Simulation-Optimization Approaches for the Network Immunization Problem with Quarantining

TL;DR

This work studies immunization in a population represented by an activity-based contact hypergraph under a SEIR model with quarantining and contact tracing. It introduces two simulation-optimization approaches: a stochastic programming heuristic that uses infection forests from baseline simulations to select up to k immunized nodes, and a parallelized genetic algorithm that combines small- and large-scale simulations to balance speed and uncertainty. Applied to DTU university data with COVID-like parameters, the SP method often yields the best performance across graphs, while the GA consistently ranks among the top methods, and both approaches outperform many centrality-based baselines. The study also shows that immunization can outperform, and further enhance, strategies that minimize distinct contacts, especially when combined; these results support the use of simulation-optimization for complex, realistic epidemic control problems and point to directions for scaling and robustness in future work.

Abstract

Vaccination has played an important role in preventing the spread of infectious diseases. However, the limited availability of vaccines and personnel at the roll-out of a new vaccine and the costs of vaccination campaigns often limit how many people can be vaccinated. Network immunization thus focuses on selecting a fixed-size subset of individuals to vaccinate so as to minimize the disease spread. In this paper, we consider simulation-optimization approaches for this selection problem. Here, the simulation of disease spread in an activity-based contact graph allows us to consider the effect of contact tracing and a limited willingness to test and quarantine. First, we develop a stochastic programming heuristic based on sampling infection forests from the simulation. Second, we propose a genetic algorithm tailored to the immunization problem that combines simulation runs of different sizes to balance the time needed to find promising solutions with the uncertainty resulting from simulation. Both approaches are tested on data from a major university in Denmark and disease characteristics representing those of COVID-19. Our results show that the proposed methods are competitive with a large number of centrality-based measures over a range of disease parameters and that especially the stochastic programming heuristic can outperform them for a considerable number of these instances. Finally, we compare network immunization against our previously proposed approach of limiting distinct contacts. Although, independently, network immunization has a larger impact in reducing disease spread, we show that the combination of both methods reduces the disease spread even further.

Figures (17)

• Figure 1: A visualization of the activity-based contact hypergraph for an example in which 12 individuals (nodes) attend three activities (blue/dash-dotted, green/dotted, and red/dashed hyperarcs) spanning six time periods. The periods in which a hyperarc is active are denoted next to the hyperarc.
• Figure 2: Transition rates for the discrete time Markov chain describing the health states of individuals at any timestep $t \in T$.
• Figure 3: Illustration of the effect of immunizing node 7 in two seperate infection forests.
• Figure 4: Illustration of our GA framework. Each solution in the solution population is first evaluated in parallel using smaller simulation runs in each iteration, after which the most promising solutions are evaluated using a larger simulation run. Moreover, crossover and mutation are applied to obtain the solution population for the next iteration.
• Figure 5: Visualization of the DTU contact graph $G'$, where each node indicates a student and an arc connects two students if they participate at least once in the same course. The node size and color intensity indicate the connectivity of a node, i.e., more connected nodes are darker and larger.

Theorems & Definitions (1)

• Definition 1