Stochastic differential equations used to model conjugation

Kirsten Riber Philipsen, Lasse Engbo Christiansen

    Research output: Contribution to conferenceConference abstract for conferenceResearch


    Stochastic differential equations (SDEs) are used to model horizontal transfer of antibiotic resis- tance by conjugation. The model describes the concentration of donor, recipient, transconjugants and substrate. The strength of the SDE model over the traditional ODE models is that the noise can be split into measurement noise and system noise. The system noise is used to compensate for those biological processes not explicitly described by the model. Many authors model conjugation by a simple mass action model first proposed by Levin et al. (1979). Also Michaelis-Menten dependence on the recipient concentration has been used to mathematically describe conjugation (Andrup et al. (1998)). We find that it is important to include substrate depletion to model conjugation for a system with exhaustible media and implement the substrate dependence as a Michaelis-Menten expression. This is supported by an experiment conducted with E. faecium. In addition, we suggest that a 3rd order time-delay must be included in the model to account for the delay before a newly conjugated plasmid is expressed. A ML estimate of the parameters based on experimental data is found using the software CTSM. The conjugation rate is estimated to 1.4e−9 ± 0.38e−9 1/h.
    Original languageEnglish
    Publication date2007
    Publication statusPublished - 2007
    Event1st Nordic-Baltic Biometric Conference 2007 - Foulum, Denmark
    Duration: 6 Jun 20078 Jun 2007


    Conference1st Nordic-Baltic Biometric Conference 2007

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