Infectious Disease Modelling Research Progress

INFECTIOUS DISEASE MODELLING RESEARCH PROGRESS\r......Page 4
CONTENTS......Page 8
PREFACE......Page 10
1.1. Introduction......Page 12
1.2. Model Equations......Page 13
1.3. Model Analysis......Page 14
1.4. Stabilizing the Corruption-Free Steady State through Control......Page 22
1.5. Discussion......Page 24
2.1. Introduction......Page 25
2.2. Formulation of Model Equations......Page 26
2.3. Age-independent Infectivity and Existence of Steady States......Page 27
2.4. Stability of Equilibria......Page 30
2.5. Age-dependent Infectivity and Existence of Steady States......Page 33
2.6. Stability of Steady States......Page 35
2.7. Discussion......Page 38
2.8.2. Age-dependent Infectivity......Page 39
References......Page 40
Abstract......Page 42
1. Introduction......Page 43
1.2. Methodology......Page 45
1.3. Brief Review of Previous Studies......Page 46
2.1. Model Framework......Page 49
2.2. Descriptions of Variables and Parameters......Page 50
2.4. Model Analysis......Page 51
2.5. Positivity of Solutions......Page 52
2.6. The Model in the Absence of Inflow of Infectives (\Z = 0)......Page 53
2.9. Computation of the Reproduction Numbers R0,RV ,RT and RV T......Page 54
2.10. Local Stability of the Disease-Free Equilibrium E0......Page 55
2.11. Global Stability of the Disease-Free Equilibrium E0......Page 56
2.12. Effects of Public Health Measures (Treatment and Vaccination)......Page 57
2.14. Endemic Equilibrium and Its Stability......Page 60
2.16. Endemic Equilibria when \Z > 0......Page 61
2.18. Existence of Backward Bifurcation......Page 64
2.19. Local Stability of the Endemic Equilibrium E1......Page 66
2.20. Global Stability of the EE E1 when RV T > 1......Page 70
2.22. Persistence of Solutions of the Model with Mass-Action Incidence......Page 73
2.23. Treatment-Only Submodel (with Mass-Action Incidence)......Page 77
2.24. Existence of Backward Bifurcation in the Treatment-Only Model......Page 80
3.1. Sensitivity Analysis......Page 81
3.2. Sensitivity Indices of RV T......Page 82
3.3. Numerical Simulations......Page 83
4.1. Discussion......Page 84
4.2. Conclusion......Page 88
Appendix C......Page 89
(1) Endemic Equilibria when \Z = 0......Page 90
References......Page 92
Abstract......Page 96
1. Introduction......Page 97
2. A Two Strain Tuberculosis Model......Page 99
2.1. Disease-Free Equilibrium and Stability Analysis......Page 102
2.2.1. Drug Resistant TB-only Equilibrium......Page 103
2.2.2. Drug Sensitive TB-only Equilibrium......Page 107
2.2.3. Co-existence of the Two TB Strains Endemic Equilibrium......Page 109
3. A Two Strain HIV/AIDS Only Model......Page 112
3.1. Disease-Free Equilibrium and Stability Analysis......Page 115
3.2.1. Anti-retroviral Resistant HIV-strain Only Equilibrium......Page 117
3.2.2. Antiretroviral Sensitive HIV-strain Only Equilibrium......Page 119
3.2.3. Co-existence of Both HIV Strains Endemic Equilibrium......Page 120
3.3. Numerical Simulations......Page 121
4. Effects of Treatment and Drug Resistance in TB IndividualsCo-infected with HIV/AIDS......Page 124
4.1. Disease-Free Equilibrium and Stability Analysis......Page 127
4.2. Endemic Equilibria......Page 128
4.3. Analysis of the Reproduction Number RAT......Page 129
5. Summary and Concluding Remarks......Page 135
Appendix B......Page 136
Appendix D......Page 138
References......Page 139
1. Introduction......Page 144
2. The Basic Model......Page 146
3. The Model with Latent Infection......Page 148
4. The Model with Quarantine......Page 151
5. A Model with Treatment......Page 154
6. Impulsive Eradication......Page 155
Acknowledgements......Page 157
References......Page 160
Abstract......Page 162
1. Introduction......Page 163
2. Malaria......Page 164
2.1. Control Strategies......Page 167
3. Malaria Immunoepidemiology......Page 171
References......Page 176
1. Introduction......Page 188
2. The Basic Mathematical Model......Page 191
3. Initial Conditions and Parameters......Page 193
4. Solution and Results from the Basic Model......Page 196
5. Sensitivity Analysis of the Parameters......Page 199
6. Model Extension......Page 201
7. Conclusion and Discussion......Page 203
References......Page 204
Abstract......Page 208
1. Introduction......Page 209
1.1.1. Macrophages......Page 211
1.1.3. Drug Resistant Bacteria Strain......Page 212
1.1.4. CD4+ T Lymphocyte Cells and CD8+ T Cytotoxic Cells......Page 213
2. Model Analysis......Page 214
2.1. Reproductive Ratio......Page 219
2.1.1. Global Stability Conditions for the Disease-Free Equilibrium......Page 222
3. Numerical Simulations......Page 225
3.2. Drug Sensitivity Levels......Page 227
4. The Impact of Adherence on the Emergenceof MDRTB-strains......Page 231
5. Discussion......Page 234
References......Page 236
Abstract......Page 240
1.1. Avascular Tumor (Solid Tumor) Growth......Page 241
1.2. View of Avascular Tumor......Page 242
1.3. Angiogenesis......Page 243
1.5. Cause of Cancer......Page 244
1.6. Treatments......Page 245
2.2. Spatio-temporal Model......Page 246
3.1. Mathematical Model......Page 250
3.2. Solution......Page 251
4.1. Introduction......Page 252
4.2. The Model......Page 253
4.3. Numerical Result......Page 254
4.4. Conclusions......Page 255
5.2. Mathematical Model......Page 256
5.2.1. Linear Spatial Dependence......Page 257
5.2.2. Exponential Spatial Dependence......Page 259
References......Page 261
Abstract......Page 264
2. What Is with-in Host Modelling......Page 265
3. Categorisation of Disease Models......Page 266
4. Challenges of with-in Host Modelling......Page 267
5. Discussion......Page 269
References......Page 270
INDEX......Page 272