著者

石川 昌明

出版者

一般社団法人 システム制御情報学会

雑誌

システム制御情報学会論文誌 (ISSN:13425668)

巻号頁・発行日

vol.30, no.4, pp.115-121, 2017-04-15 (Released:2017-07-15)

参考文献数

12

被引用文献数

1 1

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The purpose of this paper is to propose the stochastic infectious model with time delay and to study the stability of the disease-free steady state. In the realistic spread of the infectious disease, environmental change and individual difference cause some kinds of random fluctuations in the model parameters. Moreover, in the vector-borne diseases such as malaria and dengue fever, there exists time delay caused by an incubation period in the virus development in the vectors (mosquitoes) on the transmission of disease. Taking these facts into consideration, we propose a stochastic SIR(susceptible-infected-recovered) model with time delay. We analyze stability of the disease-free steady state, and study the influence of time delay and the random noise on the stability by numerical simulations.

著者

石川 昌明

出版者

自動制御連合講演会

雑誌

自動制御連合講演会講演論文集 第59回自動制御連合講演会

巻号頁・発行日

pp.276-277, 2016 (Released:2017-02-01)

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媒介生物により感染が拡大するマラリアのような感染症の数学モデルを提案し,その安定性について講演する.媒介生物を考慮した感染症モデルは必然的に時間遅れが存在するので,特に時間遅れを伴う確率感染症モデルを対象に安定性解析について考察する.

著者

石川 昌明

出版者

一般社団法人 システム制御情報学会

雑誌

システム制御情報学会論文誌 (ISSN:13425668)

巻号頁・発行日

vol.31, no.4, pp.129-136, 2018-04-15 (Released:2018-07-15)

参考文献数

17

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This paper is concerned with the stability analysis of the stochastic infectious model with time delay. In the vector-borne diseases such as malaria and Japanese encephalitis, there exists time delay caused by an incubation period in the virus development in the vectors on the transmission of disease. Moreover, environmental change and individual difference cause some kinds of random fluctuations in the infection, recovery rates, etc. Hence, we propose the stochastic infectious model with time delay. The equilibrium solution with zero infected individuals is called the disease-free steady state. Since the stability of the disease-free steady state is related to whether or not the infectious disease spreads, we analyze stability of the disease-free steady state using the stochastic Lyapunov function. Moreover, we study the influence of the random noise on the stability based on the calculation of the Lyapunov exponent, and show results of numerical simulations.

著者

石川 昌明

出版者

一般社団法人 システム制御情報学会

雑誌

システム/制御/情報 (ISSN:09161600)

巻号頁・発行日

vol.64, no.1, pp.15-20, 2020-01-15 (Released:2020-07-15)

参考文献数

13