Optimal quarantine and isolation strategies in epidemics control∗

In the absence of valid medicines or vaccine, quarantine and isolation strategies are the most important and effective measures against the SARS outbreaks. This paper discusses the application of the optimal and sub-optimal control for SARS outbreak control via the Pontryagin’s Maximum Principle and genetic algorithm, respectively. To this end, a pair of control variables representing the quarantine and isolation strategies is incorporated into our improved SARS transmission model. The simulation results demonstrate that the maximum implementation of quarantining and isolation strategies in the early stage of the epidemic are of very critical impacts in the both cases of optimal and sub-optimal control. 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.