Estimation of the SIR model parameters using neural networks

Coelho, Flávio Codeço
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In the last decades, dengue fever has become the most prevalent epidemic disease caused by an arborvirus in the world. Its socio-economic impact has been especially overloading to developing countries, which struggle with the lack of appropriate resources and policies to contain the disease. Good planning has been essential to this end and dramatically benefits from outbreak forecasts. Over time, several deterministic and stochastic mathematical models of dengue epidemics have been proposed. However, the methods used to estimate their parameters usually require complex calculations and strong distributional assumptions that may not be realistic. The goal of this study was to develop a data-driven method to estimate the parameters of epidemiological models using Machine Learning and Artificial Neural Networks (ANNs) that could circumvent such demands. To accomplish this, we created a data set of infectives time series generated with SIR models using parameters derived from previous dengue epidemics and additional random noise. We used the data to train and validate several neural network configurations using the Mean Squared Error (MSE) and the Mean Absolute Percentage Error (MAPE) as the loss function. The test of the best models showed that the MAPE network tended to estimate SIR models that fitted the data better than the MSE network. We then applied the MAPE model to the time series of dengue epidemics that occurred in Brazilian state capitals between 2007 and 2020. The overall results indicate that ANN data-driven estimation methods can be used to fit a deterministic epidemiological model to noisy data, at least in cases where the dynamic processes that underlie the generation of observations are similar to those specified in the model.

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