I have two pointers to explanations of epidemiology models for COVID-19 today.

One is a cartoon version by Zach Weinersmith, who draws the Saturday Morning Breakfast Cereal cartoon. He drew the cartoon for FiveThirtyEight:

The cartoon is intended for the general public and provides an overview of why the models have such huge uncertainties. Some of the content replicates what FiveThirtyEight wrote on 2020 March 31, but the cartoon format may make it more digestible to the public.

For people who want to dive into the details, Wolfram has released a notebook on epidemiological models:

This notebook is an excerpt from the set of full notebooks which can be found on the Wolfram Cloud, starting with: EpidemiologicalModelsForInfluenzaAndCOVID-19–part_1.nb

Introduction

The COVID-19 outbreak, initially in China and now throughout the world, has captured the interest of a large number of organizations and individuals alike. Some effort has been spent to model (or at least visualize) the geographic spread [JHU][JEP]. There have also been some reports of epidemiological models [TG][PYZ][ZCW][JDL][EGE][AA] that have been developed in an effort to estimate parameters that can be used to project the severity of the outbreak, its duration, and the mortality rate.

This report has to main goals. 1) It aims to put some of these modeling efforts into perspective so that conclusions and predictions can be better understood. We will be using compartmental models that allow one to describe the flow of individuals from one health state to another. We will attempt to employ just the right kinds of compartments and connections that are supported by the available data. As the noted statistician G. E. P. Box admonished us, “All models are wrong, but some models are useful.” It is also important know the assumptions on which the models are predicated. 2) It demonstrates the breadth of the Wolfram Language which makes these analyses relatively straight forward, from the retrieval of data from the web, to modeling and data fitting, to exposition and presentation, all in a single interactive document.

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This notebook uses Wolfram’s math tools (Mathematica) to build some of the simplest models that have any hope of fitting the data. They first show fits to some simple special cases (flu outbreaks in boarding schools), where the models do a good job of fitting the data. Then they try applying the models to data from Hubei province in China, where the first outbreak happened. The models there seem to do poor job of fitting the data—in particular, all the models they tried show a much longer exponential tail of cases towards the end of the outbreak, which does not match the data reported from China. It is not clear what assumptions in the model need to be changed to account for the discrepancy. I suspect that their models would have the same problems with South Korean data also.