A stochastic model of an early warning system for detecting anomalous incidence values of COVID-19

Ana Filipa Duarte, Amílcar Soares, Maria João Pereira, André Peralta-Santos, Pedro Pinto Leite, Leonardo Azevedo

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The ability to identify and predict outbreaks during epidemic and pandemic events is critical to the development and implementation of effective mitigation measures by the relevant health and political authorities. However, the spatiotemporal prediction of such diseases is not straightforward due to the highly non-linear behaviour of its evolution in both space and time. The methodology proposed herein is the basis of an early warning system to predict short-term anomalous values (i.e., high and low values) of the incidence of COVID-19 at the municipality level for mainland Portugal. The proposed modelling tool combines stochastic sequential simulation and machine learning, namely symbolic regression, to model the spatiotemporal evolution of the disease. The machine learning component is used to model the 14-day incidence rate curves of COVID-19, as provided by the Portuguese Directorate-General for Health, while the geostatistical simulation component models the spatial distribution of these predictions, for a simulation grid comprising the metropolitan area of Lisbon, following a pre-defined spatial continuity pattern. The method is illustrated for a period of 5 months during 2021, and considering the entire set of 19 municipalities belonging to the metropolitan area of Lisbon, Portugal. The results show the ability of the early warning system to predict and detect anomalous high and low incidence rate values for different periods of the pandemic event during this period.

Original languageEnglish
Pages (from-to)41-54
Number of pages14
JournalMathematical Geosciences
Issue number1
Publication statusPublished - Jan 2024


  • COVID-19
  • Early warning system
  • Geostatistical simulation
  • Symbolic regression


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