Abstract

This work connects models for virus spread on networks with their equivalent neural network representations. Based on this connection, we propose a new neural network architecture, called Transmission Neural Networks (TransNNs) where activation functions are primarily associated with links and are allowed to have different activation levels. This connection also leads to the discovery and the derivation of three new activation functions with tunable or trainable parameters. We show that TransNNs with a single hidden layer and a fixed non-zero bias term are universal function approximators. Moreover, we establish threshold conditions for virus spread on networks where the dynamics are characterized by TransNNs. Finally, we present new derivations of continuous time epidemic models on networks based on TransNNs.
*This is joint work with Peter E. Caines.