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<p>Epidemic control in federated societies poses significant challenges due to jurisdictional autonomy, whereby centralized interventions may encounter resistance, reducing their overall effectiveness. To address this issue, this paper develops a distributed control strategy based on distributed model predictive control (DMPC), enabling individual jurisdictions to make autonomous local decisions while coordinating to achieve society-wide disease eradication. For this purpose, the society is modeled as a three-layer network under the susceptible–infected–water–susceptible (SIWS) epidemic framework. The first layer is a communication layer that links policymakers and water agencies, facilitating coordination despite disruptions in physical connectivity. The second layer is a city-connection layer, in which local SIS epidemic dynamics are coupled through human mobility within an agent-based framework. The third layer is a water-connection layer that captures shared waterborne transmission pathways among jurisdictions. Policymakers synchronously optimize antiviral treatment strategies using information exchanged with neighboring jurisdictions, while water agencies optimize water purification strategies. A time-varying compatibility constraint is introduced to bound discrepancies in exchanged information and ensure inter-agent consistency. Furthermore, a positively invariant safe set, together with a terminal control law, guarantees recursive feasibility and constraint satisfaction. Theoretical analysis establishes closed-loop asymptotic stability and convergence to the disease-free equilibrium through Lyapunov-based cost decrease arguments and linear matrix inequality conditions. The main contributions of this work include the development of a three-layer multi-agent SIWS framework, the design of a synchronous DMPC algorithm incorporating compatibility constraints, and the establishment of rigorous guarantees for recursive feasibility and asymptotic stability. The effectiveness of the proposed approach is validated through simulations under diverse epidemic outbreak scenarios.</p>

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Distributed model predictive control for agent-based epidemic networks with waterborne coupling

  • 期刊论文

  • 发表日期：

    2026年7月27日

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  • Zohreh Abbasi,
  • Xinzhi Liu,
  • Sara Grundel,
  • Peter Benner

摘要

Epidemic control in federated societies poses significant challenges due to jurisdictional autonomy, whereby centralized interventions may encounter resistance, reducing their overall effectiveness. To address this issue, this paper develops a distributed control strategy based on distributed model predictive control (DMPC), enabling individual jurisdictions to make autonomous local decisions while coordinating to achieve society-wide disease eradication. For this purpose, the society is modeled as a three-layer network under the susceptible–infected–water–susceptible (SIWS) epidemic framework. The first layer is a communication layer that links policymakers and water agencies, facilitating coordination despite disruptions in physical connectivity. The second layer is a city-connection layer, in which local SIS epidemic dynamics are coupled through human mobility within an agent-based framework. The third layer is a water-connection layer that captures shared waterborne transmission pathways among jurisdictions. Policymakers synchronously optimize antiviral treatment strategies using information exchanged with neighboring jurisdictions, while water agencies optimize water purification strategies. A time-varying compatibility constraint is introduced to bound discrepancies in exchanged information and ensure inter-agent consistency. Furthermore, a positively invariant safe set, together with a terminal control law, guarantees recursive feasibility and constraint satisfaction. Theoretical analysis establishes closed-loop asymptotic stability and convergence to the disease-free equilibrium through Lyapunov-based cost decrease arguments and linear matrix inequality conditions. The main contributions of this work include the development of a three-layer multi-agent SIWS framework, the design of a synchronous DMPC algorithm incorporating compatibility constraints, and the establishment of rigorous guarantees for recursive feasibility and asymptotic stability. The effectiveness of the proposed approach is validated through simulations under diverse epidemic outbreak scenarios.