(3.236.214.19) 您好！臺灣時間：2021/05/06 21:14

### 詳目顯示:::

:

• 被引用:0
• 點閱:98
• 評分:
• 下載:0
• 書目收藏:0
 近年來，傳染病已經造成世界上許多人感染和死亡，因此研究傳染病的傳播行為是一個相當重要的主題。本文主要是以常微分方程組來建構模型，為了描述更符合真實的情況，我們在模型中考慮了複雜網路的結構以及飽和傳染率。此外，我們知道醫療資源是有限的，因此當某一傳染病的感染比例上升時，治療率會因有限的資源而趨近飽和。故我們也將飽和治療率加入模型中，並進一步分析此模型之平衡點的存在性與穩定性。有趣的是，我們發現加入飽和治療率會導致有多個疾病平衡點(endemic equilibrium)的存在。最後我們進行數值模擬來驗證理論分析。
 In recent years, infectious diseases have become a serious problem and have increased morbidity and mortality of individuals around the world. Thus, studying the spreading dynamics of the infectious diseases is a relevant issue. In this thesis, we will investigate an epidemic model which is composed of a system of ordinary differential equations. To fit for reality, complex network topology and saturated incidence rate are incorporated into the model. Besides, we know that the resources of treatment may be limited, and this implies that the recovery from infective individuals will reach a maximum. Therefore, we will study a network-based SIS epidemic model with saturated incidence and treatment rates. Existence and stability of the equilibria of the epidemic model will be analyzed. Interestingly, we find that incorporating the saturated treatment rate may cause the existence of two endemic equilibria. Numerical simulations will be given to demonstrate the theoretical results.
 目錄第一章 前言 1 1.1 簡介 1 1.2 研究動機 1 1.3 模型介紹 2第二章 建構模型 4第三章 研究分析 6 3.1 Positive invariance 6 3.2 Disease-Free Equilibrium 7 3.3 Endemic Equilibrium 11第四章 數值模擬 19第五章 結論 30參考文獻 31圖次1. 非單調性傳染率 32. 飽和傳染率 33. 非零θ解交點示意圖 134. α2=6,R0<1時感染比例曲線變化 195. α2=6,R0<1時θ圖解 206. α2=0.4,R0'<1時感染比例曲線變化 207. α2=0.4,R0'<1時θ圖解 218. α2=10,R0<11時感染比例曲線變化 2618.α2=3,R0>1時θ圖解 2719.α2=7,R0>1時感染比例曲線變化 2720.α2=7,R0>1時θ圖解 2821.α2=11,R0>1時感染比例曲線變化 2822.α2=11,R0>1時θ圖解 2923.α2=20,40,80時θ圖解 29
 [1]J. Cui, X. Mu and H. Wan, Saturation recovery leads to multiple endemic equilibria and backward bifurcation, J. Theor. Biol., 254 (2008), pp. 275–283.[2] A. Lajmanovich and J. Yorke, A deterministic model for gonorrhea in a nonhomogeneous population, Math. Biosci., 28 (1976), pp. 221-236.[3]C. Li, C. Tsai, and S. Yang, Analysis of epidemic spreading of an SIRS model in complex heterogeneous networks, Commun. Nonlinear Sci. Numer. Simul., 19 (2014), pp. 1042-1054.[4]C. Li, Dynamics of a network-based SIS epidemic model with nonmonotone incidencerate, Physica A, 427 (2015), pp. 234-243.[5]T. Li, Y. Wang, and Z. Guan, Spreading dynamics of a SIQRS epidemic model on scale-free networks, Commun. Nonlinear Sci. Numer.Simul., 19 (2014), pp. 686-692.[6]J. Liu and T. Zhang, Epidemic spreading of an SEIRS model in scale-free networks, Commun. Nonlinear Sci. Numer. Simul., 16 (2011), pp. 3375-3384.[7]Y. Moreno, R. Pastor-Satorras, and A. Vespignani, Epidemic outbreaks in complex heterogeneous networks, Eur. Phys. J. B., 26 (2002), pp. 521-529.[8]R. Pastor-Satorras and A. Vespignani, Epidemic spreading in scale free networks, Phys. Rev. Lett., 86 (2001), pp. 3200–3203.[9]Q. Wu, X. Fu and M. Yang 2011 Epidemic thresholds in a heterogenous population with competing strains Chin. Phys. B, (2011), 046401[10]J. Wei and J.Cui , Dynamics of SIS epidemic model with the standard incidence rate and saturated treatment function, J. Bio., 5 (2012), 1260003[11]Q. Wu, M. Small, and H. Liu, Superinfection behaviors on scale-free networks with competing strains, J. Nonlinear Sci., 23 (2013), pp. 113-127.[12]J. Yang and C. Li, Dynamics of a competing two-strain SIS epidemic model on complex networks with a saturating incidence rate, J. Phys. A: Math. Theor., 49 (2016), 215601.[13]G. Zhu, X. Fu, G. Chen, Spreading dynamics and global stability of a generalized epidemic model on complex heterogeneous networks, Appl. Math. Model., 36 (2012), pp. 5808-5817.
 電子全文(網際網路公開日期：20220629)
 國圖紙本論文
 推文當script無法執行時可按︰推文 網路書籤當script無法執行時可按︰網路書籤 推薦當script無法執行時可按︰推薦 評分當script無法執行時可按︰評分 引用網址當script無法執行時可按︰引用網址 轉寄當script無法執行時可按︰轉寄

 1 搖擺桿：建模與模擬 2 非常速遷徙SIR疾病傳染模型的穩定性分析 3 兩個出生率和人口總數相關的SEI傳染病模型 4 弦振動的動力邊界值問題 5 LorenzEquations之研究 6 繫鏈衛星系統之相對平衡狀態與穩定性 7 STEKLOV陀螺運動穩定性

 無相關期刊

 無相關點閱論文

 簡易查詢 | 進階查詢 | 熱門排行 | 我的研究室