Team:LCG-UNAM-Mexico:odes
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='''Deterministic population dynamics model'''= | ='''Deterministic population dynamics model'''= | ||
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==Populations== | ==Populations== | ||
- | <center> | + | <br><center> |
<html><head><title>Population</title> | <html><head><title>Population</title> | ||
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[[Image:6e05_0_0.png|400px|thumb|center|Normal growth of ''E. coli'' without phages in the medium. Bacterial population grows according to a logistic equation.]] | [[Image:6e05_0_0.png|400px|thumb|center|Normal growth of ''E. coli'' without phages in the medium. Bacterial population grows according to a logistic equation.]] | ||
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- | <center>Initial population vector set to '''[6e05 0 0]'''.<br> As there are no phages present, the infected and phage populations does not increase.</center><br><br> | + | <center>Initial population vector set to '''[6e05 0 0]'''.<br> As there are no phages present, the infected and phage populations does not increase and ''E. coli'' grows normally.</center><br><br> |
{| | {| | ||
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| [[Image:Zoom_6e05_0_1_5.png|400px|thumb|right|Behavior of an infection in a wild type ''E. coli''.]] | | [[Image:Zoom_6e05_0_1_5.png|400px|thumb|right|Behavior of an infection in a wild type ''E. coli''.]] | ||
+ | | [[Image:6e05_0_1_5.png|400px|thumb|left|Behavior of an infection in a wild type ''E. coli''.]] | ||
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{| | {| | ||
- | <center>Initial population vector set to '''[6e05 0 1]'''. <br> | + | <center>Initial population vector set to '''[6e05 0 1]'''. <br>Susceptibles bacteria becomes infected when phages are added. Bacterial death is only caused by phage lysis product, therefore, the death rate is set to one time the inverse of the latency period ('''μi=5''').</center><br><br> |
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<br> | <br> | ||
- | [[Image:6e05_0_1_25.png|400px|thumb|center|]] | + | [[Image:6e05_0_1_25.png|400px|thumb|center|Behavior of an infection in an engineered ''E. coli''.]] |
- | <center>Initial population vector set to '''[6e05 0 1]'''. <br> | + | <center>Initial population vector set to '''[6e05 0 1]'''. <br>when T7 infects a bacterium |
+ | which has the suicide circuit, '''μi''' (mortality rate caused by suicide system) is increased, host bacteria die before the phages reproduce itself. The mortality parameter estimated caused by the toxin is five times the inverse of the latency period ('''μi=25''').</center> | ||
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[1] Frank, S. A. 1996 Models of parasite virulence. Q. Rev. Biol. 71, 37–78.<br> | [1] Frank, S. A. 1996 Models of parasite virulence. Q. Rev. Biol. 71, 37–78.<br> | ||
[2] E. Beretta, Y. Kuang (2001): Modeling and Analysis of a Marine Bacteriophage Infection with Latency Period. Nonlinear Analysis : Real World Applications, 2, 35-74<br> | [2] E. Beretta, Y. Kuang (2001): Modeling and Analysis of a Marine Bacteriophage Infection with Latency Period. Nonlinear Analysis : Real World Applications, 2, 35-74<br> | ||
- | [3] L.F. Shampine and S. Thompson, Solving DDEs in MATLAB | + | [3] L.F. Shampine and S. Thompson, Solving DDEs in MATLAB.<br> |
- | [4] Heineman, R., Springman, R., Bull, J. (2008). Optimal Foraging by Bacteriophages through Host Avoidance | + | [4] Heineman, R., Springman, R., Bull, J. (2008). Optimal Foraging by Bacteriophages through Host Avoidance. The American Naturalist, 171(4), E149-E157. <br> |
[5] De Paepe M, Taddei F (2006) Viruses' life history: Towards a mechanistic basis of a trade-off between survival and reproduction among phages. PLoS Biol 4(7): e193. DOI: 10.1371/journal.pbio.0040193.<br> | [5] De Paepe M, Taddei F (2006) Viruses' life history: Towards a mechanistic basis of a trade-off between survival and reproduction among phages. PLoS Biol 4(7): e193. DOI: 10.1371/journal.pbio.0040193.<br> | ||
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Latest revision as of 14:01, 21 October 2009