A new formulation of compartmental epidemic modelling for arbitrary distributions of incubation and removal times

TL;DR

This paper introduces a flexible compartmental epidemic model that incorporates arbitrary distributions for incubation and removal times, improving realism over traditional exponential assumptions, and validates it against agent-based simulations.

Contribution

A novel formulation of SEIR models that allows arbitrary incubation and removal time distributions, with validation against agent-based simulations and provided software implementations.

Findings

Good agreement with agent-based models in different scenarios

Asymptotic logistic solutions fit simulation data well

Flexible modeling of incubation and removal times enhances realism

Abstract

The paradigm for compartment models in epidemiology assumes exponentially distributed incubation and removal times, which is not realistic in actual populations. Commonly used variations with multiple exponentially distributed variables are more flexible, yet do not allow for arbitrary distributions. We present a new formulation, focussing on the SEIR concept that allows to include general distributions of incubation and removal times. We compare the solution to two types of agent-based model simulations, a spatially homogeneous one where infection occurs by proximity, and a model on a scale-free network with varying clustering properties, where the infection between any two agents occurs via their link if it exists. We find good agreement in both cases. Furthermore a family of asymptotic solutions of the equations is found in terms of a logistic curve, which after a non-universal time shift, fits extremely well all the microdynamical simulations. The formulation allows for a simple numerical approach; software in Julia and Python is provided.