. Karlin, D. J. Loike and C. S. Silverstein, Determination of the critical concentration of neutrophils required to block bacterial growth in tissues,, The Journal of Experimental Medicine, 200 (2004), 613.
doi: 10.1084/jem.20040725. |
[15] |
E. Shochat and V. Rom-Kedar, Novel strategies for g-csf treatment of high-risk severe neutropenia suggested by mathematical modeling,, Clinical Cancer Research, 14 (2008), 6354.
doi: 10.1158/1078-0432.CCR-08-0807. |
[16] |
R. Arditi and L. R. Ginzburg, Coupling in predator-prey dynamics: Ratio-dependence,, Journal of Theoretical Biology, 139 (1989), 311.
doi: 10.1016/S0022-5193(89)80211-5. |
[17] |
A. D. Bazykin, F. S. Berezovskaya, G. A. Denisov and Y. A. Kuznetzov, The influence of predator saturation effect and competition among predators on predator-prey system dynamics,, Ecological Modelling, 14 (1981), 39.
doi: 10.1016/0304-3800(81)90013-2. |
[18] |
S. Ruan and D. Xiao, Global analysis in a predator-prey system with nonmonotonic functional response,, SIAM Journal of Applied Mathematics, 16 (2001), 1445.
|
[19] |
L. Edelstein-Keshet, J. Watmough and D. Grunbaum, Do travelling band solutions describe cohesive swarms? An investigation for migratory locusts,, Journal of Mathematical Biology, 36 (1998), 515.
doi: 10.1007/s002850050112. |
[20] |
Y. Mori, A. Jilkine and L. Edelstein-Keshet, Wave-pinning and cell polarity from a bistable reaction-diffusion system,, Biophysical Journal, 94 (2008), 3684.
doi: 10.1529/biophysj.107.120824. |
[21] |
M. Golubitsky, I. Stewart, P. L. Buono and J. J. Collins, A modular network for legged locomotion,, Physica D, 115 (1998), 56.
doi: 10.1016/S0167-2789(97)00222-4. |
[22] |
M. W. Hirsch and H. Smith, Monotone dynamical systems,, in, (2005), 239.
|
[23] |
D. Angeli and E. D. Sontag, Monotone control systems,, IEEE Transactions on Automatic Control, 48 (2003), 1684.
doi: 10.1109/TAC.2003.817920. |
[24] |
J. R. Pomerening, E. D. Sontag and J. E. Ferrell, Building a cell cycle oscillator: Hysteresis and bistability in the activation of cdc2,, Nature Cell Biology, 5 (2003), 346.
doi: 10.1038/ncb954. |
[25] |
D. Angeli, J. E. Ferrell and E. D. Sontag, Detection of multistability, bifurcations, and hysteresis in a large class of biological positive-feedback systems,, Proceedings of the National Academy of Sciences, 101 (2004), 1822.
doi: 10.1073/pnas.0308265100. |
[26] |
E. D. Sontag, Monotone and near-monotone biochemical networks,, Systems and Synthetic Biology, 1 (2007), 59.
doi: 10.1007/s11693-007-9005-9. |
[27] |
V. S. Afraimovich, V. P. Zhigulin and M. I. Rabinovich, On the origin of reproducible sequential activity in neural circuits,, Chaos, 14 (2004), 1123.
doi: 10.1063/1.1819625. |
[28] |
T. Gross and U. Feudel, Generalized models as a universal approach to the analysis of nonlinear dynamical systems,, Phys. Rev. E, 73 (2006).
doi: 10.1103/PhysRevE.73.016205. |
[29] |
E. Shochat, V. Rom-Kedar and L. A. Segel, G-CSF control of neutrophil dynamics in the blood,, Bull. Math. Biology, 69 (2007), 2299.
doi: 10.1007/s11538-007-9221-1. |
[30] |
M. Chromek, Z. Slamova, P. Bergman, L. Kovacs, L. Podracka, I. Ehren, T. Hokfelt, G. H. Gudmundsson, R. L. Gallo, B. Agerberth and A. Brauner, The antimicrobial peptide cathelicidin protects the urinary tract against invasive bacterial infection,, Nature Medicine, 12 (2006), 636.
doi: 10.1038/nm1407. |
[31] |
M. H. Zwietering, I. Jongenburger, F. M. Rombouts and K. VAN 'T Riet, Modeling of the bacterial growth curve,, Application of Environmental Microbiology, 56 (1990), 1875. Google Scholar |
[32] |
P. C. J. Leijh, M. T. van den Barselaar, T. L. van Zwet, I. Dubbeldeman-Rempt and R. van Furth, Kinetics of phagocytosis of Staphylococcus aureus and Escherichia coli by human granulocytes,, Immunology, 37 (1979), 453. Google Scholar |
[33] |
C. C. Clawson and J. E. Repine, Quantitation of maximal bactericidal capability in human neutrophils,, Journal of Laboratory and Clinical Medicine, 88 (1976), 316. Google Scholar |
[34] |
M. C. Hammer, A. L. Baltch, N. T. Sutphen, R. P. Smith and J. V. Conroy, Pseudomonas aeruginosa: Quantitation of maximum phagocytic and bactericidal capabilities of normal human granulocytes,, Journal of Laboratory and Clinical Medicine, 98 (1981), 938. Google Scholar |
[35] |
P. K. Peterson, J. Verhoef, D. Schmeling and P. G. Quie, Kinetics of phagocytosis and bacterial killing by human polymorphonuclear leukocytes and monocytes,, Journal of Infectious Diseases, 136 (1977), 502.
doi: 10.1093/infdis/136.4.502. |
[36] |
A. Katok and B. Hasselblatt, "Introduction to the Modern Theory of Dynamical Systems,", Cambridge University Press, (1995).
|
[37] |
K. P. Hadeler and P. Van den Driessche, Backward bifurcation in epidemic control,, Mathematical Biosciences, 146 (1997), 15.
doi: 10.1016/S0025-5564(97)00027-8. |
[38] |
J. Dushoff, W. Huang and C. Castillo-Chavez, Backwards bifurcations and catastrophe in simple models of fatal diseases,, Journal of Mathematical Biology, 36 (1998), 227.
doi: 10.1007/s002850050099. |
[39] |
F. Brauer, Backward bifurcations in simple vaccination models,, Journal of Mathematical Analysis and Applications, 298 (2004), 418.
doi: 10.1016/j.jmaa.2004.05.045. |
[40] |
S. Budhu, J. D. Loike, A. Pandolfi, S. Han, G. Catalano, A. Constantinescu, R. Clynes and S. C. Silverstein, CD8+ T cell concentration determines their efficiency in killing cognate antigen-expressing syngeneic mammalian cells in vitro and in mouse tissues,, The Journal of Experimental Medicine, 207 (2010), 223.
doi: 10.1084/jem.20091279. |
[41] |
D. L. DeAngelis, R. A. Goldstein and R. V. O'Neill, A model for tropic interaction,, Ecology, 56 (1975), 881.
doi: 10.2307/1936298. |
[42] |
A. D. Bazykin, "Nonlinear Dynamics of Interacting Populations,", World Scientific Pub Co Inc, (1998).
|
[43] |
R. Lindqvist, Estimation of Staphylococcus aureus growth parameters from turbidity data: Characterization of strain variation and comparison of methods,, Applied and Environmental Microbiology, 72 (2006), 4862.
doi: 10.1128/AEM.00251-06. |
[44] |
R. J. Carroll, D. Ruppert, L. A. Stefanski and C. M. Crainiceanu, "Measurement Error in Nonlinear Models: A Modern Perspective,", Chapman and Hall/CRC, (2006). Google Scholar |
[45] |
W. Press, S. Teukolsky, W. Vetterling and B. Flannery, "Numerical Recipes in C,", Cambridge University Press, (1992).
|
[46] |
J. C. Lagarias, J. A. Reeds, M. H. Wright and P. E. Wright, Convergence properties of the nelder-mead simplex method in low dimensions,, SIAM Journal of Optimization, 9 (1999), 112.
doi: 10.1137/S1052623496303470. |
[47] |
B. Efron, R. Tibshirani and R. J. Tibshirani, "An Introduction to the Bootstrap,", Chapman & Hall/CRC, (1993).
|
[48] |
M. A. Nowak and R. M. May, "Virus Dynamics,", Oxford University Press, (2000).
|
[49] |
A. A. Berryman, The orgins and evolution of predator-prey theory,, Ecology, 73 (1992), 1530.
doi: 10.2307/1940005. |
[50] |
V. Lee, C. K. Li, M. M. K. Shing, K. W. Chik, K. Li, K. S. Tsang, D. C. Zhao, D. H. Lai, A. Wong and P. M. P. Yuen, Single vs twice daily g-csf dose for peripheral blood stem cells harvest in normal donors and children with non-malignant diseases,, Bone Marrow Transplantation, 25 (2000), 931.
doi: 10.1038/sj.bmt.1702338. |
[51] |
J. Crawford, D. C. Dale and G. H. Lyman, Chemotherapy-induced neutropenia: Risks, consequences, and new directions for its management,, Cancer, 100 (2004), 228.
doi: 10.1002/cncr.11882. |
[52] |
C. Cheretakis, R. Leung, C. X. Sun, Y. Dror and M. Glogauer, Timing of neutrophil tissue repopulation predicts restoration of innate immune protection in a murine bone marrow transplantation model,, Blood, 108 (2006), 2821.
doi: 10.1182/blood-2006-04-018184. |
[53] |
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