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

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.