Building mean field ODE models using the generalized linear chain trick & Markov chain theory
Paul J. Hurtado, C. S. Richards
Abstract
that represent the absorption time distributions for finite-state, continuous time Markov chains (CTMCs). Here we review CTMCs and phase-type distributions, then illustrate how to use the GLCT to efficiently build ODE models from underlying stochastic model assumptions. We introduce two novel model families by using the GLCT to generalize the Rosenzweig-MacArthur predator-prey model, and the SEIR model. We illustrate the kinds of complexity that can be captured by such models through multiple examples. We also show the benefits of using a GLCT-based model formulation to speed up the computation of numerical solutions to such models. These results highlight the intuitive nature, and utility, of using the GLCT to derive ODE models from first principles.