Mathematical Analysis of an SIQR Influenza Model with Imperfect Quarantine
Mathematical Analysis of an SIQR Influenza Model with Imperfect Quarantine
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DOI：
10.1007/s11538-017-0301-6
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发表时间：
2017-07-01
影响因子：
3.5
通讯作者：
Castillo-Chavez, Carlos
中科院分区：
文献类型：
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作者：
Erdem, Mustafa;Safan, Muntaser;Castillo-Chavez, Carlos
确定负责经常性流行病爆发的机制，如年龄结构，交叉免疫和感染类的可变延迟，已经挑战和吸引了流行病学家和数学家。本文讨论了流感模型的数学工作的动机，不完善的检疫对SIR型模型的动力学的影响。被隔离的个人通过他们可能降低的能力，以产生继发性感染病例的传播动力学过程中，制定了一个易感染的，传染性的，肉毒杆菌恢复（SIQR）模型。对平衡点模型及其稳定性进行了数学和数值分析。建立了模型的一致持久性。数值模拟结果表明，该模型支持的隔离效果和其他参数的值的函数的Hopf分支。这项工作的结果有些令人惊讶，因为正如多位研究人员所示，SIQR模型的振荡行为实际上对隔离制度中的扰动并不鲁棒。
The identification of mechanisms responsible for recurrent epidemic outbreaks, such as age structure, cross-immunity and variable delays in the infective classes, has challenged and fascinated epidemiologists and mathematicians alike. This paper addresses, motivated by mathematical work on influenza models, the impact of imperfect quarantine on the dynamics of SIR-type models. A susceptible-infectious-quarantine-recovered (SIQR) model is formulated with quarantined individuals altering the transmission dynamics process through their possibly reduced ability to generate secondary cases of infection. Mathematical and numerical analyses of the model of the equilibria and their stability have been carried out. Uniform persistence of the model has been established. Numerical simulations show that the model supports Hopf bifurcation as a function of the values of the quarantine effectiveness and other parameters. The upshot of this work is somewhat surprising since it is shown that SIQR model oscillatory behavior, as shown by multiple researchers, is in fact not robust to perturbations in the quarantine regime.