Time Is Of The Essence: Incorporating Phase-Type Distributed Delays And Dwell Times Into ODE Models

TL;DR

This paper introduces a method to incorporate phase-type distributed delays and dwell times into ODE models using the Generalized Linear Chain Trick, enhancing their flexibility in modeling time delays.

Contribution

It generalizes the GLCT to create new ODE models with phase-type distributed delays, broadening the scope of delay assumptions in ODE modeling.

Findings

New ODE models with phase-type delays demonstrated.

Enhanced flexibility in modeling time delays.

Framework applicable to various scientific fields.

Abstract

Ordinary differential equations (ODE) models have a wide variety of applications in the fields of mathematics, statistics, and the sciences. Though they are widely used, these models are sometimes viewed as inflexible with respect to the incorporation of time delays. The Generalized Linear Chain Trick (GLCT) serves as a way for modelers to incorporate much more flexible delay or dwell time distribution assumptions than the usual exponential and Erlang distributions. In this paper we demonstrate how the GLCT can be used to generate new ODE models by generalizing or approximating existing models to yield much more general ODEs with phase-type distributed delays or dwell times.