Department of Mathematics, Shanghai University, 99 Shangda Road, Shanghai 200444, China.
Math Biosci Eng. 2013 Apr;10(2):425-44. doi: 10.3934/mbe.2013.10.425.
In this paper, two mathematical models, the baseline model and the intervention model, are proposed to study the transmission dynamics of echinococcus. A global forward bifurcation completely characterizes the dynamical behavior of the baseline model. That is, when the basic reproductive number is less than one, the disease-free equilibrium is asymptotically globally stable; when the number is greater than one, the endemic equilibrium is asymptotically globally stable. For the intervention model, however, the basic reproduction number alone is not enough to describe the dynamics, particularly for the case where the basic reproductive number is less then one. The emergence of a backward bifurcation enriches the dynamical behavior of the model. Applying these mathematical models to Qinghai Province, China, we found that the infection of echinococcus is in an endemic state. Furthermore, the model appears to be supportive of human interventions in order to change the landscape of echinococcus infection in this region.
本文提出了两个数学模型，即基线模型和干预模型，用于研究棘球蚴的传播动态。全局正向分歧完全刻画了基线模型的动力学行为。也就是说，当基本再生数小于 1 时，无病平衡点渐近全局稳定；当基本再生数大于 1 时，地方病平衡点渐近全局稳定。然而，对于干预模型，基本再生数本身不足以描述动力学，特别是在基本再生数小于 1 的情况下。向后分歧的出现丰富了模型的动力学行为。将这些数学模型应用于中国青海省，我们发现棘球蚴的感染处于地方病状态。此外，该模型似乎支持人类干预，以改变该地区棘球蚴感染的局面。
