Wave effects in stochastic time lagging reaction-diffusion model of quorum-sensing in bacterial populations

The paper is devoted to developing a reaction-diffusion model of bacterial quorum sensing. The mathematical model is formalized by an initial-boundary value problem for a system of time lagging reaction-diffusion partial differential equations. A stochastic algorithm describing the self-similar process of bacterial population dynamics is proposed. An implicit finite difference scheme combined with an iterative procedure is derived. Computational experiments allow us to reveal the time-dependent fluctuations of signal substances concentrations observed during bacterial population progress.