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Mathematical Biosciences and Engineering

2013, Volume 10, Issue 5&6: 1691-1701. doi: 10.3934/mbe.2013.10.1691
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Optimal isolation strategies of emerging infectious diseases with limited resources

  • 1.
    School of Mathematics and Statistics, Central South University, Changsha, Hunan 410083
  • 2.
    Centre for Disease Modeling, York University, 4700 Keele Street, Toronto, ON M3J1P3
  • 3.
    School of Information Science and Engineering, Central South University, Changsha, Hunan 410083
  • Received: 01 September 2012 Accepted: 29 June 2018 Published: 01 August 2013

  • MSC : Primary: 92D30.

  • A classical deterministic SIR model is modified to take into accountof limited resources for diagnostic confirmation/medical isolation. We show that this modificationleads to four different scenarios (instead of three scenarios in comparison with the SIR model) for optimal isolation strategies, and obtainanalytic solutions for the optimal control problem that minimize the outbreak size under the assumptionof limited resources for isolation. These solutions and their corresponding optimal control policies arederived explicitly in terms of initial conditions, model parameters and resources for isolation (such as the number of intensive care units).With sufficient resources, the optimal control strategy is the normal Bang-Bangcontrol. However, with limited resources the optimal control strategy requires to switch totime-variant isolation at an optimal rate proportional to the ratio of isolated cases over the entire infected population once the maximum capacityis reached.

    Citation: Yinggao Zhou, Jianhong Wu, Min Wu. Optimal isolation strategies of emerging infectious diseases with limited resources[J]. Mathematical Biosciences and Engineering, 2013, 10(5&6): 1691-1701. doi: 10.3934/mbe.2013.10.1691

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  • A classical deterministic SIR model is modified to take into accountof limited resources for diagnostic confirmation/medical isolation. We show that this modificationleads to four different scenarios (instead of three scenarios in comparison with the SIR model) for optimal isolation strategies, and obtainanalytic solutions for the optimal control problem that minimize the outbreak size under the assumptionof limited resources for isolation. These solutions and their corresponding optimal control policies arederived explicitly in terms of initial conditions, model parameters and resources for isolation (such as the number of intensive care units).With sufficient resources, the optimal control strategy is the normal Bang-Bangcontrol. However, with limited resources the optimal control strategy requires to switch totime-variant isolation at an optimal rate proportional to the ratio of isolated cases over the entire infected population once the maximum capacityis reached.


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