Analytical predictions of reactive and inert interaction events, from infection transmission to movement in disordered media

Interactions between a particle or an agent with other agents or with the environment underpin a large variety of physical, chemical and biological processes. A methodology to describe such interactions exactly without relying on time-consuming simulations is via a discrete space-time description, the so-called lattice random walk formalism. I will present a general theory to quantify the spatio-temporal dynamics of reactive (probability non-preserving) interactions, i.e. absorption, encounter and transmission events, as well as inert (probability preserving) interactions in a disordered environment, i.e. local biases due to e.g. permeable barriers, excluded regions, or variable diffusivity. The formalism is valid independently of the topology, the number of agents and the number of targets and I will show results with diffusive motion for hypercubic, hexagonal and triangular lattices as well as some preliminary results on networks. The theory has been extended also to the persistent case, that is the correlated lattice random walker, and in that context I will discuss recent findings to quantify an ant foraging experiment in a Y-maze (honeycomb lattice) arena