The dynamical consequences of seasonal forcing, immune boosting and demographic change in a model of disease transmission
The dynamical consequences of seasonal forcing, immune boosting and demographic change in a model of disease transmission
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DOI：
10.1016/j.jtbi.2014.07.028
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发表时间：
2014-11-21
影响因子：
2
通讯作者：
McCaw, James M.
中科院分区：
文献类型：
--
作者：
Dafilis, Mathew P.;Frascoli, Federico;McCaw, James M.
季节性影响对传染病时间进程的影响可能是巨大的。传染病传播率的季节性波动在数学上已知会诱发周期性行为，并驱动多稳态和混沌动力学的发生。强迫动力系统的这些特性以前曾被用来解释麻疹、水痘、风疹和百日咳等传染病暴发期间观察到的变化。在这里，我们详细检查了一个季节性的强迫扩展感染模型以前用于研究百日咳的动力学性质。该模型是新颖的，因为它包括一个非线性反馈项，捕捉暴露和防止再次感染的保护持续时间之间的相互作用。我们表明，当引入季节强迫时，非强迫系统中极限环和多稳定性的存在会引起复杂和复杂的行为。通过数值模拟和分岔分析相结合的方法，对参数空间混沌区域的起源进行了识别和解释。此外，我们确定了鞍节点线和不同轨道周期的倍周期级联重叠的区域，这表明系统对其参数中的小扰动特别敏感，并且易于产生多稳定行为。从公共卫生的角度来看——通过人口出生率随时间下降（预期寿命相应增加）的“人口转型”框架——我们认为，即使是微弱的季节性强迫和免疫增强也可能导致百日咳等疾病观察到的无数复杂和意想不到的流行病学行为。我们的方法有助于将这些流行病学观察纳入背景，并为如何考虑疫苗接种计划的潜在影响提供指导。(C) 2014 Elsevier Ltd.版权所有。
The impact of seasonal effects on the time course of an infectious disease can be dramatic. Seasonal fluctuations in the transmission rate for an infectious disease are known mathematically to induce cyclical behaviour and drive the onset of multistable and chaotic dynamics. These properties of forced dynamical systems have previously been used to explain observed changes in the period of outbreaks of infections such as measles, varicella (chickenpox), rubella and pertussis (whooping cough). Here, we examine in detail the dynamical properties of a seasonally forced extension of a model of infection previously used to study pertussis. The model is novel in that it includes a non-linear feedback term capturing the interaction between exposure and the duration of protection against re-infection. We show that the presence of limit cycles and multistability in the unforced system give rise to complex and intricate behaviour as seasonal forcing is introduced. Through a mixture of numerical simulation and bifurcation analysis, we identify and explain the origins of chaotic regions of parameter space. Furthermore, we identify regions where saddle node lines and period-doubling cascades of different orbital periods overlap, suggesting that the system is particularly sensitive to small perturbations in its parameters and prone to multistable behaviour. From a public health point of view - framed through the 'demographic transition' whereby a population's birth rate drops over time (and life-expectancy commensurately increases) - we argue that even weak levels of seasonal-forcing and immune boosting may contribute to the myriad of complex and unexpected epidemiological behaviours observed for diseases such as pertussis. Our approach helps to contextualise these epidemiological observations and provides guidance on how to consider the potential impact of vaccination programs. (C) 2014 Elsevier Ltd. All rights reserved.