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Modeling approaches
This can be thought of as a general approach to modeling rather than a specific model.
The population is divided into compartments, with the assumption that every individual in the same compartment has the same characteristics.The models are usually investigated through ordinary differential equations (which are deterministic), but can also be viewed in a stochastic framework, which is more realistic but also more complicated to analyze.
https://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology
This model uses death rates rather than confirmed cases, and essentially curve fits the data rather than trying to assume an underlying model.
https://github.com/mrc-ide/COVID19_CFR_submission Use a Gamma model to account for exponential growth, using a growth rate of 0.14 a day and Bayesian estimates of variance
Here's a different approach https://www.washingtonpost.com/graphics/2020/world/corona-simulator/
German Robert-Koch-Institut (in German!) https://www.rki.de/DE/Content/InfAZ/N/Neuartiges_Coronavirus/Modellierung_Deutschland.pdf?__blob=publicationFile