The Mathematics of Deep Neural Networks with Application in Predicting the Spread of Avian Influenza Through Disease-Informed Neural Networks (DINNs)

Woldegebriel AssefaWoldegerima

York University

"The Mathematics of Deep Neural Networks with Application in Predicting the Spread of Avian Influenza Through Disease-Informed Neural Networks (DINNs)"

Deep learning has emerged in many fields in recent times where neural networks are used to learn and understand data. This study combines deep learning frameworks with epidemiological models and is aimed specifically at the creation and testing of DINNs with a view to modeling the infection dynamics of epidemics. Our research thus trains the DINN on synthetic data derived from an SI-SIR model designed for Avian influenza and shows the model’s accuracy in predicting extinction and persistence conditions. In the method, a twelve hidden layer model was constructed with sixty-four neurons per layer and ReLU activation function was used. The network is trained to predict the time evolution of five state variables for birds and humans over 50,000 epochs. The overall loss minimized to 0.000006, characterized by a combination of data and physics losses, enabling the DINN to follow the differential equations describing the disease progression.
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