Prediction and Prevention of Pandemics via Graphical Model Inference and Convex Programming

TL;DR

This paper models pandemic spread using graphical models and convex programming to predict infection probabilities and identify minimal control actions for prevention, providing a computational framework for public health decision-making.

Contribution

It introduces a novel approach combining Ising models and convex optimization to infer infection spread and optimize prevention strategies in dense networks.

Findings

Most dense Ising models exhibit bi-modal infection states.

Prevention strategies can be formulated as convex optimization problems.

The approach enables efficient computation of minimal intervention sets.

Abstract

Hard-to-predict bursts of COVID-19 pandemic revealed significance of statistical modeling which would resolve spatio-temporal correlations over geographical areas, for example spread of the infection over a city with census tract granularity. In this manuscript, we provide algorithmic answers to the following two inter-related public health challenges. (1) Inference Challenge: assuming that there are $N$ census blocks (nodes) in the city, and given an initial infection at any set of nodes, what is the probability for a subset of census blocks to become infected by the time the spread of the infection burst is stabilized? (2) Prevention Challenge: What is the minimal control action one can take to minimize the infected part of the stabilized state footprint? To answer the challenges, we build a Graphical Model of pandemic of the attractive Ising (pair-wise, binary) type, where each node represents a census track and each edge factor represents the strength of the pairwise interaction between a pair of nodes. We show that almost all attractive Ising Models on dense graphs result in either of the two modes for the most probable state: either all nodes which were not infected initially became infected, or all the initially uninfected nodes remain uninfected. This bi-modal solution of the Inference Challenge allows us to re-state the Prevention Challenge as the following tractable convex programming: for the bare Ising Model with pair-wise and bias factors representing the system without prevention measures, such that the MAP state is fully infected for at least one of the initial infection patterns, find the closest, in $l_1$ norm, set of factors resulting in all the MAP states of the Ising model, with the optimal prevention measures applied, to become safe.