Extending ODE models using the Generalized Linear Chain Trick: An SEIR Model Example

Paul Hurtado (May 6, 2020)

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The Linear Chain Trick (LCT) has long been used to build ODE models (specifically, mean field state transition models) by replacing the implicit assumption of exponentially distributed passage times through each state with more "hump shaped" gamma (or more specifically, Erlang) distributions. Recently, we introduced a Generalized Linear Chain Trick (GLCT) where we showed that there was a straightforward way of writing down mean field ODEs for a much broader family of assumed "dwell-time" distributions known as the Phase-type distributions. These are essentially the hitting-time or absorbing-time distributions for Continuous Time Markov Chains (CTMCs), and include Erlang, Hypoexponential, Coxian, and related distributions. Methods for fitting these matrix exponential distributions to data have been developed for applications of queuing theory, allowing for more flexibility than just incorporating best-fit Gamma distributions into ODE model assumptions. In this presentation, I will illustrate how the SEIR model can be extended using the LCT and the GLCT, and how the structure of the resulting model, when viewed through the lens of the GLCT, can be leveraged in subsequent analytical and computational analyses.