Deterministic Bounding Systems for Stochastic Compartmental Spreading Processes

TL;DR

This paper introduces a novel bounding system approach for stochastic compartmental spreading processes that provides guaranteed upper and lower bounds on process moments without requiring prior covariance knowledge.

Contribution

It develops a new method for bounding the dynamics of spreading processes, improving over prior models by not needing initial covariance assumptions and allowing for tighter bounds.

Findings

Bounding systems effectively approximate process moments.

Comparison shows improved bounds over traditional methods.

Applicable to various compartmental spreading models.

Abstract

This paper studies a novel approach for approximating the behavior of compartmental spreading processes. In contrast to prior work, the methods developed describe a dynamics which bound the exact moment dynamics, without explicitly requiring a priori knowledge of non-negative (or non-positive) covariance between pairs of system variables. Moreover, we provide systems which provide both upper- and lower- bounds on the process moments. We then show that when system variables are shown to be non-negatively (or non-positively) correlated for all time in the system's evolution, we may leverage the knowledge to create better approximating systems. We then apply the technique to several previously studied compartmental spreading processes, and compare the bounding systems' performance to the standard approximations studied in prior literature.