Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission
Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission
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DOI：
10.1016/s0025-5564(02)00108-6
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发表时间：
2002-11-01
影响因子：
4.3
通讯作者：
Watmough, J
中科院分区：
文献类型：
--
作者：
van den Driessche, P;Watmough, J
对一类基于常微分方程组的疾病传播模型，给出了基本再生数go的精确定义。证明了当R-0 < 1时，无病平衡点是局部渐近稳定的，而当R-0 > 1时，无病平衡点是不稳定的.因此，go是模型的阈值参数。对局部中心流形的分析给出了一个简单的判据，证明了R-0附近的超阈值和亚阈值地方病平衡点的存在性和稳定性。该标准以及R-0的定义通过治疗、多组、分期进展、多菌株和载体-宿主模型进行了说明，并可应用于更复杂的模型。研究结果对病害防治具有重要意义。(C)2002年爱思唯尔科技有限公司All rights reserved.
A precise definition of the basic reproduction number, go, is presented for a general compartmental disease transmission model based on a system of ordinary differential equations. It is shown that, if R-0 < 1, then the disease free equilibrium is locally asymptotically stable; whereas if R-0 > 1, then it is unstable. Thus, go is a threshold parameter for the model. An analysis of the local centre manifold yields a simple criterion for the existence and stability of super- and sub-threshold endemic equilibria for R-0 near one. This criterion, together with the definition of R-0, is illustrated by treatment, multigroup, staged progression, multistrain and vector-host models and can be applied to more complex models. The results are significant for disease control. (C) 2002 Elsevier Science Inc. All rights reserved.