Quorum sensing is a system of stimulus and responses correlated to population density that is used by bacteria to coordinate gene-expression. I am looking for a simple computational/mathematical model of quorum sensing that abstracts away from the details of the mechanism implementing it inside the agent, but keeps the key inter-agent properties like diffusion rate, range, and timing.
Is there a standard abstract mathematical model of quorum sensing used by biologists?
I am not interested in the particulars of a specific organism, but would like a general model I could apply to capture the 'gist' for any organism that relies on quorum sensing for part of its behavior.
Bernardini et al. (2007) provided an extension to P-systems incorporating the basics of quorum sensing, and Romero-Campero & Pérez-Jiménez (2008) have used their approach to model bioluminosity in vibrio fischeri. This approach is conceptually appealing to me, but that is because I am predominantly a computer scientists. Although P-system can be used for modeling biological systems (Ardelean & Cavaliere, 2003), they still feel fundamentally computer-science-y and are typically not published in orthodox biological venues. This makes me suspect there is a more standard approach among biologists, probably via dynamic systems and diffusion equations.