輪狀病毒、瘧疾和絳蟲病繼續(xù)在全世界,特別是在發(fā)展中國家造成相當(dāng)大的突發(fā)公共衛(wèi)生事件。本論文進(jìn)行了兩項(xiàng)研究:一是考慮接種的輪狀病毒和瘧疾協(xié)同感染傳播模型,二是具有公共衛(wèi)生教育效果的潛蚤病流行病模型。第一項(xiàng)研究提出了一種針對輪狀病毒和瘧疾傳播的8維動力學(xué)模型,旨在研究它們在接種疫苗時的協(xié)同關(guān)系。該研究重點(diǎn)探討疫苗接種對動力學(xué)狀態(tài)的影響,特別是在輪狀病毒-瘧疾共存流行的撒哈拉以南非洲地區(qū)。我們首先研究了僅輪狀病毒傳播和僅瘧疾傳播的子模型,以便深入了解疫苗接種如何分別影響每種疾病的傳播動力學(xué),接著,我們研究了完整模型的動力學(xué)性態(tài)。我們首先計(jì)算了輪狀病毒和瘧疾子模型的基本再生數(shù),在此基礎(chǔ)上證明了平衡點(diǎn)的存在性和穩(wěn)定性。利用中心流形理論和Lyapunov穩(wěn)定性理論,我們分別證明了完整模型地方病的局部和全局穩(wěn)定性。最后,我們研究了疫苗接種對輪狀病毒和瘧疾傳播動力學(xué)的影響。結(jié)果表明,僅輪狀病毒和僅瘧疾的子模型的無病平衡點(diǎn)在其基本再生數(shù)小于1時全局漸近穩(wěn)定,而完整的協(xié)同感染模型存在分支現(xiàn)象。進(jìn)一步,輪狀病毒疫苗接種將有效減少瘧疾的協(xié)同感染,從而改變疾病傳播結(jié)果。在第二項(xiàng)研究中,我們利用常微分方程構(gòu)造了一...

【文章頁數(shù)】：118 頁

【學(xué)位級別】：博士

【文章目錄】：
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



本文編號：4000989

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