A number of PDEs occurring in mathematical biology are of the
advection-diffusion-reaction type. With a view toward solving such
systems in quite irregular or moving geometry, we consider some
aspects of a smoothed particle hydrodynamics (SPH) or finite mass
method approach. The advection properties of these Lagrangian
methods are quite good. Challenges are the efficient modeling of
diffusion and incorporation of nonlinear reactions. We will
discuss some options and provide numerical results for simple
test problems.