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多稳态逻辑型流行病学模型中的随机动力学分析

Analysis of stochastic dynamics in a multistable logistic-type epidemiological model.

作者信息

Bashkirtseva Irina, Ryashko Lev

机构信息

Ural Federal University, Ekaterinburg, Russia.

出版信息

Eur Phys J Spec Top. 2022;231(18-20):3563-3575. doi: 10.1140/epjs/s11734-022-00618-2. Epub 2022 Jun 14.

DOI:10.1140/epjs/s11734-022-00618-2
PMID:35729926
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC9196167/
Abstract

Motivated by the important problem of analyzing and predicting the spread of epidemics, we propose and study a discrete susceptible-infected model. This logistic-type model accounts such significant parameters as the rate of infection spread due to contacts, mortality caused by disease, and the rate of recovery. We present results of the bifurcation analysis of regular and chaotic survival regimes for interacting susceptible and infected subpopulations. Parametric zones of multistability are found and basins of coexisting attractors are determined. We also discuss the particular role of specific transients. In-phase and anti-phase synchronization in the oscillations of the susceptible and infected parts of the population is studied. An impact of inevitably present random disturbances is studied numerically and by the analytical method of confidence domains. Various mechanisms of noise-induced extinction in this epidemiological model are discussed.

摘要

受分析和预测流行病传播这一重要问题的驱动，我们提出并研究了一个离散的易感 - 感染模型。这个逻辑型模型考虑了诸如因接触导致的感染传播速率、疾病造成的死亡率以及康复速率等重要参数。我们给出了相互作用的易感和感染亚群体的规则和混沌生存状态的分岔分析结果。找到了多稳态的参数区域并确定了共存吸引子的盆地。我们还讨论了特定瞬态的特殊作用。研究了群体易感部分和感染部分振荡中的同相和反相同步。通过数值方法和置信域分析方法研究了不可避免存在的随机干扰的影响。讨论了该流行病模型中噪声诱导灭绝的各种机制。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e588/9196167/a779b8beface/11734_2022_618_Fig13_HTML.jpg
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https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e588/9196167/bbce1f11bea8/11734_2022_618_Fig5_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e588/9196167/f7b1448ac412/11734_2022_618_Fig6_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e588/9196167/4c2c84c03d37/11734_2022_618_Fig7_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e588/9196167/3bce6ac7f09c/11734_2022_618_Fig8_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e588/9196167/9282f4ccf803/11734_2022_618_Fig9_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e588/9196167/38df4be020b6/11734_2022_618_Fig10_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e588/9196167/39ded56bea2a/11734_2022_618_Fig11_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e588/9196167/4c668eefe4d5/11734_2022_618_Fig12_HTML.jpg
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