It is of vital importance to understand and track the dynamics of rapidly unfolding epidemics. The health and economic consequences of the current COVID-19 pandemic provide a poignant case. Here we demonstrate that a class of widely used models is fundamentally flawed and cannot account for some important features of the viral spread . We suggest an integral equation based method that can be implemented in most of the reported models . Taking the example of COVID-19 data for New York City, we show that our model yields a significantly larger estimate for the initial basic reproduction rate than other models, much more accurately accounts for the dynamics of the epidemic after  restrictive public congregation measures were introduced, and provides a novel way to determine the incubation period . We suggest that no decisions about public health or economic measuresshould be based on any unimproved model .
It is of vital importance to understand and track the dynamics of rapidly unfolding epidemics. The health and economic consequences of the current COVID-19 pandemic provide a poignant case. Here we point out that since they are based on differential equations, the most widely used models of epidemic spread are plagued by an approximation that is not justified in the case of the current COVID-19 pandemic . Taking the example of data from New York City, we show that currently used models significantly underestimate the initial basic reproduction number (R_0). The correct description, based on integral equations, can be implemented in most of the reported models and it much more accurately accounts for the dynamics of the epidemic after sharp changes in R_0 due to restrictive public congregation measures . It also provides a novel way to determine the incubation period , and most importantly, as we demonstrate for several countries, this method allows an accurate monitoring of R_0 and thus a fine-tuning of any restrictive measures. Integral equation based models do not only provide the conceptually correct description, they also have more predictive power than differential equation based models, therefore we do not see any reason for using the latter .
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. We suggest that no decisions about public health or economic measuresshould be based on any unimproved model
, and most importantly, as we demonstrate for several countries, this method allows an accurate monitoring of R_0 and thus a fine-tuning of any restrictive measures. Integral equation based models do not only provide the conceptually correct description, they also have more predictive power than differential equation based models, therefore we do not see any reason for using the latter