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The exchange of small molecular signals within microbial populations isgenerally referred to as quorum sensing (QS). QS is ubiquitous in nature andenables microorganisms to respond to fluctuations in living environments byworking together. In this study, a QS-based molecular communication systemwithin a microbial population in a two-dimensional (2D) environment isanalytically modeled. Microorganisms are randomly distributed on a 2D circlewhere each one releases molecules at random times. The number of moleculesobserved at each randomly-distributed bacterium is first derived bycharacterizing the diffusion and degradation of signaling molecules within thepopulation. Using the derived result and some approximation, the expecteddensity of cooperative bacteria is derived. Our model captures the basicfeatures of QS. The analytical results for noisy signal propagation agree withsimulation results where the Brownian motion of molecules is simulated by aparticle-based method. Therefore, we anticipate that our model can be used topredict the density of cooperative bacteria in a variety of QS-coordinatedactivities, e.g., biofilm formation and antibiotic resistance.

Expected Density of Cooperative Bacteria in a 2D Quorum Sensing Based Molecular Communication System