Mathematical structures of epidemic systems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin u.a.
Springer
1993
|
| Series: | Lecture notes in biomathematics
97 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 265 - 277 |
| Physical Description: | XIV, 283 S. graph. Darst. |
| ISBN: | 3540565264 0387565264 |
Staff View
MARC
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| 100 | 1 | |a Capasso, Vincenzo |d 1945- |e Verfasser |0 (DE-588)110728556 |4 aut | |
| 245 | 1 | 0 | |a Mathematical structures of epidemic systems |c Vincenzo Capasso |
| 264 | 1 | |a Berlin u.a. |b Springer |c 1993 | |
| 300 | |a XIV, 283 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in biomathematics |v 97 | |
| 500 | |a Literaturverz. S. 265 - 277 | ||
| 650 | 7 | |a Epidemieën |2 gtt | |
| 650 | 7 | |a Wiskundige modellen |2 gtt | |
| 650 | 4 | |a Épidémies - Modèles mathématiques | |
| 650 | 4 | |a Épidémiologie - Modèles mathématiques | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Epidemiologic Methods | |
| 650 | 4 | |a Epidemiology |x Mathematical models | |
| 650 | 4 | |a Models, Theoretical | |
| 650 | 0 | 7 | |a Mathematisches Modell |0 (DE-588)4114528-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Epidemiologie |0 (DE-588)4015016-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Epidemiologie |0 (DE-588)4015016-1 |D s |
| 689 | 0 | 1 | |a Mathematisches Modell |0 (DE-588)4114528-8 |D s |
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Record in the Search Index
| _version_ | 1804122569207447552 |
|---|---|
| adam_text | Table of Contents
1. Introduction 1
2. Linear models 7
2.1 One population models 7
2.1.1 SIR model with vital dynamics 8
2.1.2 SIR model with temporary immunity 9
2.1.3 SIR model with carriers 10
2.1.4 The general structure of bilinear systems 10
2.2 Epidemic models with two or more interacting populations 13
2.2.1 Gonorrhea model 13
2.2.2 SIS model in two communities with migration 14
2.2.3 SIS model for two dissimilar groups 15
2.2.4 Host vector host model 16
2.3 The general structure 17
2.3.1 Constant total population 18
2.3.1.1 Case A 21
2.3.1.1.1 SIR model with vital dynamics 21
2.3.1.1.2 SIRS model with temporary immunity 22
2.3.1.1.3 SIR model with carriers 22
2.3.1.1.4 SIR model with vertical transmission 23
2.3.1.2 Case B 24
2.3.1.2.1 Gonorrhea model 24
2.3.1.2.2 SIS model in two communities with migra¬
tion 25
2.3.1.2.3 SIS model for two dissimilar groups 26
2.3.1.2.4 Host vector host model 27
2.3.2 Nonconstant total population 30
2.3.2.1 The parasite host system 35
2.3.2.2 An SIS model with vital dynamics 38
2.3.2.3 An SIRS model with vital dynamics in a population
with varying size 39
2.3.2.4 An SIR model with vertical transmission and vary¬
ing population size. A model for AIDS 44
2.3.4 Multigroup models 47
2.3.4.1 SIS model for n dissimilar groups. A model for go¬
norrhea in an heterogeneous population 47
2.3.4.2 SIR model for n dissimilar groups 49
XI
Strongly nonlinear models 57
3.1 The nonlinear SEIRS model 59
3.1.1 Stability of the nontrivial equilibria 66
3.2 A general nonlinear SEIRS model 69
3.2.1 Stability of equilibria 75
3.3 An epidemic model with nonlinear dependence upon the popu¬
lation size 77
3.4 Mathematical models for HIV/AIDS infections 81
3.4.1 One population models. One stage of infection 81
3.4.2 One population models. Distributed time of infectiousness 90
3.4.3 One population models. Multiple stages of infection, with
variable infectiousness 93
3.4.4 Multigroup models with multiple stages of infectiousness 97
L Quasimonotone systems. Positive feedback systems.
Cooperative systems 109
4.1 Introduction 109
4.2 The spatially homogeneous case 110
4.3 Epidemic models with positive feedback 112
4.3.1 Gonorrhea 113
4.3.2 Schistosomiasis 114
4.3.3 The Ross malaria model 115
4.3.4 A man environment man epidemic system 117
4.4 Qualitative analysis of the space homogeneous autonomous case 118
4.5 The periodic case 129
4.6 Multigroup models 133
4.6.1 A model for gonorrhea in a nonhomogeneous population 133
4.6.2 Macdonald s model for the transmission of schistosomiasis
in heterogeneous populations 141
5. Spatial heterogeneity 149
5.1 Introduction 149
5.2 Quasimonotone systems 152
5.3 The periodic case 163
5.3.1 Existence and stability of a nontrivial periodic endemic
state 166
5.4 Saddle point behavior 169
5.5 Boundary feedback systems 174
5.6 Lyapunov methods for spatially heterogeneous systems 182
XII
6. Age structure 191
6.1 An SIS model with age structure 193
6.1.1 The intracohort case 194
6.1.2 The intercohort case 198
6.2 An SIR model with age structure 201
7. Optimization problems 207
7.1 Optimal control 207
7.2 Identification 210
Appendix A. Ordinary differential equations and dynamical
systems in finite dimensional spaces 211
A.I The initial value problem for systems of ODE s 211
A. 1.1 Autonomous systems 214
A.1.1.1 Autonomous systems. Limit sets, invariant sets 217
A.1.1.2 Two dimensional autonomous systems 218
A.2 Linear systems of ODE s 220
A.2.1 General linear systems 220
A.2.2 Linear systems with constant coefficients 222
A.3 Stability 226
A.3.1 Linear systems with constant coefficients 228
A.3.2 Stability by linearization 228
A.4 Quasimonotone (cooperative) systems 229
A.4.1 Quasimonotone linear systems 230
A.4.2 Nonlinear quasimonotone autonomous systems 232
A.4.2.1 Lower and upper solutions, invariant rectangles,
contracting rectangles 235
A.5 Lyapunov methods. LaSalle Invariance Principle 236
Appendix B. Dynamical systems in infinite dimensional spaces 239
B.I Banach spaces 239
B.I.I Ordered Banach spaces 242
B.1.2 Functions 243
B.I.3 Linear operators on Banach spaces 246
B.1.4 Dynamical systems and C0 semigroups 249
B.2 The initial value problem for systems of semilinear parabolic
equations (reaction diffusion systems) 252
B.2.1 Semilinear quasimonotone parabolic autonomous systems 255
B.2.1.1 The linear case 257
B.2.1.2 The nonlinear case 259
B.2.1.3 Lower and upper solutions. Existence of nontrivial
equilibria 260
XIII
B.2.2 Lyapunov methods for PDE s. LaSalle Invariance
Principle in Banach spaces 263
References 265
Notation 279
Subject index 281
XIV
|
| any_adam_object | 1 |
| author | Capasso, Vincenzo 1945- |
| author_GND | (DE-588)110728556 |
| author_facet | Capasso, Vincenzo 1945- |
| author_role | aut |
| author_sort | Capasso, Vincenzo 1945- |
| author_variant | v c vc |
| building | Verbundindex |
| bvnumber | BV008184042 |
| callnumber-first | R - Medicine |
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| callnumber-raw | RA652.2.M3 |
| callnumber-search | RA652.2.M3 |
| callnumber-sort | RA 3652.2 M3 |
| callnumber-subject | RA - Public Medicine |
| classification_rvk | SI 840 |
| classification_tum | BIO 105f |
| ctrlnum | (OCoLC)27813994 (DE-599)BVBBV008184042 |
| dewey-full | 614.4/0151 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 614 - Forensic medicine; incidence of disease |
| dewey-raw | 614.4/0151 |
| dewey-search | 614.4/0151 |
| dewey-sort | 3614.4 3151 |
| dewey-tens | 610 - Medicine and health |
| discipline | Biologie Mathematik Medizin |
| format | Book |
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| id | DE-604.BV008184042 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:15:57Z |
| institution | BVB |
| isbn | 3540565264 0387565264 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005401181 |
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| physical | XIV, 283 S. graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in biomathematics |
| series2 | Lecture notes in biomathematics |
| spelling | Capasso, Vincenzo 1945- Verfasser (DE-588)110728556 aut Mathematical structures of epidemic systems Vincenzo Capasso Berlin u.a. Springer 1993 XIV, 283 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in biomathematics 97 Literaturverz. S. 265 - 277 Epidemieën gtt Wiskundige modellen gtt Épidémies - Modèles mathématiques Épidémiologie - Modèles mathématiques Mathematisches Modell Epidemiologic Methods Epidemiology Mathematical models Models, Theoretical Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Epidemiologie (DE-588)4015016-1 gnd rswk-swf Epidemiologie (DE-588)4015016-1 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Lecture notes in biomathematics 97 (DE-604)BV005875746 97 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005401181&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Capasso, Vincenzo 1945- Mathematical structures of epidemic systems Lecture notes in biomathematics Epidemieën gtt Wiskundige modellen gtt Épidémies - Modèles mathématiques Épidémiologie - Modèles mathématiques Mathematisches Modell Epidemiologic Methods Epidemiology Mathematical models Models, Theoretical Mathematisches Modell (DE-588)4114528-8 gnd Epidemiologie (DE-588)4015016-1 gnd |
| subject_GND | (DE-588)4114528-8 (DE-588)4015016-1 |
| title | Mathematical structures of epidemic systems |
| title_auth | Mathematical structures of epidemic systems |
| title_exact_search | Mathematical structures of epidemic systems |
| title_full | Mathematical structures of epidemic systems Vincenzo Capasso |
| title_fullStr | Mathematical structures of epidemic systems Vincenzo Capasso |
| title_full_unstemmed | Mathematical structures of epidemic systems Vincenzo Capasso |
| title_short | Mathematical structures of epidemic systems |
| title_sort | mathematical structures of epidemic systems |
| topic | Epidemieën gtt Wiskundige modellen gtt Épidémies - Modèles mathématiques Épidémiologie - Modèles mathématiques Mathematisches Modell Epidemiologic Methods Epidemiology Mathematical models Models, Theoretical Mathematisches Modell (DE-588)4114528-8 gnd Epidemiologie (DE-588)4015016-1 gnd |
| topic_facet | Epidemieën Wiskundige modellen Épidémies - Modèles mathématiques Épidémiologie - Modèles mathématiques Mathematisches Modell Epidemiologic Methods Epidemiology Mathematical models Models, Theoretical Epidemiologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005401181&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV005875746 |
| work_keys_str_mv | AT capassovincenzo mathematicalstructuresofepidemicsystems |