Speaker: Lynn Schreyer (Department of Mathematics and Statistics, Washington State University)
Title: Compartment Models with Memory

Abstract: The beauty and simplicity of compartment modeling makes it a useful approach for simulating dynamics in an amazingly wide range of applications, including pharmacokinetics (where e.g. a liver is considered a compartment), global carbon cycling (different depths of soils are considered compartments), and epidemiology (SIR models!) and population dynamics. These contexts, however, often involve compartment-to-compartment flows that are physically incongruent with the conventional assumption of complete mixing that results in exponential residence times in linear models. Here we detail a general method for assigning any desired residence time distribution to a given intercompartmental flow, extending compartment modeling capability to transport operations, power-law residence times, diffusions, etc., without resorting to composite compartments, fractional calculus, or partial differential equations (PDEs) for diffusive transport. This is achieved by writing the mass exchange rate coefficients as functions of age-in-compartment as done in one of the first compartment models (epidemiology!) in 1917, at the cost of converting the usual ordinary differential equations to a system of first-order PDEs. Example calculations demonstrate incorporation of advective lags, advective-dispersive transport, power-law residence time distributions, or diffusive domains in compartment models. We also provide simulations of the generalized SIR model presented by Kissler et al. (2020) 11 compartment-model for the COVID epidemic.