We derive and demonstrate a step.dynamics using differential equations. Almost from the onset, mathematical modeling of QS using differential equations has been an interdisciplinary endeavor and many of the works we revised here will be placed into their biological context.ĭifferential Equation Models for Sharp Threshold Dynamicsĭynamics, and the Lanchester model of armed conflict, where the loss of a key capability drastically changes dynamics. Both types of models often consist of systems (i.e., more than one equation) of equations, such as equations for bacterial growth and autoinducer concentration dynamics. PDE models can be used to follow changes in more than one independent variable, for example, time and space. ODE models allow describing changes in one independent variable, for example, time. Rates of change are represented mathematically by derivatives, i.e., in terms of DE. The chapter is divided into two sections: ordinary differential equations (ODE) and partial differential equations (PDE) models of QS. In this chapter, we focus on giving an overview of models consisting of differential equations (DE), which can be used to describe changing quantities, for example, the dynamics of one or more signaling molecule in time and space, often in conjunction with bacterial growth dynamics. A wide spectrum of mathematical tools and methods such as dynamical systems, stochastics, and spatial models can be employed. Mathematical models to study quorum sensing (QS) have become an important tool to explore all aspects of this type of bacterial communication. Pérez-Velázquez, Judith Hense, Burkhard A Differential Equations Models to Study Quorum Sensing.
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