Team:LCG-UNAM-Mexico:odes
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(→Deterministic population dynamics model) |
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='''Deterministic population dynamics model'''= | ='''Deterministic population dynamics model'''= | ||
- | As a first approach to solve our problem, the infection was mathematically modeled with a system of differential equations. | + | As a first approach to solve our problem, the infection process was mathematically modeled with a system of differential equations. |
It is important to consider that the amount of phages at a certain time depends on the amount of phages on a previous point in time due to the latency period (once the phage has inserted its genome, it requires a period of time to redirect the molecular machinery of the bacteria, reproduce and start assembling). To tackle this problem, we modeled the phage infection using a system of [http://en.wikipedia.org/wiki/Delay_differential_equation DELAY DIFFERENTIAL EQUATIONS (DDE)] based on the system proposed by Beretta[1]. The use of DDE allows us to update the system depending on the states of the system in previous points in time. | It is important to consider that the amount of phages at a certain time depends on the amount of phages on a previous point in time due to the latency period (once the phage has inserted its genome, it requires a period of time to redirect the molecular machinery of the bacteria, reproduce and start assembling). To tackle this problem, we modeled the phage infection using a system of [http://en.wikipedia.org/wiki/Delay_differential_equation DELAY DIFFERENTIAL EQUATIONS (DDE)] based on the system proposed by Beretta[1]. The use of DDE allows us to update the system depending on the states of the system in previous points in time. | ||
- | It is noteworthy that the success of system, on a population level, depends on the efficiency of our suicide system after a | + | It is noteworthy that the success of system, on a population level, depends on the efficiency of our suicide system after a bacterium has been infected by a phage. To include this in our model, our system of equations must consider the mortality rate of bacteria after they have been infected by a phage (it is precisely this parameter the one we are trying to modify experimentally). |
In an infection we have three distinct populations: | In an infection we have three distinct populations: |
Revision as of 20:14, 19 October 2009