Optimal and sub-optimal quarantine and isolation control in SARS epidemics.

*(English)*Zbl 1134.92033Summary: This paper discusses the application of optimal and sub-optimal controls to a SE QIJR SARS model via the Pontryagin maximum principle. To this end, two control variables representing the quarantine and isolation strategies are considered in the model. The numerical optimal control laws are implemented in an iterative method, and the sub-optimal solution is computed using a genetic algorithm. The simulation results demonstrate that the maximal applications of quarantining and isolation strategies in the early stage of the epidemic are of very critical impacts in both cases of optimal and sub-optimal control. Otherwise, the control effect will be much worse. This gives a theoretical interpretation to the practical experiences that the early quarantine and isolation strategies are critically important to control the outbreaks of epidemics. Furthermore, our results also show that the proposed sub-optimal control can lead to performances close to the optimal control, but with much simpler strategies for long periods of time in practical use.

##### MSC:

92D30 | Epidemiology |

49N90 | Applications of optimal control and differential games |

90C59 | Approximation methods and heuristics in mathematical programming |

49J15 | Existence theories for optimal control problems involving ordinary differential equations |

##### Keywords:

optimal and sub-optimal control; quarantine; isolation; epidemics control; genetic algorithm
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\textit{X. Yan} and \textit{Y. Zou}, Math. Comput. Modelling 47, No. 1--2, 235--245 (2008; Zbl 1134.92033)

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