We consider a global (location independent) model of pandemic growth which generalizes the SIR model to accommodate important features of the COVID-19 pandemic, notably the implementation of pandemic reduction measures. This SHIR model is applied to COVID-19 data, and shows promise as a simple, tractable formalism with few parameters that can be used to model pandemic case numbers. As an example we show that the average time dependence of new COVID-19 cases per day from 15 Central and Western European countries is in good agreement with the analytic, parameter-free prediction of the model
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