Network Epidemic Control via Model Predictive Control: Extended Version
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866917529769738240 |
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| author | Talaei, Mahtab Olshevsky, Alex White, Laura F. Paschalidis, Ioannis Ch. |
| author_facet | Talaei, Mahtab Olshevsky, Alex White, Laura F. Paschalidis, Ioannis Ch. |
| contents | Balancing the societal costs of non-pharmaceutical interventions with epidemic suppression requires adaptive feedback control. Rather than relying on state-dependent operational caps, we formulate an infinite-horizon optimal control problem for a networked SIQR model that strictly enforces suppression via a hard spectral constraint on the transmission dynamics. We derive a safety-critical Model Predictive Control (MPC) approximation that embeds this spectral certificate stage-wise, yielding a tunable exponential decay rate. Furthermore, we construct a terminal set ensuring recursive feasibility and a feasible continuation that decays globally, proving positive invariance directly via the physical depletion of susceptibles rather than standard quadratic Lyapunov functions. To handle prediction uncertainty, we develop a robust counterpart that replaces nominal constraints by upper-envelope versions, recovering recursive feasibility and finite-horizon realized decay. We conclude by validating our approaches using simulation studies that leverage public data from counties in the state of Massachusetts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_13357 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Network Epidemic Control via Model Predictive Control: Extended Version Talaei, Mahtab Olshevsky, Alex White, Laura F. Paschalidis, Ioannis Ch. Optimization and Control Systems and Control Adaptation and Self-Organizing Systems Physics and Society Balancing the societal costs of non-pharmaceutical interventions with epidemic suppression requires adaptive feedback control. Rather than relying on state-dependent operational caps, we formulate an infinite-horizon optimal control problem for a networked SIQR model that strictly enforces suppression via a hard spectral constraint on the transmission dynamics. We derive a safety-critical Model Predictive Control (MPC) approximation that embeds this spectral certificate stage-wise, yielding a tunable exponential decay rate. Furthermore, we construct a terminal set ensuring recursive feasibility and a feasible continuation that decays globally, proving positive invariance directly via the physical depletion of susceptibles rather than standard quadratic Lyapunov functions. To handle prediction uncertainty, we develop a robust counterpart that replaces nominal constraints by upper-envelope versions, recovering recursive feasibility and finite-horizon realized decay. We conclude by validating our approaches using simulation studies that leverage public data from counties in the state of Massachusetts. |
| title | Network Epidemic Control via Model Predictive Control: Extended Version |
| topic | Optimization and Control Systems and Control Adaptation and Self-Organizing Systems Physics and Society |
| url | https://arxiv.org/abs/2604.13357 |