Network-Based Interventions for HIV Prevention via Cascade-Aware Suppression of Transmission

Many important outcomes unfold as dynamic cascades, including product adoption, disease spread, financial distress, and information diffusion. A central challenge is to recover the hidden influence network behind these cascades. Existing methods typically assume a specific diffusion model, and their performance degrades substantially when that assumption is misspecified. We propose CascadeNet, a Jacobian-based machine learning framework for network recovery that does not require specifying a diffusion mechanism. The key idea is that the underlying influence structure can be characterized by the Jacobian of the one-step transition function. CascadeNet first constructs a flexible estimator of the transition function, and further applies Neyman-orthogonal debiasing via the Riesz representer, so that the debiased Jacobian is $\sqrt{n}$-consistent and asymptotically normal, enabling formal inference on the network structure. We validate CascadeNet in both a simulation exercise and a real-world empirical application. In simulations, where the data-generating process is known, CascadeNet achieves the highest network recovery accuracy across nine common data-generating processes. In an empirical application to COVID-19 transmission across Spain's 52 provinces, CascadeNet recovers transmission networks that are significantly correlated with the true inter-province mobility network, whereas networks recovered by baseline methods show no significant alignment with the ground truth.

Networked systems, from power grids to traffic networks and cloud clusters, carry loads across nodes with limited capacity. A node whose load exceeds its capacity fails and sheds its load onto its neighbors, which can trigger a system-wide cascade. We study how to allocate a fixed capacity budget across nodes to resist these cascades under local load redistribution. The problem is difficult because no optimal allocation is known, and the fail-or-survive objective is non-differentiable and piecewise constant, so exact and gradient-based optimization methods do not directly apply. We introduce TANGCO (Topology-Aware Neural Graph-Guided Capacity Optimization), which uses a graph neural network policy trained through the cascade simulator with policy-gradient learning and a heuristic anchor. We evaluate TANGCO on five synthetic graph families and five real networks spanning power, road, air, and Internet topologies. The learned policy improves on the best of four hand-designed heuristics in all 450 synthetic instances and in 40 of 45 real-network conditions, with robustness gains ranging from 1.6% to 246%. The learned policies transfer to unseen graphs within a family and partially across related topologies, and TANGCO$^{pre}$, pre-trained on synthetic graphs, matches per-network training on unseen real networks. Training scales near-linearly with graph size, and TANGCO$^{pre}$ allocates on a new network with no per-target training, matching the deployment cost of a hand-designed heuristic. Free-vector variants without the GNN, stay close to the heuristics, so the graph representation carries the gain beyond numerical search. Finally, analysis of the learned allocations identifies when local risk is sufficient, leads to an improved closed-form heuristic, and reveals the regimes where a topology-aware learned policy remains necessary.

Intense wildfire seasons require critical prioritization decisions to allocate scarce suppression resources over a dispersed geographical area. This paper develops a predictive and prescriptive approach to jointly optimize crew assignments and wildfire suppression. The problem features a discrete resource-allocation structure with endogenous wildfire demand and non-linear wildfire dynamics. We formulate an integer optimization model with crew assignments on a time-space-rest network, wildfire dynamics on a time-state network, and linking constraints between them. We develop a two-sided branch-and-price-and-cut algorithm based on: (i) a two-sided column generation scheme that generates fire suppression plans and crew routes iteratively; (ii) a new family of cuts exploiting the knapsack structure of the linking constraints; and (iii) novel branching rules to accommodate non-linear wildfire dynamics. We also propose a data-driven double machine learning approach to estimate wildfire spread as a function of covariate information and suppression efforts, mitigating observed confounding between historical crew assignments and wildfire growth. Extensive computational experiments show that the optimization algorithm scales to otherwise intractable real-world instances; and that the methodology can enhance suppression effectiveness in practice, resulting in significant reductions in area burned over a wildfire season and guiding resource sharing across wildfire jurisdictions.