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Related Concept Videos

Modeling with Differential Equations01:25

Modeling with Differential Equations

Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
Transmission-Line Differential Equations01:26

Transmission-Line Differential Equations

Transmission lines are essential components of electrical power systems. They are characterized by the distributed nature of resistance (R), inductance (L), and capacitance (C) per unit length. To analyze these lines, differential equations are employed to model the variations in voltage and current along the line.
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured from the...
Separable Differential Equations01:20

Separable Differential Equations

A separable differential equation is a type of first-order differential equation where the derivative dy/dx can be expressed as a product of two functions: one that depends only on x and another that depends only on y. This allows for the rearrangement of the equation so that all terms involving y are on one side, and all terms involving x are on the other. This process, known as the separation of variables, simplifies the process of solving the equation by enabling the integration of both...
Partial Differential Equations01:21

Partial Differential Equations

A stone dropped into a still pond generates waves that propagate outward in circular patterns, creating a dynamic surface whose elevation depends on both position and time. At any given location, the water level oscillates as the wave passes, while at any fixed moment, the surface exhibits smooth, curved structures extending across space. This dual dependence requires a mathematical description that accounts for variation in multiple variables simultaneously.At a fixed point on the water...
Exponential Equations for Modeling Growth01:26

Exponential Equations for Modeling Growth

Exponential models are essential for describing rapid, multiplicative changes in natural systems, such as population growth. When a population doubles at regular intervals, the process can be modeled using a suitable base. For instance, a bacterial culture that doubles every three hours follows the model n(t)=n0⋅2t/3, where n(t) is the population at the time t.A more general model uses the natural base e, especially for continuous growth. This takes the form n(t)=n0⋅ert, where r is the relative...
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...

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Related Experiment Video

Updated: Jun 18, 2026

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
06:55

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

Modelling conjugation with stochastic differential equations.

K R Philipsen1, L E Christiansen, H Hasman

  • 1DTU Informatics, Technical University of Denmark, Richard Petersens Plads, Building 321, DK-2800, Kgs. Lyngby, Denmark. krp@imm.dtu.dk

Journal of Theoretical Biology
|November 28, 2009
PubMed
Summary
This summary is machine-generated.

This study introduces a new mathematical model for bacterial conjugation, focusing on Enterococcus faecium. The model enhances understanding of resistance transfer in microbial populations using stochastic differential equations.

More Related Videos

The Use of Chemostats in Microbial Systems Biology
13:19

The Use of Chemostats in Microbial Systems Biology

Published on: October 14, 2013

Related Experiment Videos

Last Updated: Jun 18, 2026

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
06:55

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

The Use of Chemostats in Microbial Systems Biology
13:19

The Use of Chemostats in Microbial Systems Biology

Published on: October 14, 2013

Area of Science:

  • Microbiology
  • Mathematical Biology
  • Biostatistics

Background:

  • Bacterial conjugation is a key mechanism for antibiotic resistance gene transfer.
  • Understanding conjugation dynamics is crucial for controlling microbial infections.
  • Enterococcus faecium is a significant opportunistic pathogen.

Purpose of the Study:

  • To develop a novel stochastic differential equation model for bacterial growth and conjugation.
  • To introduce a new substrate-dependent conjugation rate.
  • To compare different model structures and noise assumptions.

Main Methods:

  • Stochastic differential equation modeling (continuous-time state, discrete-time measurement).
  • Maximum likelihood estimation for parameter fitting.
  • Likelihood-ratio tests and Akaike's Information Criterion for model comparison.
  • Incorporation of agar plate conjugation into the measurement equation.

Main Results:

  • A new model accurately describes Enterococcus faecium growth and conjugation in a defined medium.
  • A substrate-dependent conjugation rate was successfully implemented.
  • Model comparison identified the best-fitting model structure, including plate conjugation effects.
  • The modeling approach is broadly applicable to dynamical systems.

Conclusions:

  • The developed stochastic model provides a robust framework for studying bacterial conjugation.
  • The substrate-dependent rate and plate conjugation significantly improve model accuracy.
  • This approach can be applied to other microbial systems and dynamical processes.