Team:LCG-UNAM-Mexico:odes
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* Bacteriophages | * Bacteriophages | ||
- | == | + | ==Description of the system of nonlinear differential equations== |
[[Image:Beretta_eq.jpg|500px|thumb|System of delay differential equations]] | [[Image:Beretta_eq.jpg|500px|thumb|System of delay differential equations]] | ||
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* Bacteria (either susceptible or infected) grows logistically with a carrying capacity C. | * Bacteria (either susceptible or infected) grows logistically with a carrying capacity C. | ||
* According to the law of mass action, when a P (phage) encounters a S (susceptible bacterium), it attaches itself to the cell wall of the bacterium. The bacterium becomes I (infected) at rate K (Bacteriophage Adsorption Rate). | * According to the law of mass action, when a P (phage) encounters a S (susceptible bacterium), it attaches itself to the cell wall of the bacterium. The bacterium becomes I (infected) at rate K (Bacteriophage Adsorption Rate). | ||
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* The term mi take into account the death rate caused by the suicide system. So the term e is the probability that infected bacteria do not die in the course of infection because suicide system. | * The term mi take into account the death rate caused by the suicide system. So the term e is the probability that infected bacteria do not die in the course of infection because suicide system. | ||
* If the suicide system do not kill the infected bacteria at previous time tau, it will result in a number b of phages. | * If the suicide system do not kill the infected bacteria at previous time tau, it will result in a number b of phages. | ||
- | <br> | + | <br>The system was solved using matlab.<br> |
=='''Results'''== | =='''Results'''== | ||
- | The | + | |
+ | The initial population was coded as a population vector '''[Susceptible Infected Phages]''' . | ||
{| | {| | ||
- | [[Image:6e05_0_0.png|400px|thumb|Normal growth of ''E. coli'' without phages in the medium. Bacteria population density grows according to a logistic equation.]] | + | [[Image:6e05_0_0.png|400px|thumb|center|Initial population vector was set to '''[6e05 0 0]'''. Normal growth of ''E. coli'' without phages in the medium. Bacteria population density grows according to a logistic equation.]] |
- | [[Image:6e05_0_1_5.png|400px|thumb|Behavior of an infection in a wild type ''E. coli''.]] | + | Normal growth of ''E. coli'' without phages in the medium. Bacteria population density grows according to a logistic equation. |
- | [[Image:6e05_0_1_25.png|400px|thumb|When μi | + | [[Image:6e05_0_1_5.png|400px|thumb|center|Initial population vector was set to '''[6e05 0 1]'''. Death is only caused by the lysis because phage infection, so death rate was set equal to one time the inverse of latency period (μi=5). Behavior of an infection in a wild type ''E. coli''.]] |
+ | Behavior of an infection in a wild type ''E. coli''. | ||
+ | [[Image:6e05_0_1_25.png|400px|thumb|center|Initial population vector was set to '''[6e05 0 1]'''. When μi is increased host bacteria dies before the phage can reproduces copies of itself. Death parameter by toxin is five times the inverse of latency period (μi=25). ]] | ||
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+ | When μi is increased host bacteria dies before the phage can reproduces copies of itself. Death parameter by toxin is five times the inverse of latency period (μi=25). | ||
|} | |} | ||
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==References== | ==References== | ||
[1] 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> | [1] 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] Heineman, R., Springman, R., Bull, J. (2008). Optimal Foraging by Bacteriophages through Host Avoidance.. | + | [2] Heineman, R., Springman, R., Bull, J. (2008). Optimal Foraging by Bacteriophages through Host Avoidance.. The American Naturalist, 171(4), E149-E157. <br> |
[3] 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> | [3] 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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Revision as of 19:08, 19 October 2009