Transmission Neural Networks: Approximate Receding Horizon Control for Virus Spread on Networks

TL;DR

This paper introduces a neural network-based approach to approximate and control virus spread on networks, offering computational efficiency and less conservative strategies compared to traditional methods.

Contribution

It establishes TransNNs as upper bounds for infection probabilities and develops a receding horizon control method that improves efficiency and reduces conservativeness.

Findings

TransNNs provide upper bounds on infection probabilities.

The proposed control method achieves significant computational savings.

Numerical results show less conservative control actions.

Abstract

Transmission Neural Networks (TransNNs) proposed by Gao and Caines (2022) serve as both virus spread models over networks and neural network models with tuneable activation functions. This paper establishes that TransNNs provide upper bounds on the infection probability generated from the associated Markovian stochastic Susceptible-Infected-Susceptible (SIS) model with 2^n state configurations where n is the number of nodes in the network, and can be employed as an approximate model for the latter. Based on such an approximation, a TransNN-based receding horizon control approach for mitigating virus spread is proposed and we demonstrate that it allows significant computational savings compared to the dynamic programming solution to Markovian SIS model with 2^n state configurations, as well as providing less conservative control actions compared to the TransNN-based optimal control. Finally, numerical comparisons among (a) dynamic programming solutions for the Markovian SIS model, (b) TransNN-based optimal control and (c) the proposed TransNN-based receding horizon control are presented.