最优阻隔控制在一类SIRS多组群传染病中的应用

Optimal Delay and Isolation Control for a Class of SIRS Multigroup Epidemics

该文基于一类SIRS多组群传染病模型讨论了传染病控制中的最优阻隔控制。模型中的控制变量表示为达到阻滞和隔离组群之间接触所采取的各种措施的强度。利用Pontryagin极大值原理求解了最优控制问题并给出了相应的数值迭代算法。仿真结果表明该文提出的最优阻隔控制策略在使传染病代价最小化的同时可以有效地控制传染病的流行,同时也表明现实中采取的"早发现早隔离"策略在传染病控制中的重要性。

This paper discusses the optimal delay and isolation strategies in epidemics control based on a class of SIRS muhigroup epidemics model. Controls representing the rates at the administration of delay and isolation strategies are incorporated in the model. Conditions for cost optimization are obtained from the Maximum Principle and numerical solutions of the problem are presented. The simulation results illustrate the effectiveness of the optimal strategy for the multigroup epidemics control and give a theoretical interpretation to the fact that the early quarantine and isolation strategies are critical- ly important to control the outbreaks of epidemics.