  We propose an interacting particle system with a moving boundary to model the
spread of an epidemic. Each individual in a given population starts from some
level of shielding, given by a non-negative real number, and this level then
evolves over time according to diffusive dynamics driven by independent
Brownian motions. If the level of shielding gets too low, individuals will find
themselves in `at-risk' situations, as captured by proximity to a lower moving
boundary, which we call the `advancing front' of the epidemic. Specifically,
local time is accumulated along this boundary and, while individuals are
initially reflected, infection may eventually occur with a likelihood depending
on the accumulated local time as well as the intrinsic infectiousness of the
disease and the current contagiousness within the population. Our main
technical contribution is to give a rigorous formulation of this model in the
form of a well-posed interacting particle system. Moreover, we exploit the
precise construction of the system to establish an important martingale
property of the infected proportion and present a result on its limiting
behaviour if the size of the population is sent to infinity.
