具有年龄结构和时滞的SEIRS模型的HOPF分支

IF 1.3 4区数学 Q3 BIOLOGY

Journal of Biological Systems Pub Date : 2023-01-26 DOI:10.1142/s0218339023500122

Hui Cao, Mengmeng Han, Junyuan Yang, Lili Liu, Haiyan Li

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引用次数: 0

摘要

年龄结构和延迟在决定疾病的动态中起着重要作用。研究了具有年龄结构和时滞的SEIRS流行病模型，该模型考虑了获得性免疫的损失和时滞。通过严密的分析，得出了模型基本再现数的显式公式，并给出了模型平衡点稳定性和不稳定性的一些结果。研究结果表明，年龄结构和延迟可以产生SEIRS模型的Hopf分岔。通过数值算例对理论结果进行了验证。

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HOPF BIFURCATION OF AN SEIRS MODEL WITH AGE STRUCTURE AND TIME DELAY

Age structure and delay play a significant role in determining the dynamics of the diseases. In this paper, an SEIRS epidemic model with age structure and time delay is investigated, where the loss of the acquired immunity and delay are incorporated. Through some rigorous analyses, an explicit formula for the basic reproduction number of the model is calculated, and some results about stability and instability of equilibria for the model are established. The findings show that the age structure and delay can produce Hopf bifurcation for an SEIRS model. The numerical examples are executed to illustrate the theoretical results.

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来源期刊

Journal of Biological Systems 生物-生物学

CiteScore

2.80

自引率

12.50%

发文量

审稿时长

1 months

期刊介绍： The Journal of Biological Systems is published quarterly. The goal of the Journal is to promote interdisciplinary approaches in Biology and in Medicine, and the study of biological situations with a variety of tools, including mathematical and general systems methods. The Journal solicits original research papers and survey articles in areas that include (but are not limited to): Complex systems studies; isomorphies; nonlinear dynamics; entropy; mathematical tools and systems theories with applications in Biology and Medicine. Interdisciplinary approaches in Biology and Medicine; transfer of methods from one discipline to another; integration of biological levels, from atomic to molecular, macromolecular, cellular, and organic levels; animal biology; plant biology. Environmental studies; relationships between individuals, populations, communities and ecosystems; bioeconomics, management of renewable resources; hierarchy theory; integration of spatial and time scales. Evolutionary biology; co-evolutions; genetics and evolution; branching processes and phyllotaxis. Medical systems; physiology; cardiac modeling; computer models in Medicine; cancer research; epidemiology. Numerical simulations and computations; numerical study and analysis of biological data. Epistemology; history of science. The journal will also publish book reviews.