The COVID-19 pandemic has motivated a resurgence in the use of phenomenological growth models for predicting the early dynamics of infectious diseases. These models assume that time is a continuous variable, whereas in the present contribution the discrete versions of Gompertz and Generalized Logistic models are used for early monitoring and short-term forecasting of the spread of an epidemic in a region. The time-continuous models are represented mathematically by first-order differential equations, while their discrete versions are represented by first-order difference equations that involve parameters that should be estimated prior to forecasting. The methodology for estimating such parameters is described in detail. Real data of COVID-19 infection in Cuba is used to illustrate this methodology. The proposed methodology was implemented for the first thirty-five days and was used to predict accurately the data reported for the following twenty days.
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