Modeling and Dynamics of Infectious Diseases (Series in Contemporary Applied Mathematics)

Contents......Page 10
Preface......Page 6
1 Basic knowledge on epidemic dynamics......Page 12
1.1 Adequate contact rate and incidence......Page 13
1.2 Basic reproduction number......Page 14
2 Epidemic models with vaccination......Page 15
3 Epidemic models with quarantine strategy......Page 21
4 Epidemic models with complicated structures......Page 23
5 Epidemic models with natural age and infection age structures......Page 27
6 Epidemic models with time dependent coefficients......Page 30
7 Epidemic models combining with population ecology......Page 32
8 Epidemic models combining with ecotoxicology......Page 34
9 The phenomenon of stability switches on some epidemic models with time delay......Page 35
10 Study on HIV / AIDS......Page 37
11 Modeling and study for SARS transmission and control in China......Page 39
References......Page 43
1 Introduction......Page 47
2 Progresses on specific diseases: scientific contributions......Page 49
2.1 SARS......Page 50
2.2 Pandemic influenza......Page 53
2.3 West Nile Virus......Page 56
3 Other progress and networking activities......Page 60
4.1 Summer school/intensive course, seminar series......Page 62
4.2 International collaboration......Page 66
4.3 The future......Page 67
5 Final remarks......Page 69
Acknowledgement......Page 70
References......Page 71
1 Foreword — Notations......Page 75
2.1 Introduction......Page 77
2.2 The connection graph......Page 78
2.3 Dynamics in the vertices......Page 82
2.3.1 Properties of the movement matrix......Page 84
2.3.2 Case of an irreducible movement matrix......Page 86
2.3.3 Case of a reducible movement matrix......Page 87
3 Methodological aspects......Page 90
3.1 The models under consideration......Page 91
3.1.1 Simple SEIRS......Page 92
3.1.2 SEIRS for multiple species......Page 93
3.1.3 SEIRS model with residency patch......Page 94
3.1.4 Types of movement matrices......Page 96
3.2.2 Nonnegativity and/or positivity of solutions......Page 97
3.2.3 Boundedness of solutions......Page 98
3.3 Behavior of the demographic component......Page 100
3.4 Existence of a disease free equilibrium (DFE)......Page 102
3.5.1 Simple SEIRS......Page 103
3.5.2 SEIRS with multiple species......Page 105
3.5.3 SEIRS with residency patch......Page 107
3.6.1 Simple SEIRS......Page 108
3.6.2 SEIRS with multiple species......Page 109
3.6.3 SEIRS with residence patch......Page 111
3.7.1 Model with classic movement......Page 112
3.7.2 Model with residency patch......Page 114
3.8.1 SEIRS with residency patch......Page 115
3.9.2 Understand the effect of movement......Page 118
4.2 Early works......Page 119
4.3 Kermack-McKendrick-type models......Page 120
4.4 Migration models......Page 122
4.5 Model including residency patch......Page 124
4.6.1 True patch heterogeneity......Page 125
4.6.2 Models with infinite dimensional aspects......Page 126
References......Page 128
1 Introduction......Page 134
2 The network corresponding to a disease outbreak......Page 135
3 Transmissibility......Page 137
4 Some examples of contact networks......Page 141
References......Page 144
1 Introduction......Page 147
2 Mathematical models of pathogen evolution......Page 148
2.1 The underlying epidemiological model......Page 149
2.2 Invasion analysis technique......Page 150
2.3 Price equation technique......Page 153
Appendix......Page 157
References......Page 158
Abstract......Page 161
1 Introduction......Page 162
2 Models with quarantine and isolation......Page 163
3 Reproductive numbers of the general model......Page 166
4 Comparison of models with different sojourn distributions......Page 169
5 Conclusion......Page 175
References......Page 176
Abstract......Page 178
2 Risk of infection......Page 179
3 Assessing the burden......Page 180
3.1 Assessment methods......Page 181
3.2 Assessment examples......Page 182
4 Mitigation strategies......Page 184
5 Evaluating the options......Page 185
5.1 Dynamic modeling......Page 186
5.2 Modeling example......Page 187
6 Monitoring the impact......Page 193
References......Page 194
1 Introduction......Page 198
2 A model with horizontal and vertical transmission......Page 199
3 The persistence equilibrium......Page 201
3.1 Uniqueness and existence......Page 202
3.2 Global stability of the persistence equilibrium......Page 203
4 The multiple strain model......Page 204
5.1 Coexistence equilibrium......Page 208
5.2 Dynamic coexistence......Page 210
6 Global stability for constant contact function and per capita birth rate......Page 211
7 Uniform strong coexistence......Page 217
Appendix: Elements of persistence theory......Page 222
References......Page 225
1 Introduction......Page 227
2 Logistic and Richards models......Page 229
3 Single wave out break......Page 230
4 Outbreaks with multiple waves......Page 235
5 Conclusions and remarks......Page 241
References......Page 245
2 A general disease transmission model......Page 248
3 The basic reproduction number......Page 251
4 The final size of a simple epidemic......Page 252
5 A final size inequality for a general model......Page 254
6.1 The constant rate SIR epidemic model......Page 255
6.2 Simple compartmental models......Page 257
6.3 The SLIAR model for influenza......Page 259
7 Further Reading......Page 261
References......Page 262
1 Introduction......Page 264
2 SIR model in a given population......Page 266
4 SIR model with demographic renewal......Page 269
5 Homogeneous demographic model......Page 272
6 Special homogeneous system......Page 275
7 Case fatality......Page 276
References......Page 277
1 Introduction......Page 279
2 Preliminaries......Page 283
3 Proof of Theorem 1.1......Page 288
Acknowledgments......Page 296
References......Page 297
1 Introduction......Page 300
2.1 Models without demographic structure......Page 301
2.2 Model with vital dynamics......Page 302
3 Analysis of local stability......Page 304
3.1 Models with constant coefficients......Page 305
3.2 Models with delay-dependent coefficients......Page 307
4 Liapunov direct methods......Page 315
5 Conditions of disease persistence......Page 319
References......Page 322
1 Introduction......Page 326
2 Methods......Page 328
3 Model......Page 331
4 Results......Page 335
5 Conclusion and discussion......Page 339
References......Page 340
1 Introduction......Page 342
2 The model formulation......Page 343
3 Surveillance data and numerical simulations......Page 345
3.2 Mosquitoes......Page 346
3.4 Bird ecology with WNV......Page 349
3.5 Simulation results, with the best fit non crow family birds recover rate r = 1/365......Page 350
Acknowledgement......Page 352
References......Page 353