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Spread of viral infection of immobilized bacteria
1. | School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, USA 85287, United States |
2. | School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287-1804 |
3. | School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, United States |
References:
[1] |
E. Beretta and Y. Kuang, Modeling and analysis of a marine bacteriophage infection with latency, Nonlinear Analysis RWA, 2 (2001), 35-74.
doi: 10.1016/S0362-546X(99)00285-0. |
[2] |
C. Beaumont, J.-B. Burie, A. Ducrot and P. Zongo, Propogation of Salmonella within an industrial hens house, SIAM J. Appl. Math., 72 (2012), 1113-1148.
doi: 10.1137/110822967. |
[3] |
A. Campbell, Conditions for existence of bacteriophages, Evolution, 15 (1961), 153-165.
doi: 10.2307/2406076. |
[4] |
P. DeLeenheer and H. L. Smith, Virus dynamics: A global analysis, SIAM J. Appl. Math., 63 (2003), 1313-1327.
doi: 10.1137/S0036139902406905. |
[5] |
O. Diekmann, Limiting behaviour in an epidemic model, Nonlinear Analysis, TMA, 1 (1977), 459-470. |
[6] |
O. Diekmann and H. G. Kaper, On the bounded solutions of a nonlinear convolution equation, Nonlinear Analysis, TMA, 2 (1978), 721-737.
doi: 10.1016/0362-546X(78)90015-9. |
[7] |
E. Ellis and M. Delbrück, The growth of bacteriophage, J. of Physiology, 22 (1939), 365-384.
doi: 10.1085/jgp.22.3.365. |
[8] |
J. Fort and V. Mendez, Time-delayed spread of viruses in growing plaques, Physical Review Letters, 89 (2002), 178101.
doi: 10.1103/PhysRevLett.89.178101. |
[9] |
D. A. Jones, G. Röst, H. L. Smith and H. R.Thieme, On spread of phage infection of bacteria in a petri dish, SIAM J. Appl. Math., 72 (2012), 670-688.
doi: 10.1137/110848360. |
[10] |
A. L. Koch, The growth of viral plaques during enlargement phase, J. Theor. Biol., 6 (1964), 413-431.
doi: 10.1016/0022-5193(64)90056-6. |
[11] |
Y. Lee and J. Yin, Imaging the propagation of viruses, Communication to the Editor, Biotechnology and Bioengineering, 52 (1996), 438-442.
doi: 10.1002/(SICI)1097-0290(19961105)52:3<438::AID-BIT11>3.0.CO;2-F. |
[12] |
B. Levin, F. Stewart and L. Chao, Resource-limited growth, competition, and predation: A model, and experimental studies with bacteria and bacteriophage, Amer. Naturalist, 111 (1977), 3-24.
doi: 10.1086/283134. |
[13] |
M. A. Lewis, B. Li and H. F. Weinberger, Spreading speed and linear determinacy for two-species competition models, J. Math. Biol., 45 (2002), 219-233.
doi: 10.1007/s002850200144. |
[14] |
M. A. Nowak and R. M. May, "Virus Dynamics," Oxford University Press, New York, 2000. |
[15] |
V. Ortega-Cejas, J. Fort, V. Mendez and D. Campos, Approximate solution to the speed of spreading viruses, Physical Review E, 69 (2004), 031909.
doi: 10.1103/PhysRevE.69.031909. |
[16] |
A. S. Perelson and P. W. Nelson, Mathematical analysis of HIV-1 dynamics in vivo, SIAM Rev., 41 (1999), 3-44.
doi: 10.1137/S0036144598335107. |
[17] |
H. L. Smith and H. R. Thieme, Persistence of bacteria and phages in a chemostat, J. Math. Biol., 64 (2012), 951-979.
doi: 10.1007/s00285-011-0434-4. |
[18] |
H. R. Thieme, A model for the spatial spread of an epidemic, J. Math. Biol., 4 (1977), 337-351.
doi: 10.1007/BF00275082. |
[19] |
H. R. Thieme, Asymptotic estimates of the solutions of nonlinear integral equations and asymptotic speeds for the spread of populations, J. Reine Angew. Math., 306 (1979), 94-121.
doi: 10.1515/crll.1979.306.94. |
[20] |
H. R. Thieme, Density-dependent regulation of spatially distributed populations and their asymptotic speed of spread, J. Math. Biol., 8 (1979), 173-187.
doi: 10.1007/BF00279720. |
[21] |
H. R. Thieme, "Mathematics in Population Biology," Princeton University Press, Princeton, 2003. |
[22] |
H. R. Thieme and X.-Q. Zhao, Asymptotic speeds of spread and traveling waves for integral equations and delayed reaction-diffusion models, JDE, 195 (2003), 430-470.
doi: 10.1016/S0022-0396(03)00175-X. |
[23] |
H. F. Weinberger, M. A. Lewis and B. Li, Analysis of linear determinacy for spread in cooperation models, J. Math. Biol., 45 (2002), 183-218.
doi: 10.1007/s002850200145. |
[24] |
J. Yin and J. S. McCaskill, Replication of viruses in a growing plaque: A reaction-diffusion model, Biophysics J., 61 (1992), 1540-1549.
doi: 10.1016/S0006-3495(92)81958-6. |
[25] |
J. Yin and L. You, Amplification and spread of viruses in a growing plaque, J. Theor. Biol., 200 (1999), 365-373. |
show all references
References:
[1] |
E. Beretta and Y. Kuang, Modeling and analysis of a marine bacteriophage infection with latency, Nonlinear Analysis RWA, 2 (2001), 35-74.
doi: 10.1016/S0362-546X(99)00285-0. |
[2] |
C. Beaumont, J.-B. Burie, A. Ducrot and P. Zongo, Propogation of Salmonella within an industrial hens house, SIAM J. Appl. Math., 72 (2012), 1113-1148.
doi: 10.1137/110822967. |
[3] |
A. Campbell, Conditions for existence of bacteriophages, Evolution, 15 (1961), 153-165.
doi: 10.2307/2406076. |
[4] |
P. DeLeenheer and H. L. Smith, Virus dynamics: A global analysis, SIAM J. Appl. Math., 63 (2003), 1313-1327.
doi: 10.1137/S0036139902406905. |
[5] |
O. Diekmann, Limiting behaviour in an epidemic model, Nonlinear Analysis, TMA, 1 (1977), 459-470. |
[6] |
O. Diekmann and H. G. Kaper, On the bounded solutions of a nonlinear convolution equation, Nonlinear Analysis, TMA, 2 (1978), 721-737.
doi: 10.1016/0362-546X(78)90015-9. |
[7] |
E. Ellis and M. Delbrück, The growth of bacteriophage, J. of Physiology, 22 (1939), 365-384.
doi: 10.1085/jgp.22.3.365. |
[8] |
J. Fort and V. Mendez, Time-delayed spread of viruses in growing plaques, Physical Review Letters, 89 (2002), 178101.
doi: 10.1103/PhysRevLett.89.178101. |
[9] |
D. A. Jones, G. Röst, H. L. Smith and H. R.Thieme, On spread of phage infection of bacteria in a petri dish, SIAM J. Appl. Math., 72 (2012), 670-688.
doi: 10.1137/110848360. |
[10] |
A. L. Koch, The growth of viral plaques during enlargement phase, J. Theor. Biol., 6 (1964), 413-431.
doi: 10.1016/0022-5193(64)90056-6. |
[11] |
Y. Lee and J. Yin, Imaging the propagation of viruses, Communication to the Editor, Biotechnology and Bioengineering, 52 (1996), 438-442.
doi: 10.1002/(SICI)1097-0290(19961105)52:3<438::AID-BIT11>3.0.CO;2-F. |
[12] |
B. Levin, F. Stewart and L. Chao, Resource-limited growth, competition, and predation: A model, and experimental studies with bacteria and bacteriophage, Amer. Naturalist, 111 (1977), 3-24.
doi: 10.1086/283134. |
[13] |
M. A. Lewis, B. Li and H. F. Weinberger, Spreading speed and linear determinacy for two-species competition models, J. Math. Biol., 45 (2002), 219-233.
doi: 10.1007/s002850200144. |
[14] |
M. A. Nowak and R. M. May, "Virus Dynamics," Oxford University Press, New York, 2000. |
[15] |
V. Ortega-Cejas, J. Fort, V. Mendez and D. Campos, Approximate solution to the speed of spreading viruses, Physical Review E, 69 (2004), 031909.
doi: 10.1103/PhysRevE.69.031909. |
[16] |
A. S. Perelson and P. W. Nelson, Mathematical analysis of HIV-1 dynamics in vivo, SIAM Rev., 41 (1999), 3-44.
doi: 10.1137/S0036144598335107. |
[17] |
H. L. Smith and H. R. Thieme, Persistence of bacteria and phages in a chemostat, J. Math. Biol., 64 (2012), 951-979.
doi: 10.1007/s00285-011-0434-4. |
[18] |
H. R. Thieme, A model for the spatial spread of an epidemic, J. Math. Biol., 4 (1977), 337-351.
doi: 10.1007/BF00275082. |
[19] |
H. R. Thieme, Asymptotic estimates of the solutions of nonlinear integral equations and asymptotic speeds for the spread of populations, J. Reine Angew. Math., 306 (1979), 94-121.
doi: 10.1515/crll.1979.306.94. |
[20] |
H. R. Thieme, Density-dependent regulation of spatially distributed populations and their asymptotic speed of spread, J. Math. Biol., 8 (1979), 173-187.
doi: 10.1007/BF00279720. |
[21] |
H. R. Thieme, "Mathematics in Population Biology," Princeton University Press, Princeton, 2003. |
[22] |
H. R. Thieme and X.-Q. Zhao, Asymptotic speeds of spread and traveling waves for integral equations and delayed reaction-diffusion models, JDE, 195 (2003), 430-470.
doi: 10.1016/S0022-0396(03)00175-X. |
[23] |
H. F. Weinberger, M. A. Lewis and B. Li, Analysis of linear determinacy for spread in cooperation models, J. Math. Biol., 45 (2002), 183-218.
doi: 10.1007/s002850200145. |
[24] |
J. Yin and J. S. McCaskill, Replication of viruses in a growing plaque: A reaction-diffusion model, Biophysics J., 61 (1992), 1540-1549.
doi: 10.1016/S0006-3495(92)81958-6. |
[25] |
J. Yin and L. You, Amplification and spread of viruses in a growing plaque, J. Theor. Biol., 200 (1999), 365-373. |
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