McLennan-Smith Timothy A, Mercer Geoffry N
National Centre for Epidemiology and Population Health, Australian National University, Canberra, Australia.
Math Biosci. 2014 Feb;248:22-30. doi: 10.1016/j.mbs.2013.11.003. Epub 2013 Nov 28.
In recent decades, dengue fever and dengue haemorrhagic fever have become a substantial public health concern in many subtropical and tropical countries throughout the world. Many of these regions have strong seasonal patterns in rainfall and temperature which are directly linked to the transmission of dengue through the mosquito vector population. Our study focuses on the development and analysis of a strongly seasonally forced, multi-subclass dengue model. This model is a compartment-based system of first-order ordinary differential equations with seasonal forcing in the vector population and also includes host population demographics. Our analysis of this model focuses particularly on the existence of deterministic chaos in regions of the parameter space which potentially hinders application of the model to predict and understand future outbreaks. The numerically efficient 0-1 test for deterministic chaos suggested by Gottwald and Melbourne (2004) [18] is used to analyze the long-term behaviour of the model as an alternative to Lyapunov exponents. Various solutions types were found to exist within the studied parameter range. Most notable are the existence of isola n-cycle solutions before the onset of deterministic chaos. Analysis of the seasonal model with the 0-1 test revealed the existence of three disconnected regions in parameter space where deterministic chaos exists in the single subclass model. Knowledge of these regions and how they relate to the parameters of the model gives greater confidence in the predictive power of the seasonal model.
近几十年来，登革热和登革出血热已成为全球许多亚热带和热带国家的重大公共卫生问题。这些地区中的许多地方在降雨和温度方面都有强烈的季节性模式，而这些模式与登革热通过蚊媒种群的传播直接相关。我们的研究重点是开发和分析一个具有强烈季节性强迫的多亚类登革热模型。该模型是一个基于 compartments 的一阶常微分方程组系统，在蚊媒种群中有季节性强迫，并且还包括宿主种群统计学特征。我们对该模型的分析特别关注参数空间区域中确定性混沌的存在，这可能会阻碍该模型用于预测和理解未来疫情爆发。我们使用了 Gottwald 和 Melbourne（2004 年）[18]提出的用于确定性混沌的数值高效 0 - 1 检验来分析该模型的长期行为，以替代李雅普诺夫指数。在所研究的参数范围内发现存在各种解类型。最值得注意的是在确定性混沌开始之前存在孤立 n 周期解。用 0 - 1 检验对季节性模型进行分析后发现，在参数空间中存在三个不相连的区域，在单亚类模型中存在确定性混沌。了解这些区域以及它们与模型参数的关系，能让我们对季节性模型的预测能力更有信心。
