USask Mathematics & Statistics Colloquium: Wesley Ridgway

Abstract: Agent-based models (ABMs) are widely used to describe within-host disease dynamics, with individual cells and bacteria governed by prescribed rules. While these models can capture complex biological interactions, they are often computationally expensive and are difficult to analyse mathematically. In systems with many agents, systematic coarse-graining provides a way to derive continuum models that capture the collective behaviour of the underlying agents.

In this talk, I will discuss two examples of coarse-graining motivated by within-host bacterial infections. First, I will consider an ABM in which immune cells ingest nearby bacteria, and intracellular bacterial loads evolve through stochastic birth and clearance processes. Coarse-graining yields a reaction-diffusion system structured by intracellular bacterial load. Using a Smulochowski-type analysis of an auxillary diffusion problem, I will show how effective coefficients can be obtained explicitly in terms of the original ABM parameters.  Second, I will consider chemical signalling by cells undergoing Brownian motion. Using Green’s functions and asymptotic analysis, I will show how the signal concentration experienced by individual cells can be decomposed into a mean-field contribution and a self-signalling contribution, the latter of which is absent from conventional mean-field descriptions. These examples illustrate how systematic coarse-graining can simplify complex models while retaining important features of the underlying microscopic dynamics.