具有反馈性能的传染病传播模型

The Spread Models of Epidemic with the Feedback Function

传染病是人类社会面对的严重威胁之一,也是困扰世界医学界的长期难题.文中首先对传染病的传播机理进行了分析研究,将其传播分为自然传播和人为控制两种状态,然后以微分方程理论为基础,运用反馈控制理论分别建立了自然传播状态的闭环自激正反馈微分方程模型和有人为控制时的闭环负反馈微分方程模型,并引入控制度概念把上述两种反馈模型结合起来以反映人为控制因素对传染病传播系统的影响,最后以2003年爆发的SARS为例采用计算机编程仿真,结果与实际比较吻合,并提出了应对传染病的若干对策,为传染病的传播预测、有效预防和控制提供了一定的理论依据.

As one of the serious threats for human beings, epidemics have been a world problem in medical field for a long time. The paper firstly analyses the spread mechanism of epidemics, and holds that the spread state can be divided into the two tpyes--natural spread and artificial control. Secondly, Based on theories of differential equation, the differ- ential equation models of closed ring self-positive feedback for the natural spread state and closed ring self-negative feedback for the artificial control state are established on the basis of feedback control theories respectively. And then a concept of the control degree is intro- duced so as to combine the two feedback models to indicate the influence of the artificial control factors on the spread system of epidemic.Finally, with the emulation of computer programming of Matlab, taking the SARS which broke out in＇ the world in 2003 as example, the paper concludes that the emulation result is very similar to its initial state.Furthermore, some tactics to the epidemics are put forward for suggested to effectively prevent and control infectious disease.