# A Quantum-Compliant Formulation for Network Epidemic Control

## TL;DR

This paper presents a quantum-compatible optimization framework for controlling epidemic spread on networks through mobility bans, balancing healthcare and social costs, and leveraging quantum computing for NP-hard problem solving.

## Contribution

It introduces a QUBO formulation for epidemic control via mobility bans, enabling quantum computing approaches to address the NP-hard optimization problem.

## Key findings

- QUBO formulation effectively models the control problem.
- Quantum computing can potentially solve the NP-hard problem efficiently.
- Framework balances epidemic control with social and economic costs.

## Abstract

We deal with controlling the spread of an epidemic disease on a network by isolating one or multiple locations by banning people from leaving them. To this aim, we build on the susceptible-infected-susceptible and the susceptible-infected-removed discrete-time network models, encapsulating a control action that captures mobility bans via removing links from the network. Then, we formulate the problem of optimally devising a control policy based on mobility bans that trades-off the burden on the healthcare system and the social and economic costs associated with interventions. The binary nature of mobility bans hampers the possibility to solve the control problem with standard optimization methods, yielding a NP-hard problem. Here, this is tackled by deriving a Quadratic Unconstrained Binary Optimization (QUBO) formulation of the control problem, and leveraging the growing potentialities of quantum computing to efficiently solve it.