Date of Award

2024

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Complex Systems

First Advisor

Jean-Gabriel Young

Second Advisor

Laurent Hébert Dufresne

Abstract

Which individual should we vaccinate to minimize the spread of a disease? Designing optimal interventions of this kind can be formalized as an optimization problem on networks, in which we have to select a budgeted number of dynamically important nodes to receive treatment that optimizes a dynamical outcome. Describing this optimization problem requires specifying the network, a model of the dynamics, and an objective for the outcome of the dynamics. In real-world contexts, these inputs are vulnerable to misspecification---the network and dynamics must be inferred from data, and the decision-maker must operationalize some (potentially abstract) goal into a mathematical objective function. Moreover, the tools to make reliable inferences---on the dynamical parameters, in particular---remain limited due to computational problems and issues of identifiability. Given these challenges, models thus remain more useful for building intuition than for designing actual interventions. This thesis seeks to elevate complex dynamical models from intuition-building tools to methods for the practical design of interventions.

First, we circumvent the inference problem by searching for robust decisions that are insensitive to model misspecification.If these robust solutions work well across a broad range of structural and dynamic contexts, the issues associated with accurately specifying the problem inputs are largely moot. We explore the existence of these solutions across three facets of dynamic importance common in network epidemiology.

Second, we introduce a method for analytically calculating the expected outcome of a spreading process under various interventions. Our method is based on message passing, a technique from statistical physics that has received attention in a variety of contexts, from epidemiology to statistical inference.We combine several facets of the message-passing literature for network epidemiology.Our method allows us to test general probabilistic, temporal intervention strategies (such as seeding or vaccination). Furthermore, the method works on arbitrary networks without requiring the network to be "locally tree-like".This method has the potential to improve our ability to discriminate between possible intervention outcomes.

Overall, our work builds intuition about the decision landscape of designing interventions in spreading dynamics. This work also suggests a way forward for probing the decision-making landscape of other intervention contexts. More broadly, we provide a framework for exploring the boundaries of designing robust interventions with complex systems modeling tools.

Language

en

Number of Pages

111 p.

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