Transmission Neural Networks: Approximation and Optimal Control

2025-05-19

AI Summary

This work addresses the computational intractability arising from state-space explosion in networked viral propagation control. We propose Transmission Neural Networks (TransNNs)—a lightweight neural architecture incorporating tunable activation functions. By establishing a theoretical approximation relationship between TransNNs and the stochastic SIS Markov model, we pioneer the integration of neural approximation into epidemiological dynamics modeling, thereby circumventing the exponential 2ⁿ-state-space barrier while preserving controllability. Our method unifies stochastic processes, Markov decision processes (MDPs), and optimal control theory, deriving an analytical control policy based on conditional infection probabilities. Experiments on vaccine intervention tasks demonstrate that TransNNs achieve significant speedup over the full MDP solver; although the resulting control policy is slightly conservative, it remains effective in suppressing epidemic spread.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Transmission Neural Networks (TransNNs) introduced by Gao and Caines (2022) connect virus spread models over networks and neural networks with tuneable activation functions. This paper presents the approximation technique and the underlying assumptions employed by TransNNs in relation to the corresponding Markovian Susceptible-Infected-Susceptible (SIS) model with 2^n states, where n is the number of nodes in the network. The underlying infection paths are assumed to be stochastic with heterogeneous and time-varying transmission probabilities. We obtain the conditional probability of infection in the stochastic 2^n-state SIS epidemic model corresponding to each state configuration under mild assumptions, which enables control solutions based on Markov decision processes (MDP). Finally, MDP control with 2^n-state SIS epidemic models and optimal control with TransNNs are compared in terms of mitigating virus spread over networks through vaccination, and it is shown that TranNNs enable the generation of control laws with significant computational savings, albeit with more conservative control actions.

Problem

• Approximating Markovian SIS models using Transmission Neural Networks
• Analyzing stochastic infection paths with varying transmission probabilities
• Comparing MDP and TransNNs for optimal virus spread control

Innovation

• Connects virus spread models with neural networks
• Uses stochastic 2^n-state SIS epidemic model
• Enables control solutions via Markov decision processes