考虑接种的轮状病毒和疟疾协同传播模型与考虑公共卫生教育效果的潜蚤病传播模型研究

发布时间：2024-07-05 03:46

　　轮状病毒、疟疾和绦虫病继续在全世界,特别是在发展中国家造成相当大的突发公共卫生事件。本论文进行了两项研究:一是考虑接种的轮状病毒和疟疾协同感染传播模型,二是具有公共卫生教育效果的潜蚤病流行病模型。第一项研究提出了一种针对轮状病毒和疟疾传播的8维动力学模型,旨在研究它们在接种疫苗时的协同关系。该研究重点探讨疫苗接种对动力学状态的影响,特别是在轮状病毒-疟疾共存流行的撒哈拉以南非洲地区。我们首先研究了仅轮状病毒传播和仅疟疾传播的子模型,以便深入了解疫苗接种如何分别影响每种疾病的传播动力学,接着,我们研究了完整模型的动力学性态。我们首先计算了轮状病毒和疟疾子模型的基本再生数,在此基础上证明了平衡点的存在性和稳定性。利用中心流形理论和Lyapunov稳定性理论,我们分别证明了完整模型地方病的局部和全局稳定性。最后,我们研究了疫苗接种对轮状病毒和疟疾传播动力学的影响。结果表明,仅轮状病毒和仅疟疾的子模型的无病平衡点在其基本再生数小于1时全局渐近稳定,而完整的协同感染模型存在分支现象。进一步,轮状病毒疫苗接种将有效减少疟疾的协同感染,从而改变疾病传播结果。在第二项研究中,我们利用常微分方程构造了一...

【文章页数】：118 页

【学位级别】：博士

【文章目录】：
摘要
Abstract
1 General Introduction
    1.1 Background Information and Motivation
    1.2 Research Objectives
    1.3 Thesis Overview
    1.4 Significance of the Study
    1.5 Research Methodology
2 Analysis of the Effects of Vaccination on Rotavirus and Malaria Co-infectionDynamics
    2.1 Introduction
    2.2 Model description and formulation
    2.3 Rotavirus-only sub-model
        2.3.1 Well-posedness of the rotavirus-only sub-model
        2.3.2 Stability analysis of the rotavirus-only sub-model
    2.4 Malaria-only sub-model
        2.4.1 Well-posedness of the malaria-only sub-model
        2.4.2 Stability analysis of the malaria-only sub-model
    2.5 Numerical simulations and discussion
    2.6 Conclusion
3 Analysis of the Dynamics of the Rotavirus and Malaria Co-infection Modelwith Vaccination
    3.1 Introduction
    3.2 Basic properties of the model
        3.2.1 Positivity and boundedness of solutions
    3.3 Stability analysis of the rotavirus-malaria co-epidemic model with vaccination
        3.3.1 Local stability of the disease-free equilibrium point
        3.3.2 Global stability of the disease-free equilibrium point
        3.3.3 Existence of backward bifurcation
        3.3.4 Global stability of the disease-endemic equilibrium point
    3.4 Numerical simulations and discussion
    3.5 Conclusion
4 Dynamic Analysis of the Effects of Public Health Education on the Spread ofTungiasis
    4.1 Introduction
    4.2 Model formulation and description
    4.3 Positivity and boundedness of solutions
    4.4 Stability analysis of the tungiasis epidemic model
        4.4.1 Jigger-free equilibrium point
        4.4.2 Basic reproduction number, RE

        4.4.3 Local stability of the jigger-free equilibrium point
        4.4.4 Global stability of the jigger-free equilibrium point
        4.4.5 Jigger-present equilibrium point
        4.4.6 Local stability of the jigger-present equilibrium point
        4.4.7 Global stability of the jigger-present equilibrium point
    4.5 Numerical simulations and discussion
    4.6 Conclusion
5 General Conclusion and Scope for Future Research
    5.1 General Conclusion
    5.2 Scope for Future Research
Bibliography
List of Publications
Acknowledgements



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