Norman Rachel, Ross David, Laurenson M Karen, Hudson Peter J
Stirling Mathematical Ecology Group, Department of Computing Science and Mathematics, University of Stirling, Stirling, FK9 4LA, UK.
J Math Biol. 2004 Feb;48(2):119-34. doi: 10.1007/s00285-002-0183-5. Epub 2003 Aug 6.
There exist many tick borne infections that are of either economic or public health interest. Mathematical models have previously been used to describe the dynamics of these infections. However it has recently come to light that there is an alternative mechanism for the transmission of these diseases that has not been considered in a modelling framework. This is transmission through ticks co-feeding on non-viraemic hosts. This paper extends a simple mathematical model to include this alternative transmission mechanism. The model is used to describe the dynamics of Louping ill virus in red grouse (the viraemic host) and hares (the non-viraemic host). However, these results are applicable to many other systems. The model is analysed using joint threshold density curves. It is found that the presence of a non-viraemic host allows the virus to persist more readily than it would in the presence of a host that simply amplified the tick population. More importantly, if the level of non-viraemic transmission is high enough the virus can persist in the absence of the viraemic host. This result has important implications for the control of tick borne diseases.
存在许多由蜱传播的感染，这些感染在经济或公共卫生方面都备受关注。数学模型此前已被用于描述这些感染的动态。然而，最近人们发现存在一种这些疾病传播的替代机制，而该机制在建模框架中尚未被考虑。这就是蜱通过共同叮咬非病毒血症宿主进行传播。本文扩展了一个简单的数学模型，以纳入这种替代传播机制。该模型用于描述跳跃病病毒在红松鸡（病毒血症宿主）和野兔（非病毒血症宿主）中的动态。然而，这些结果适用于许多其他系统。使用联合阈值密度曲线对该模型进行分析。结果发现，非病毒血症宿主的存在使得病毒比在仅使蜱种群数量增加的宿主存在时更容易持续存在。更重要的是，如果非病毒血症传播水平足够高，病毒可以在没有病毒血症宿主的情况下持续存在。这一结果对蜱传播疾病的控制具有重要意义。
