2021 Fiscal Year Final Research Report
Analysis of Infectious diseases based on the stochastic System Theory under some Structure and Its Application
| Project/Area Number |
19K04442
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 21040:Control and system engineering-related
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| Research Institution | Yamaguchi University (2019, 2021)
Yamaguchi Gakugei College (2020) |
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Principal Investigator |
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| Project Period (FY) |
2019-04-01 – 2022-03-31
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| Keywords | 感染症モデル / 確率システム / ワクチン接種 / 年齢構造 / 確率分岐 / 確率安定性 / 確率リヤプノフ指数 / シミュレーション |
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| Outline of Final Research Achievements |
Most of the conventional infectious models are deterministic models. Then, we have constructed the realistic infectious model including the age-structure and the random fluctuations in the infection and recovery rates. Moreover, using the stochastic stability analysis and the bifurcation theory, we have considered the stability of the steady states of the stochastic infectious models proposed in this research. By this analysis, we are able to estimate the necessary vaccination rate to control the infectious disease spreading.
Noting that one of characteristics of COVID-19 is the existence of subclinical infections, we have proposed the stochastic infectious model under subclinical infections and vaccination with waning immunity. We have analyzed the influence of the random fluctuation in the infection, recovery and vaccination rates on the stability using the stochastic Lyapunov exponent. By numerical simulations, we show the efficacy of the stability theorems derived in this paper.
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| Free Research Field |
確率システム理論
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| Academic Significance and Societal Importance of the Research Achievements |
従来の感染症解析の大半は確定感染症モデルに基づいており実際問題への応用に難点があった．そこで，本研究は感染率・回復率などの揺らぎを考慮した実際的な確率感染症モデルを構築し，安定性解析により感染症流行抑制に必要なワクチン接種率の推定法を確立した点に学術的意義がある．
感染症の流行は社会や経済だけではなく，従来の人間の生活様式にも大きな影響をもたらしている．このように新型コロナ感染症をはじめとする種々の感染症により大きな打撃を受けている現代社会において効果的な感染症抑制戦略の立案やその流行過程の解析に対する社会的要請が高まっており，本研究はこのような社会的要請にこたえるものである．
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