User:Federico Castro M/Horizontal Transfer/Models Simulations

[[Team:Mexico-UNAM-IPN/Horizontal_Transfer| <font face="trebuchet ms" style="color:Green"> <big>'''Back Horizontal Transfer'''</big> </font>]]

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The mathematical study and simulations are based on population
dynamics models. We assume that each bacterium type grows according to
a logistic equation:

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[[Image:Ecuaciones_HGT(2).jpg]]

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where a is the growth rate and K is the carrying capacity.
Therefore, type A and B have a specific grow rate and carrying capacity, since 
they are in a medium where only one antibiotic is present, to which each one is resistent.

Later on, both populations are exposed to the two antibiotics in lethal concentrations and so only those 
bacteria that have acquired resistence to the other antibiotic will be able to survive. This is represented
in turn by a change of sign in the growth rate. For those in which horizontal transport has not taken place yet it becomes negative, while for the third kind, already resistant to both ampicillin and tetracycline a new logistic equation with positive growth rate is used.

This is seen in the following  figures. In the first one both curves increase, while in the second two decrease (corresponding to 
the nonresistent types) and a third increasing curve corresponding to the strain resistent to both.
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|[[Image:Fig4UNAMIPN.JPG |400px]]
|[[Image:Fig3UNAMIPN.JPG |460px]]

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It is possible to approximate when the event of Horizontal Gene Tranfer happened making a few changes in the simulation.