Mathematical Modeling of Ebola Virus Epidemic

发布时间：2021-01-11 08:08

　　尽管各国政府和世界卫生组织（WHO）在根除非洲埃博拉病毒等相关疾病（EVD）方面做出来了极大努力,但许多人仍然没有意识到一些潜在的埃博拉病毒疾病的传播方式。一些研究人员也忽视了这些潜在的EVD传播模式,以及EVD与其他疾病的共同感染,恢复后EVD的复发以及已经恢复的埃博拉病毒感染者对埃博拉病毒的再感染。在本论文中,我们提出了一个新的但现实的埃博拉病毒相关疾病（EVD）传播动态模型。我们首先给出论文的背景介绍,第一章介绍了埃博拉病毒的生态学和传播,埃博拉病毒病的复发和再感染,埃博拉病毒和疟疾的共感染,埃博拉病毒的生命周期,埃博拉病毒物种,预防EVD,治疗EVD,埃博拉疫苗,相关文献综述,论文目标以及论文的组成。第二章主要研究EVD的各种传播模式,并结合恢复后可能再次感染EVD,长久和暂时恢复的埃博拉病毒受害者。我们计算出了 R₀,讨论了无埃博拉病毒和地方病平衡点的稳定性和存在性。如果R₀<1,无埃博拉病毒平衡点是渐近稳定的,但如果R₀>1则它是不稳定。利用Lasalle的不变原理,在模型中讨论了无病和地方病平衡... 

【文章来源】：华中师范大学湖北省 211工程院校 教育部直属院校

【文章页数】：134 页

【学位级别】：博士

【文章目录】：
中文摘要
Abstract
Acknowledgement
Dedication
List of Abbreviation
Chapter 1 Introduction
    1.1 Preface
    1.2 Ebola virus Ecology and Modes of Transmission
    1.3 Recurrence,Relapse and Reinfection ofEbola Virus Disease
    1.4 Ebola and Malaria Co-infections
    1.5 Life Cycle of Ebola Virus
    1.6 Ebola Virus Species
    1.7 Prevention and Treatment of Ebola Virus Disease
        1.7.1 Prevention of Ebola Virus Disease
        1.7.2 Treatment of Ebola Virus Disease
    1.8 Ebola Vaccine
    1.9 Review of Related Literature
    1.10 Objectives of the Thesis
    1.11 Organization of the Thesis
Chapter 2 An Epidemiological model of Ebola virus disease transmissionwith reinfection and Optimal Control
    2.1 Introduction
    2.2 Model Description
        2.2.1 Well-Posedness of the Model
    2.3 Model Analysis
        2.3.1 Equilibria
        2.3.2 Ebola- Free Equilibrium
        2.3.3 Basic Reproduction Number
        2.3.4 Existence of Endemic Equilibrium
    2.4 Global Stability
        2.4.1 Global Stability of the Ebola-free equilibrium
        2.4.2 Global Stability of endemic equilibrium
    2.5 Sensitivity Analysis
    2.6 Epidemiological Model of Ebola VirusDisease with Optimal control
        2.6.1 Existence of an optimal control
        2.6.2 Characterization of the optimal controls
        2.6.3 The Optimality System
    2.7 Numerical Simulations
1）and treatment （u₂）control only">        2.7.1 Prevention（u₁）and treatment （u₂）control only
1）and（u₃）vaccination control only">        2.7.2 Prevention（u₁）and（u₃）vaccination control only
2）and vaccination（u₃）only">        2.7.3 Treatment（u₂）and vaccination（u₃）only
1,u₂,u₃）">        2.7.4 Prevention,treatment and vaccination（u₁,u₂,u₃）
    2.8 Discussion and Conclusion
Chapter 3 An SITR theoretical model of Ebola transmission dynamics withrecurrence, relapse and reinfection
    3.1 Introduction
    3.2 Model Description
    3.3 Model Analysis
        3.3.1 Basic Properties
        3.3.2 Ebola-Free Equilibrium and Basic Reproduction Number
        3.3.3 Local Stability of Ebola-Free Equilibrium
        3.3.4 Global Stability of Ebola-Free Equilibrium
        3.3.5 Existence of Endemic Equilibrium
        3.3.6 Local Stability of Endemic Equilibrium andBifurcation Analysis
        3.3.7 Sensitivity analysis of the basic reproductionnumber
    3.4 Discussion and Conclusions
Chapter 4 Modeling and analysis of Ebola and Malaria co-infections withoptimal control
    4.1 Introduction
    4.2 Model Description
        4.2.1 Model Asumptions
        4.2.2 Positivity solutions of the model
        4.2.3 Boundedness of solutions
    4.3 Ebola only model
        4.3.1 Ebola-free equilibrium and basic reproduction number
        4.3.2 Local stability analysis of Ebola-free equilibrium
        4.3.3 Existence of Endemic equilibrium
    4.4 Malaria only model
        4.4.1 Malaria-free equilibrium and basic reproduction number
        4.4.2 Local Stability of Malaria-free equilibrium
        4.4.3 Existence of Endemic equilibrium （EE）
    4.5 Analysis of Ebola and Malaria co-infection model
em">        4.5.1 Analysis of the basic reproduction number Rem

        4.5.2 Existence of backward bifurcation
        4.5.3 Sensitivity Analysis of the basic reproductionnumber
    4.6 Discussion and Conclusions
Chapter 5 Conclusion, Future work and Recommendations
    5.1 Conclusion
    5.2 Future work
    5.3 Recommendations
References
List of Publications



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