Non-local model of chemotaxis based on peer attraction

Movement is critical for bacterial species inhabiting soils because nutrient availability is limited and heterogeneously distributed both in space and time. Recent live microscopy experiments show that bacteria form flocks when navigating through porous medium, and complex cell-cell interactions may be required to maintain such flocks. Here we propose a non-local model to study how peer attraction can affect flocking patterns in a porous medium. We establish the existence and uniqueness of the solution of the problem, propose a numerical scheme for simulations of the non-local convection-diffusion equation, and investigate the numerical convergence of the scheme. Numerical simulations showed that the strength of peer attraction is critical to control the size, shape, and nature of movement of the flocks in a porous network. MSC Classification 35F31, 92Cxx, 92-10