Control of Epidemics by Quarantine and Isolation Strategies in Highly Mobile Populations

In the absence of valid medicines or vaccine, quarantine and isolation strategies are the most important and effective measures against the outbreaks of epidemic diseases such as SARS. This paper discusses the application of the optimal quarantine and isolation strategies for SARS outbreak control via the Pontryagin’s Maximum Principle. We construct a multigroup SARS transmission model for traveling population and introduce pairs of control variables in terms of the quarantine and isolation strategies. A quadratic cost on the controls and a linear cost on the number of infected individuals are imposed. The simulation results illustrate how the disease spreads from region to region by means of travelers. And the results also demonstrate the importance of the early quarantine and isolation strategies and the necessity of the observation and quarantine of travelers to control the outbreaks of epidemics. This gives a theoretical interpretation to the practical experiences that the early quarantine and isolation strategies, as well as the observation and quarantine of travelers, are critically important to contain the epidemic.