# Inference, Prediction, and Control of Networked Epidemics

## TL;DR

This paper introduces a feedback control framework for networked epidemic processes that uses incomplete observations to precisely control and predict epidemic outbreaks without relying on mean field approximations.

## Contribution

It presents a novel feedback control approach leveraging conditional independence and Bayesian inference for epidemic management based on partial observations.

## Key findings

- Conditional independence of infection variables given observations
- Tractable inference and prediction mechanisms for epidemic states
- Effective one-step control to ensure epidemic die-out

## Abstract

We develop a feedback control method for networked epidemic spreading processes. In contrast to most prior works which consider mean field, open-loop control schemes, the present work develops a novel framework for feedback control of epidemic processes which leverages incomplete observations of the stochastic epidemic process in order to control the exact dynamics of the epidemic outbreak. We develop an observation model for the epidemic process, and demonstrate that if the set of observed nodes is sufficiently well structured, then the random variables which denote the process' infections are conditionally independent given the observations. We then leverage the attained conditional independence property to construct tractable mechanisms for the inference and prediction of the process state, avoiding the need to use mean field approximations or combinatorial representations. We conclude by formulating a one-step lookahead controller for the discrete-time Susceptible-Infected-Susceptible (SIS) epidemic process which leverages the developed Bayesian inference and prediction mechanisms, and causes the epidemic to die out at a chosen rate.