Seasonally forced disease dynamics explored as switching between attractors
Seasonally forced disease dynamics explored as switching between attractors
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DOI：
10.1016/s0167-2789(00)00187-1
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发表时间：
2001-01-15
影响因子：
4
通讯作者：
Grenfell, BT
中科院分区：
文献类型：
--
作者：
Keeling, MJ;Rohani, P;Grenfell, BT
生物现象提供了丰富多样的问题，可以使用数学技术来理解。许多生物系统共有的三个关键特征是时间强迫、随机性和非线性。在这里，我们使用简单的疾病模型与数据进行比较，研究这三个因素如何相互作用以产生一系列复杂的动态。疾病动力学研究一直是数学生物学中理论最发达的领域之一。简单的模型在解释多种疾病的动态方面非常成功。儿童疾病模型考虑了接触率的季节性变化，因为与学校假期相比，在校期间接触率增加。季节性强迫的这种“二元”性质导致了动力学，可以将其解释为两个非线性螺旋汇之间的切换。最后，我们考虑吸引子的稳定性，以理解确定性动力学与人口和环境随机性之间的相互作用。整个注意力都集中在麻疹、百日咳和风疹的行为上。 (C) 2001 Elsevier Science B.V. 保留所有权利。
Biological phenomena offer a rich diversity of problems that can be understood using mathematical techniques. Three key features common to many biological systems are temporal forcing, stochasticity and nonlinearity. Here, using simple disease models compared to data, we examine how these three factors interact to produce a range of complicated dynamics. The study of disease dynamics has been amongst the most theoretically developed areas of mathematical biology; simple models have been highly successful in explaining the dynamics of a wide variety of diseases. Models of childhood diseases incorporate seasonal variation in contact rates due to the increased mixing during school terms compared to school holidays. This 'binary' nature of the seasonal forcing results in dynamics that can be explained as switching between two nonlinear spiral sinks. Finally, we consider the stability of the attractors to understand the interaction between the deterministic dynamics and demographic and environmental stochasticity. Throughout attention is focused on the behaviour of measles, whooping cough and rubella. (C) 2001 Elsevier Science B.V. All rights reserved.