Ferguson N M, Nokes D J, Anderson R M
Wellcome Centre for the Epidemiology of Infectious Disease, Department of Zoology, Oxford University, United Kingdom.
Math Biosci. 1996 Dec;138(2):101-30. doi: 10.1016/s0025-5564(96)00127-7.
This article explores the effect of increasingly finely stratified age structure on the dynamical properties of deterministic metapopulation models of the transmission of the measles virus. The dynamical simplicity of earlier age-structured models is shown to break down once the age-specific force of infection is no longer assumed to be constant across all child age classes below 5 years of age. While the biennial epidemics characteristic of earlier models are still observed, additional higher period stable cycles arise and coexist with the biennial cycle. The existence of multiple stable limit cycles necessarily implies model sensitivity on initial conditions, and for certain parameter values, chaotic dynamics are observed. Using a novel parameterization of the magnitude of seasonal forcing we are also able to make more biologically relevant comparisons between the dynamics of age- and non-age-structured models than have hitherto been possible. The epidemiological significance of these results is discussed, and we demonstrate that perturbations of the kind produced by intensive vaccination programs can shift transmission dynamics between biennial and triennial cycles. The possible implications of this work for studies of intermittency and infection persistence are also considered.
本文探讨了日益精细分层的年龄结构对麻疹病毒传播确定性集合种群模型动力学特性的影响。结果表明，一旦不再假定5岁以下所有儿童年龄组的年龄特异性感染力恒定，早期年龄结构模型的动力学简单性就会瓦解。虽然仍能观察到早期模型特有的两年一次的流行，但会出现额外的高周期稳定周期，并与两年周期共存。多个稳定极限环的存在必然意味着模型对初始条件敏感，并且在某些参数值下，会观察到混沌动力学。通过对季节性强迫幅度进行新颖的参数化，我们还能够在年龄结构模型和非年龄结构模型的动力学之间进行比以往更具生物学相关性的比较。本文讨论了这些结果的流行病学意义，并证明了强化疫苗接种计划产生的那种扰动可以使传播动力学在两年周期和三年周期之间转变。还考虑了这项工作对间歇性和感染持续性研究的可能影响。
