Feasibility assessments of a dynamical approach to compartmental modelling on graphs: Scaling limits and performance analysis

Abstract

Sharkey, Kiss and others developed a dynamical approach to modelling epidemic disease on a contact graph by generating systems of first-order ordinary differential equations expressing the model dynamics [1,2], which are solved to yield exact and deterministic modelling results. However, they left algorithmic generation (and solving) of systems and runtime assessment of the approach as an open question. To address this, we give an open source implementation that takes both a compartmental model and a contact graph as input and then generates and solves a system of equations exactly describing the dynamics of the system. Our implementation uses a moment closure result on single-vertex cutsets in the contact graph to reduce the number of equations required. In runtime experiments, we find that the implementation of the dynamical approach is almost always slower than a comparable Monte Carlo simulation in finding the expected state of the modelling system at a specified time. To complement our runtime evaluations, we give results and bounds on the number of equations required to describe a system as a function of the size of the compartmental model and input graph. We show that a natural extension of the moment closure result on single-vertex cutsets to larger cutsets is only possible for restricted projections of the model states on the cutset. We conclude that the dynamical approach is unlikely to be suitable unless exact, deterministic (rather than simulated) results are essential.