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A new formulation of compartmental epidemic modelling for arbitrary distributions of incubation and removal times
Populations and Evolution · Submitted 20 May 2020
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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.
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The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The paradigm for compartment models in epidemiology assumes exponentially distributed incubation and removal times, which is not realistic in actual populations. | background 0.94 | 0.05 | 0.03 | asserted 1.00 |
| s1 | Commonly used variations with multiple exponentially distributed variables are more flexible, yet do not allow for arbitrary distributions. | gap 0.52 | 0.05 | 0.02 | asserted 1.00 |
| s2 | We present a new formulation, focussing on the SEIR concept that allows to include general distributions of incubation and removal times. | contribution 1.00 | 0.94 | 0.23 | asserted 1.00 |
| s3 | 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. | method 0.96 | 0.92 | 0.04 | asserted 0.91 |
| s4 | We find good agreement in both cases. | result 1.00 | 0.96 | 0.22 | asserted 1.00 |
| s5 | 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. | result 0.99 | 0.96 | 0.34 | asserted 1.00 |
| s6 | The formulation allows for a simple numerical approach; software in Julia and Python is provided. | contribution 0.72 | 0.86 | 0.06 | asserted 1.00 |
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Original 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.
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A prominent and frequently applied type is the classical epidemiological framework [ref] modeling susceptible, exposed, infected, and recovered agents (SEIR) that has also found its application in several forecasting approaches [ref] .
Backtesting the predictability of COVID-19 · Introduction · 0.93
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