疟疾和非洲猪瘟传播的数学模型

发布时间：2021-09-22 06:20

　　Malaria is a common and life-threatening disease in many tropical and sub-tropical regions.It is caused by the protozoan parasite of the genus Plasmodium.Human malaria is caused by four different species of Plasmodium:P.falciparum,P.malariae,P.ovale and P.vivax.Among these species,P.falciparum causes the most severe form of malaria.The species P.Knowlesi infect animals but occasion-ally it can infect humans with the plasmodium parasite.The severity of malarial illness depends mostly on the immun... 

【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】：140 页

【学位级别】：博士

【文章目录】：
Abstract
Acknowledgements
List of Abbreviations
Chapter 1 Introduction and Overview
    1.1 Overview of Malaria
    1.2 Vector-borne Diseases
    1.3 Vectors and Their Distributions
    1.4 Life Cycle of Malaria Parasites
    1.5 Malaria Species
    1.6 Malaria Control and Treatments
    1.7 Malaria Symptoms
        1.7.1 Symptoms of Uncomplicated Malaria
        1.7.2 Symptoms of Severe(Complicated)Malaria
    1.8 Optimal Control Theory
    1.9 Overview of African Swine Fever
    1.10 Transmission and Spread of African Swine Fever
    1.11 Vaccination and Control of African Swine Fever
    1.12 Effects of the ASF on Human Health
    1.13 African Swine Fever Symptoms
        1.13.1 In the Acute Cases, the Disease Has the Following Symptoms
        1.13.2 In the Normal Cases, the ASF Has the Following Symptoms
        1.13.3 In the Chronic Cases, the Disease Has the Following Symptoms
    1.14 Objective of the Thesis
    1.15 Outline of the Thesis
Chapter 2 A Mathematical Model of Malaria Transmission in theDemocratic Republic of the Congo
    2.1 Mathematical Framework Overview
    2.2 Model Formulation
        2.2.1 Model Description
    2.3 Model Analysis
        2.3.1 Positivity and Boundedness of the Solutions
        2.3.2 Existence of Equilibria
        2.3.3 Local Stability of Disease-free Equilibrium
        2.3.4 Endemic Equilibrium and Bifurcation
        2.3.5 Local Stability of Endemic Equilibrium
        2.3.6 Global Asymptotic Stability of Disease-free Equilibrium
    2.4 Numerical Simulations
    2.5 Sensitivity Analysis
    2.6 Optimal Control
    2.7 Numerical Simulations for Optimal Control
        2.7.1 Prevention of Malaria Through the Use of Treated Bed-net u_1(t) Only
        2.7.2 Prevention of Malaria Through Treatment with Drugs u_2(t)Only
        2.7.3 Prevention of Malaria Through the Use of Treated Bed-net u_1(t) and Treatment with Drugs u_2(l)
    2.8 Conclusion of Chapter 2
Chapter 3 Analysis of A vector-bias Malaria Transmission Modelwith Application to Mexico, Sudan and the Democrat-ic Republic of the Congo
    3.1 Mathematical Famework
    3.2 Model Formulation
    3.3 Existence and Stability of Equilibria
    3.4 Numerical Simulations and Applications to Mexico,Sudan and Con-go, DR
    3.5 Sensitivity Analysis
    3.6 Discussions and Conclusion for Chapter 3
Chapter 4 Mathematical Model of Malaria Transmission withOptimal Control in the Democratic Republic of theCongo
    4.1 Mathematical Framework Overview
    4.2 Mathematical Model
        4.2.1 Model Description
        4.2.2 Positivity and Boundedness of the Solutions
    4.3 Existence of Equilibria
        4.3.1 Disease-free Equilibrium and Basic Reproduction Number
        4.3.2 Endemic Equilibria and Backward Bifurcation
        4.3.3 Global Stability of the Endemic Equilibrium
    4.4 Numerical Simulations
    4.5 Analysis of Optimal Control
    4.6 Numerical Simulations of Optimal Control
        4.6.1 Prevention of Disease Using u_1 Only
        4.6.2 Prevention of Disease Using u_2 Only
        4.6.3 Prevention of Disease Using u_3 Only
        4.6.4 Prevention of Disease Using u_1 and u_2 Only
        4.6.5 Prevention of Disease Using u_1 and u_3 Only
        4.6.6 Prevention of Disease Using u_2 and u_3 Only
        4.6.7 Prevention of Disease Using u_1,u_2 and u_3 Only
    4.7 Conclusion for Chapter 4
Chapter 5 A mathematical Model Using Quarantine for Control-ling the Spread of African Swine Fever
    5.1 Mathematical Framework Overview
    5.2 Mathematical Model
        5.2.1 Model Description
    5.3 Model Analysis
        5.3.1 Positivity and Boundedness of the Solutions
        5.3.2 Basic Reproduction Number and Existence of Equilibria
        5.3.3 Stability of the Disease-free Equilibrium
        5.3.4 Existence of Endemic Equilibrium
    5.4 Numerical Simulation
    5.5 Sensitivity Analysis (SA) of R_0
    5.6 Conclusion of Chapter 5
Chapter 6 Conclusion and Future Work
    6.1 Conclusion
    6.2 Future Work
Appendix
References
List of Publications



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