控制时机和力度对传染病传播的影响

Influence of Control Timing and Strength on the Spreading of Epidemic

隔离是控制传染病传播的最主要手段之一,控制时机和力度都会给控制效果带来不可忽视的影响。为找到最合适的控制时机和力度,本文基于无标度网络和SIR传播模型,研究控制时机和力度对传染病传播范围以及个体活动性的影响。结果表明,控制模式为只控制染病态时,无论是在不相关随机无标度网络模型还是在真实无标度网络中,当控制力度相同时,控制时机越早控制效果越好;当控制时机相同时,控制力度越大控制效果越好。无论是在网络模型还是在真实网络中,个体活动性大小的变化则是非单调的:当控制力度不变时,个体活动性随着控制时机的增大有先减小后增大的趋势,表明较早或较晚控制在传染病传播结束时活动受控制的总个体数量越少,而当在传染病传播的高峰前后开始施加控制时将需要控制更多的染病个体;当控制时机不变但在峰值之前时,个体活动性也是先减小后增大,而在峰值之后个体活动性是单调下降的。综合起来看,控制时机越早控制力度越大控制效果越好、个体受到的影响越小,即假如为实现传播范围最小被控制个体数量最少这一目的,在观测到传染病后的第1时步就开始采用最强的控制力度1,将取得最好的控制效果,传播范围从未控制的55.9%降低到0.1%,而且人群中仅有总人数0.2%的个体被控制。

Isolation is one of the most important means to control the epidemic spreading,and the control timing and strength have great significance in the control effects.To find the most appropriate control timing and strength,in this paper,and based on uncorrelated random scale-free network and SIR spreading model,the effects of control timing and strength on the range of infectious disease spreading and individual activity are studied.The results show that if the control mode is to control the infectious state only,in both of the scale-free network model and in the real scale-free networks,when the control strength keeps the same,the earlier the control time is,the better the control effect is,and when the control time is the same,the greater the control effort is,the better the control effect is.Whether in the network model or in the real networks,the change of individual activity is non-monotonous:when the control strength is unchanged,the individual activity decreases first and then increases with the increase of control time,indicating that the number of total individuals whose activities are controlled earlier or later at the end of the epidemic transmission is less,and more infected individuals will need to be controlled when control is started around the peak of infectious disease transmission;When the control time is unchanged but before the peak value,the individual activity also decreases first and then increases,while after the peak value,the individual activity decreases monotonously.To sum up,the earlier the control time is,the greater the control force is,the better the control effect will be,and the less the individual will be affected.That is,if the strongest control strength 1 is used at the first step after the epidemic is observed,the best control effect will be achieved.The transmission range will be reduced from 55.9%to 0.1%,and only 0.2%of the total population will be controlled.