受时间影响的疫苗接种活动中的控制、双稳定性和混乱偏好

Enrique C. Gabrick, Eduardo L. Brugnago, Ana L. R. de Moraes, Paulo R. Protachevicz, Sidney T. da Silva, Fernando S. Borges, Iberê L. Caldas, Antonio M. Batista, Jürgen Kurths
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引用次数: 0

摘要

在这项工作中,我们研究了恒定疫苗接种率和随时间变化的疫苗接种率对易感-暴露-感染-恢复-易感(SEIRS)季节性模型的影响。通过计算李雅普诺夫指数,我们发现在给定的恒定疫苗接种率和另一个模型参数组合下,会出现典型的复杂结构,例如虾。在某些特定情况下,恒定疫苗接种率并不起到混沌抑制作用,在疫苗接种率较高(如$> 0.95$)时也会出现混沌带。此外,我们还得到了一个控制参数与恒定疫苗接种之间的线性和非线性关系,从而建立了无疾病解。我们还验证了无论动力学是混沌的还是周期性的,总感染数都不会改变。引入随时间变化的疫苗是通过加入具有确定振幅和频率的非周期性函数。在这种情况下,我们研究了不同振幅和频率对混沌矢量的影响,得出了低、中和高季节性接触度。对于给定的参数集,这些结构主要通过危机和某些情况下的周期加倍来实现。之后,我们研究了当混沌吸引子和周期吸引子共存时,随时间变化的疫苗如何在双稳态动力学中发挥作用。我们发现,这种疫苗通过破坏几乎所有周期性盆地起到了控制作用。我们的解释是,在双稳定状态下,混沌吸引子比周期吸引子表现出更理想的流行病特征。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Control, bi-stability and preference for chaos in time-dependent vaccination campaign
In this work, effects of constant and time-dependent vaccination rates on the Susceptible-Exposed-Infected-Recovered-Susceptible (SEIRS) seasonal model are studied. Computing the Lyapunov exponent, we show that typical complex structures, such as shrimps, emerge for given combinations of constant vaccination rate and another model parameter. In some specific cases, the constant vaccination does not act as a chaotic suppressor and chaotic bands can exist for high levels of vaccination (e.g., $> 0.95$). Moreover, we obtain linear and non-linear relationships between one control parameter and constant vaccination to establish a disease-free solution. We also verify that the total infected number does not change whether the dynamics is chaotic or periodic. The introduction of a time-dependent vaccine is made by the inclusion of a periodic function with a defined amplitude and frequency. For this case, we investigate the effects of different amplitudes and frequencies on chaotic attractors, yielding low, medium, and high seasonality degrees of contacts. Depending on the parameters of the time-dependent vaccination function, chaotic structures can be controlled and become periodic structures. For a given set of parameters, these structures are accessed mostly via crisis and in some cases via period-doubling. After that, we investigate how the time-dependent vaccine acts in bi-stable dynamics when chaotic and periodic attractors coexist. We identify that this kind of vaccination acts as a control by destroying almost all the periodic basins. We explain this by the fact that chaotic attractors exhibit more desirable characteristics for epidemics than periodic ones in a bi-stable state.
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