Skip to main content
NCBI home page
Elsevier - PMC COVID-19 Collection logoLink to Elsevier - PMC COVID-19 Collection
. 2021 Nov 1;54(14):476–481. doi: 10.1016/j.ifacol.2021.10.400

On the Use of MPC Techniques to Decide Intervention Policies against COVID-19

Zonglin Liu ⁎, Olaf Stursberg ⁎
PMCID: PMC8559534  PMID: 38620907

Abstract

This paper aims at demonstrating how and that model predictive control (MPC) strategies can be used to determine optimal intervention policies against the COVID-19 pandemic. Especially for the time after a first wave of infection and before a vaccine can be safely distributed to a sufficient extent, the intervention experience from the first outbreak can be utilized to guide the policy decision in this period. The MPC problem in this paper takes the pandemic in different regions of a country and its neighboring countries into account, while policies such as wearing masks or social distancing are selected as inputs to be optimized. This optimized policy balances the risk of a second outbreak and socio-economic costs, while considering that the measure should not be too severe to be rejected by the population. Effectiveness of this policy compared to standard intervention policies is compared through numerical simulations.

Keywords: Nonlinear Model Predictive Control, Biomedical Systems, Networked Systems

References

  1. Bernardini, D. and Bemporad, A. (2009). Scenario-based model predictive control of stochastic constrained linear systems. In 48h IEEE Conf. on Decision and Control, 6333–6338.
  2. Bock H., Diehl M., Leineweber D., Schlöder J. Nonlinear Model Predictive Control. Springer; 2000. A direct multiple shooting method for real-time optimization of nonlinear DAE processes; pp. 245–267. [Google Scholar]
  3. Campo, P. and Morari, M. (1987). Robust model predictive control. In IEEE American Control Conf., 1021–1026.
  4. Fall A., Iggidr A., Sallet G., Tewa J. Epidemiological models and lyapunov functions. Mathematical Modelling of Natural Phenomena. 2007;2(1):62–83. [Google Scholar]
  5. Giordano G., Blanchini F., Bruno R., Colaneri P., Di Filippo A., Di Matteo A., Colaneri M. Modelling the Covid-19 epidemic and implementation of population-wide interventions in Italy. Nature Medicine. 2020:1–6. doi: 10.1038/s41591-020-0883-7. [DOI] [PMC free article] [PubMed] [Google Scholar]
  6. Gourdin, E., Omic, J., and Van Mieghem, P. (2011). Optimization of network protection against virus spread. In 8th IEEE Int. Workshop on the Design of Reliable Communication Networks, 86–93.
  7. Kantner M., Koprucki T. Beyond just flattening the curve: Optimal control of epidemics with purely non-pharmaceutical interventions. Journal of Mathematics in Industry. 2020;10(1):1–23. doi: 10.1186/s13362-020-00091-3. [DOI] [PMC free article] [PubMed] [Google Scholar]
  8. Kermack W., McKendrick A. Contributions to the mathematical theory of epidemics. II.the problem of endemicity. Proc. of the Royal Society of London. Series A. 1932;138(834):55–83. [Google Scholar]
  9. Khanafer A., Başar T., Gharesifard B. Stability of epidemic models over directed graphs: A positive systems approach. Automatica. 2016;74:126–134. [Google Scholar]
  10. Köhler J., Schwenkel L., Koch A., Berberich J., Pauli P., Allgöwer F. Robust and optimal predictive control of the Covid-19 outbreak. Annual Reviews in Control. 2020 doi: 10.1016/j.arcontrol.2020.11.002. [DOI] [PMC free article] [PubMed] [Google Scholar]
  11. Liu, Z. and Stursberg, O. (2019). Recursive feasibility and stability of MPC with time-varying and uncertain state constraints. In 18th IEEE European Control Conf., 1766–1771.
  12. Liu, Z. and Stursberg, O. (2021). A study on model-based optimization of vaccination strategies against epidemic virus spread. In 18th Int. Conf. on Informatics in Control, Automation and Robotics.-to appear.
  13. Preciado, V., Zargham, M., Enyioha, C., Jadbabaie, A., and Pappas, G. (2013). Optimal vaccine allocation to control epidemic outbreaks in arbitrary networks. In 52nd IEEE Conf. on decision and control, 7486–7491.
  14. Sahneh, F. and Scoglio, C. (2012). Optimal information dissemination in epidemic networks. In 51st IEEE Conf. on Decision and Control, 1657–1662.
  15. Van Mieghem P., Omic J., Kooij R. Virus spread in networks. IEEE/ACM Transactions On Networking. 2008;17(1):1–14. [Google Scholar]
  16. Wan, Y., Roy, S., and Saberi, A. (2007). Network design problems for controlling virus spread. In 46th IEEE Conf. on Decision and Control, 3925–3932.
  17. Wan Y., Roy S., Saberi A. Designing spatially heterogeneous strategies for control of virus spread. IET Systems Biology. 2008;2(4):184–201. doi: 10.1049/iet-syb:20070040. [DOI] [PubMed] [Google Scholar]
  18. Wang, Y., Chakrabarti, D., Wang, C., and Faloutsos, C. (2003). Epidemic spreading in real networks: An eigenvalue viewpoint. In 22nd IEEE Int. Symposium on Reliable Distributed Systems., 25–34.

Articles from Ifac-Papersonline are provided here courtesy of Elsevier

RESOURCES