On the Stability Analysis of the Stochastic Age-structured Infectious Model
On the Stability Analysis of the Stochastic Age-structured Infectious Model
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DOI：
10.5687/sss.2019.111
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发表时间：
2019-07
期刊：
影响因子：
--
通讯作者：
M. Ishikawa
中科院分区：
文献类型：
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作者：
M. Ishikawa
研究了一类具有年龄结构的随机传染病模型的稳定性。即使在医疗技术高度发达的现代社会，我们也面临着传染病的威胁。因此，传染病的预防和控制被列为重要的社会问题之一。到目前为止，传染病的有趣和有影响力的研究已经使用各种数学模型进行。然而，大多数研究都是基于确定性模型，没有考虑年龄结构。在现实的传染病传播过程中，环境变化和个体差异会引起感染率、治愈率和接种效果的随机波动。不同年龄段感染的传播强度存在差异。考虑到这些事实，我们提出了随机年龄结构传染病模型。由于传染病的传播与随机传染病模型的无病稳态（DFS）的稳定性有关，本文利用随机李雅普诺夫定理分析了无病稳态的稳定性。
This paper is concerned with the stability analysis of the stochastic age-structured infectious model. We have been faced with a threat of the infectious disease even in the modern society with a high medical technology. Hence, infection prevention and control of epidemic are cited as one of the important social problems. Until now, interesting and impactful research of infectious diseases has been performed using various kinds of mathematical models. However, most of the research is based on the deterministic model and the age-structure has not been taken into account. In the realistic spread of the infectious disease, environmental change and individual difference cause some kinds of random fluctuations in the infection, the recovery rates and the vaccination effect. Moreover, there exists the difference in the transmission intensity of infection by age. Taking these facts into consideration, we propose the stochastic age-structured infectious model. Since the spread of infection has reference to the stability of the disease-free steady state (DFS) of the stochastic infectious models, we analyze the stability of the DFS by using the stochastic Lyapunov theorem.