A Quantum Approach for Optimal Transient Control in Network-Based Epidemic Models

TL;DR

The paper addresses the NP-hard problem of optimally deploying mobility restrictions in network-based epidemics with limited pharmaceutical options. It proposes a QUBO formulation that enables both quantum annealing and gate-based quantum algorithms (e.g., QAOA) to determine transient, rolling-horizon isolation policies for SIS and SIR dynamics, using realistic Italian mobility data and synthetic networks. Results show quantum methods achieve infection reductions comparable to classical solvers while offering orders-of-magnitude faster solve times, particularly in high-dimensional networks, demonstrating potential for real-time decision support in public health. The work highlights the practical viability of quantum optimization for complex networked dynamical systems and points to future extensions, including longer horizons, alternative interventions, and quantum-inspired approaches.

Abstract

Effective epidemic control is crucial for mitigating the spread of infectious diseases, particularly when pharmaceutical interventions such as vaccines or treatments are limited. Non-pharmaceutical strategies, including mobility restrictions, are key in reducing transmission rates but require careful optimization to balance public health benefits and socioeconomic costs. Quantum computing is emerging as a powerful tool for solving complex optimization problems that are intractable for classical methods and can thus be leveraged to handle mobility restrictions. This article presents a new approach to optimizing epidemic control strategies using quantum computing techniques. We focus on non-pharmaceutical interventions, particularly mobility restriction, modeled as a discrete-time network epidemic process based on the susceptible-infected-susceptible and susceptible-infected-removed frameworks. The control problem is formulated as a combinatorial optimization task, inherently NP-hard due to the binary nature of intervention decisions. To tackle this computational complexity, we derive a Quadratic Unconstrained Binary Optimization representation of the control problem, enabling its efficient solution via quantum computing resources. Our methodology is validated through numerical simulations on realistic case studies, showcasing the potential of quantum algorithms for enhancing epidemic control strategies. These findings pave the way for leveraging quantum optimization in broader applications of networked dynamical systems, demonstrating its viability for complex decision-making processes in public health management.

Figures (11)

• Figure 1: Proposed quantum approach for optimal transient control in network-based epidemic models.
• Figure 2: Network population model with the entries of weight matrix $A$.
• Figure 3: Schematic of the SIS and SIR epidemic models.
• Figure 4: Map of Italy showing the first-level administrative divisions (regions) and the connections between them. The thickness of each link is proportional to the corresponding weight in the adjacency matrix $\mathbf{A}$.
• Figure 5: Results of our numerical simulations (SIS). In (a--d) and (e--h), we report the plots obtained at the granularity of regions and provinces, respectively, with different starting dates.