INFECTIOUS DISEASE MODELLINGRESEARCH PROGRESS -- INFECTIOUS DISEASE MODELLINGRESEARCH PROGRESS -- CONTENTS -- PREFACE -- EPIDEMIOLOGY OF CORRUPTION AND DISEASETRANSMISSION AS A SATURABLE INTERACTION:THE SIS CASE∗ -- Abstract -- 1. Epidemiology of Corruption -- 1.1. Introduction -- 1.2. Model Equations -- 1.3. Model Analysis -- 1.4. Stabilizing the Corruption-Free Steady State through Control -- 1.5. Discussion -- 2. Disease Transmission as a Saturable Interaction: The SISCase -- 2.1. Introduction -- 2.2. Formulation of Model Equations -- 2.3. Age-independent Infectivity and Existence of Steady States -- 2.4. Stability of Equilibria -- 2.5. Age-dependent Infectivity and Existence of Steady States -- 2.6. Stability of Steady States -- 2.7. Discussion -- 2.8. Summary of Results -- 2.8.1. Age-independent Infectivity -- 2.8.2. Age-dependent Infectivity -- Acknowledgments -- References -- A MATHEMATICAL ANALYSIS OF INFLUENZAWITH TREATMENT AND VACCINATION -- Abstract -- 1. Introduction -- 1.1. Motivation and Objectives -- 1.2. Methodology -- 1.3. Brief Review of Previous Studies -- 2. Model Framework and Analysis -- 2.1. Model Framework -- 2.2. Descriptions of Variables and Parameters -- 2.3. The Model -- 2.4. Model Analysis -- 2.5. Positivity of Solutions -- 2.6. The Model in the Absence of Inflow of Infectives (ˆ = 0) -- 2.7. Non-existence of the Trivial Equilibrium -- 2.8. Disease-Free Equilibrium (E0) -- 2.9. Computation of the Reproduction Numbers R0,RV ,RT and RV T -- 2.10. Local Stability of the Disease-Free Equilibrium E0 -- 2.11. Global Stability of the Disease-Free Equilibrium E0 -- 2.12. Effects of Public Health Measures (Treatment and Vaccination) -- 2.13. The Role of RV T on Disease Eradication -- 2.14. Endemic Equilibrium and Its Stability -- 2.15. Stability Analysis when RV T > 1 -- 2.16. Endemic Equilibria when ˆ > 0.

2.17. Equilibria when ˆ = 0 -- 2.18. Existence of Backward Bifurcation -- 2.19. Local Stability of the Endemic Equilibrium E1 -- 2.20. Global Stability of the EE E1 when RV T > 1 -- 2.21. The Model with Mass-Action Incidence -- 2.22. Persistence of Solutions of the Model with Mass-Action Incidence -- 2.23. Treatment-Only Submodel (with Mass-Action Incidence) -- 2.24. Existence of Backward Bifurcation in the Treatment-Only Model -- 3. Sensitivity Analysis and Numerical Simulations -- 3.1. Sensitivity Analysis -- 3.2. Sensitivity Indices of RV T -- 3.3. Numerical Simulations -- 4. Discussion and Conclusion -- 4.1. Discussion -- 4.2. Conclusion -- Appendix A -- Appendix B -- Appendix C -- Appendix D -- (1) Endemic Equilibria when ˆ = 0 -- (2) Endemic Equilibrium when ˆ > 0 and = 0 -- References -- A THEORETICAL ASSESSMENT OF THE EFFECTSOF CHEMOPROPHYLAXIS, TREATMENT AND DRUGRESISTANCE IN TB INDIVIDUALS CO-INFECTEDWITH HIV/AIDS -- Abstract -- 1. Introduction -- 2. A Two Strain Tuberculosis Model -- 2.1. Disease-Free Equilibrium and Stability Analysis -- 2.2. Endemic Equilibria -- 2.2.1. Drug Resistant TB-only Equilibrium -- 2.2.2. Drug Sensitive TB-only Equilibrium -- 2.2.3. Co-existence of the Two TB Strains Endemic Equilibrium -- 3. A Two Strain HIV/AIDS Only Model -- 3.1. Disease-Free Equilibrium and Stability Analysis -- 3.2. Endemic Equilibria -- 3.2.1. Anti-retroviral Resistant HIV-strain Only Equilibrium -- 3.2.2. Antiretroviral Sensitive HIV-strain Only Equilibrium -- 3.2.3. Co-existence of Both HIV Strains Endemic Equilibrium -- 3.3. Numerical Simulations -- 4. Effects of Treatment and Drug Resistance in TB IndividualsCo-infected with HIV/AIDS -- 4.1. Disease-Free Equilibrium and Stability Analysis -- 4.2. Endemic Equilibria -- 4.3. Analysis of the Reproduction Number RAT -- 5. Summary and Concluding Remarks -- Acknowledgements -- Appendix A.

Appendix B -- Appendix C -- Appendix D -- References -- WHEN ZOMBIES ATTACK!: MATHEMATICALMODELLING OF AN OUTBREAK OF ZOMBIEINFECTION -- Abstract -- 1. Introduction -- 2. The Basic Model -- 3. The Model with Latent Infection -- 4. The Model with Quarantine -- 5. A Model with Treatment -- 6. Impulsive Eradication -- 7. Discussion -- Acknowledgements -- References -- A REVIEW OF MATHEMATICAL MODELLINGOF THE EPIDEMIOLOGY OF MALARIA -- Abstract -- 1. Introduction -- 2. Malaria -- 2.1. Control Strategies -- 3. Malaria Immunoepidemiology -- 4. Conclusion -- References -- A MATHEMATICAL MODEL OF THE WITHIN -VECTOR DYNAMICS OF THE Plasmodium FalciparumPROTOZOAN PARASITE -- Abstract -- 1. Introduction -- 2. The Basic Mathematical Model -- 3. Initial Conditions and Parameters -- 4. Solution and Results from the Basic Model -- 5. Sensitivity Analysis of the Parameters -- 6. Model Extension -- 7. Conclusion and Discussion -- References -- MYCOBACTERIUM TUBERCULOSIS TREATMENTAND THE EMERGENCE OF A MULTI-DRUGRESISTANT STRAIN IN THE LUNGS -- Abstract -- 1. Introduction -- 1.1. Model Development -- 1.1.1. Macrophages -- 1.1.2. Drug Sensitive Bacteria Strain -- 1.1.3. Drug Resistant Bacteria Strain -- 1.1.4. CD4+ T Lymphocyte Cells and CD8+ T Cytotoxic Cells -- 2. Model Analysis -- 2.1. Reproductive Ratio -- 2.1.1. Global Stability Conditions for the Disease-Free Equilibrium -- 3. Numerical Simulations -- 3.1. Efficacy Levels -- 3.2. Drug Sensitivity Levels -- 3.3. Mono Drug Resistance -- 4. The Impact of Adherence on the Emergenceof MDRTB-strains -- 5. Discussion -- References -- MATHEMATICAL MODELING FOR TUMOR GROWTHAND CONTROL STRATEGIES -- Abstract -- 1. Introduction -- 1.1. Avascular Tumor (Solid Tumor) Growth -- 1.2. View of Avascular Tumor -- 1.3. Angiogenesis -- 1.4. Vascularized Tumor Penetrated by Capillaries -- 1.5. Cause of Cancer -- 1.6. Treatments.

2. An Ordinary Mathematical Model for Tumor Growth -- 2.1. Temporal Model -- 2.2. Spatio-temporal Model -- 2.3. Conclusions -- 3. A Model for the Interaction between Tumors Cell Density andImmune Response -- 3.1. Mathematical Model -- 3.2. Solution -- 3.3. Conclusion -- 4. A Model for Tumor Treatment with Chemotherapy -- 4.1. Introduction -- 4.2. The Model -- 4.3. Numerical Result -- 4.4. Conclusions -- 5. A Model of Radioimmunotherapy for Tumor Treatment -- 5.1. Introduction -- 5.2. Mathematical Model -- 5.2.1. Linear Spatial Dependence -- 5.2.2. Exponential Spatial Dependence -- 5.3. Discussion -- References -- WITH-IN HOST MODELLING: THEIRCOMPLEXITIES AND LIMITATIONS -- Abstract -- 1. Introduction -- 2. What Is with-in Host Modelling -- 3. Categorisation of Disease Models -- 4. Challenges of with-in Host Modelling -- 5. Discussion -- References -- INDEX.