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研究生： 胡雅媛
Hu, Ya-Yuan
論文名稱： 具有疫苗接種的隨機SIS傳染病模型和兩個相關性擾動的影響
A Stochastic SIS Epidemic Model with Vaccination and the Effects of Two correlated Perturbations
指導教授： 李金龍
Li, Chin-Lung
口試委員: 張延彰
Chang, Yen-Chang
李俊憲
Li, Chun-Hsien
學位類別： 碩士
Master
系所名稱： 理學院 - 計算與建模科學研究所
Institute of Computational and Modeling Science
論文出版年： 2021
畢業學年度： 109
語文別： 英文
論文頁數： 45
中文關鍵詞： 傳染病模型 、隨機擾動 、布朗運動 、隨機微分方程 、疫苗 、閾值 、滅絕 、持續存在
外文關鍵詞： Epidemic model, Stochastic perturbation, Brownian motion, Stochastic differential equations, Vaccination, Threshold, Extinction, Persistence
相關次數： 點閱：3  下載：0 
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    • 我們提出了一個考慮疫苗接種和相關性影響的隨機SIS傳染病模型，更準確地說，我們利用兩個獨立布朗運動在傳播係數和治癒率上引入相關性影響。本篇論文中，我們首先證明了該模型具有唯一性正解，接著提出了保證疾病滅絕和持續存在的特定充分條件。特別地，這些噪聲的強度和相關性參數都對控制疾病的行為起到了重要的作用；此外，我們使用量綱分析來探討所有模型參數和閾值的物理量，達到符合理論結果一致性的驗證。最後，我們討論了相關性參數ρ對於模型的影響，並且給出了一些數值模擬來支持我們的理論結果。

    A stochastic SIS epidemic model is proposed to take vaccination and correlation effects into account. More precisely, the correlation effects are involved in the transmission coefficient and the recovery rate by two independent Brownian motions. In this thesis, we presented the specific sufficient conditions to guarantee the extinction and persistence of the disease. In particular, the intensities of these noises and the correlation coefficient both play important roles to control the behaviors of the disease. Based on the dimensional analysis, the physical quantities of all parameters and the threshold values are characterized to consist with our results. Finally, we discuss the effects of the correlation coefficient ρ and give some numerical simulations to support our theoretical results.

    Abstract----------------------------------------------i Acknowledgments-------------------------------------iii 1 Introduction----------------------------------------1 2 Preliminaries---------------------------------------6 3 Mathematical Formulation for Epidemic Model--------10 3.1 Existence of Unique Positive Solution------------10 3.2 Extinction of the Disease------------------------14 3.3 Persistence of the Disease-----------------------19 3.4 Dimensional Analysis-----------------------------22 4 Numerical Simulations------------------------------25 4.1 Examples of Extinction---------------------------25 4.2 Examples of Persistence--------------------------29 4.3 The Effects of the Parameter ρ-------------------33 5 Conclusions----------------------------------------39 References-------------------------------------------40 Appendix---------------------------------------------42

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