Vertically transmitted diseases: models and dynamics
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1993
|
| Schriftenreihe: | Biomathematics
23 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 248 S. graph. Darst. |
| ISBN: | 354052004X 038752004X |
Internformat
MARC
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| 100 | 1 | |a Busenberg, Stavros N. |d 1941-1993 |e Verfasser |0 (DE-588)11935022X |4 aut | |
| 245 | 1 | 0 | |a Vertically transmitted diseases |b models and dynamics |c Stavros Busenberg ; Kenneth Cooke |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1993 | |
| 300 | |a XI, 248 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Biomathematics |v 23 | |
| 650 | 7 | |a Disease Transmission |2 cabt | |
| 650 | 7 | |a Mathematical Models |2 cabt | |
| 650 | 7 | |a Biologie - Modèles mathématiques |2 ram | |
| 650 | 7 | |a Biomathématiques |2 ram | |
| 650 | 7 | |a Biométrie |2 ram | |
| 650 | 7 | |a Epidémiologie |2 jussieu | |
| 650 | 7 | |a Foetussen |2 gtt | |
| 650 | 7 | |a Infectieziekten |2 gtt | |
| 650 | 7 | |a Maladies infectieuses - Transmission - Modèles mathématiques |2 ram | |
| 650 | 7 | |a Modèle différence |2 jussieu | |
| 650 | 7 | |a Modèle différentiel |2 jussieu | |
| 650 | 7 | |a Modèle retard |2 jussieu | |
| 650 | 7 | |a Ouder-kind-relaties |2 gtt | |
| 650 | 7 | |a Pasgeborenen |2 gtt | |
| 650 | 7 | |a Populatiedynamica |2 gtt | |
| 650 | 7 | |a Statistiek |2 gtt | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Statistik | |
| 650 | 4 | |a Communicable Diseases |x transmission | |
| 650 | 4 | |a Communicable diseases in newborn infants |x Forecasting | |
| 650 | 4 | |a Communicable diseases in newborn infants |x Mathematical models | |
| 650 | 4 | |a Communicable diseases in the fetus |x Forecasting | |
| 650 | 4 | |a Communicable diseases in the fetus |x Mathematical models | |
| 650 | 4 | |a Infant, Newborn, Diseases |x epidemiology | |
| 650 | 4 | |a Models, Statistical | |
| 650 | 4 | |a Pregnancy Complications, Infectious |x epidemiology | |
| 650 | 0 | 7 | |a Vertikal übertragbare Krankheit |0 (DE-588)4311530-5 |2 gnd |9 rswk-swf |
| 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 |
| 650 | 0 | 7 | |a Vertikale Übertragung |0 (DE-588)4376600-6 |2 gnd |9 rswk-swf |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-003696968 | ||
Datensatz im Suchindex
| _version_ | 1804120094411849728 |
|---|---|
| adam_text | Contents
1 Introduction 1
1.1 What is Vertical Transmission? 1
1.2 Methodology, Terminology and Notation 2
1.3 Examples of Vertically Transmitted Diseases 5
1.4 Organization and Principal Results 7
2 Differential Equations Models 11
2.1 A Classical Model Extended 11
2.2 Some Biological and Modeling Considerations 15
2.3 Model Without Immune Class 17
2.4 Discussion of the Global Result 22
2.5 Proofs of the Results 30
2.6 No Horizontal Transmission 32
2.7 The Model with Immune Class 34
2.7.1 The SIR Model with Vaccination 37
2.8 The Case of Constant Population 38
2.9 A Model with Vaccination 39
2.10 Models with Latency or Maturation Time 41
2.11 Models with Density Dependent Death Rate 44
2.12 Parameter Estimation 46
2.13 Models of Chagas Disease 49
2.13.1 Proportional Mixing and Vector Transmission 49
2.13.2 An SIS Model with Proportional Mixing 56
2.13.3 Logistic Control 59
2.14 An SIRS Model with Proportional Mixing 61
x Contents
2.15 Evolution of Viruses 64
2.16 The Mathematical Background 66
2.16.1 Positivity and Invariant Regions 67
2.16.2 Equilibria and Stability Analysis 68
2.16.3 Global Stability in One and Two Dimensions 71
2.16.4 General Global Stability 73
2.16.5 A Special Global Stability Result 74
2.16.6 Existence and Bifurcation of Periodic Solutions 76
3 Difference Equations Models 79
3.1 Introduction 79
3.2 A Model for the Transmission of Keystone Virus 80
3.3 Population Size Control via Vertical Transmission 84
3.3.1 Fine Structure of Population Size Control 90
3.3.2 Proofs of the Theorems 94
3.4 Vertical Transmission in Insect Populations 106
3.5 Logistic Control in the Reproduction Rate 114
3.5.1 Complicated Dynamics and Long Term Transients 122
3.6 Logistic Control through the Death Terms 129
3.6.1 Synchronous Oviposition 129
3.6.2 Distributed Asynchronous Oviposition 134
3.7 Mathematical Background 135
3.7.1 Positivity and Invariant Regions 135
3.7.2 Equilibria and Stability Analysis 136
3.7.3 Global Stability 138
3.7.4 Periodic Solutions, Bifurcation and Chaos 139
4 Delay Differential Equations Models 143
4.1 The Role of Delays in Epidemic Models 143
4.2 A Model with Maturation Delays 144
4.3 Delays Due to Partial Immunity 148
4.4 Delay Due to an Incubation Period 151
4.5 A Model with Spatial Diffusion 154
Contents xi
4.6 Diseases with Long Subclinical Periods 156
4.7 Mathematical Background 159
4.7.1 Positivity and Invariant Regions 160
4.7.2 Equilibria and Stability Analysis 161
4.7.3 Liapunov Stability Theory 165
4.7.4 Existence and Bifurcation of Periodic Solutions 167
4.7.5 Invariant Integral Conditions 168
5 Age and Internal Structure 171
5.1 Age Structure and Vertical Transmission 171
5.2 Modeling Internal Structure 173
5.3 Derivation of the Model Equations 176
5.4 Age Structure and the Catalytic Curve 179
5.5 An s —? i Model with Vertical Transmission 184
5.6 Analysis of the Intracohort Model 193
5.7 Analysis of the Intercohort s —» i —* s Model 198
5.8 Numerical Simulations 201
5.9 Global Behavior of the s i * s Model 206
5.10 Destabilization Due to Age Structure 215
5.11 Thresholds in Age Dependent Models 217
5.12 Spatial Structure 222
5.13 The Force of Infection Terms 225
References 231
Author Index 241
Subject Index 245
|
| any_adam_object | 1 |
| author | Busenberg, Stavros N. 1941-1993 Cooke, Kenneth |
| author_GND | (DE-588)11935022X |
| author_facet | Busenberg, Stavros N. 1941-1993 Cooke, Kenneth |
| author_role | aut aut |
| author_sort | Busenberg, Stavros N. 1941-1993 |
| author_variant | s n b sn snb k c kc |
| building | Verbundindex |
| bvnumber | BV005903586 |
| callnumber-first | R - Medicine |
| callnumber-label | RG629 |
| callnumber-raw | RG629.I53 |
| callnumber-search | RG629.I53 |
| callnumber-sort | RG 3629 I53 |
| callnumber-subject | RG - Gynecology and Obstetrics |
| ctrlnum | (OCoLC)260148871 (DE-599)BVBBV005903586 |
| dewey-full | 618.32 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 618 - Gynecology, obstetrics, pediatrics, geriatrics |
| dewey-raw | 618.32 |
| dewey-search | 618.32 |
| dewey-sort | 3618.32 |
| dewey-tens | 610 - Medicine and health |
| discipline | Medizin |
| format | Book |
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| id | DE-604.BV005903586 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:36:37Z |
| institution | BVB |
| isbn | 354052004X 038752004X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003696968 |
| oclc_num | 260148871 |
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| owner | DE-12 DE-29 DE-188 |
| owner_facet | DE-12 DE-29 DE-188 |
| physical | XI, 248 S. graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Springer |
| record_format | marc |
| series | Biomathematics |
| series2 | Biomathematics |
| spelling | Busenberg, Stavros N. 1941-1993 Verfasser (DE-588)11935022X aut Vertically transmitted diseases models and dynamics Stavros Busenberg ; Kenneth Cooke Berlin [u.a.] Springer 1993 XI, 248 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Biomathematics 23 Disease Transmission cabt Mathematical Models cabt Biologie - Modèles mathématiques ram Biomathématiques ram Biométrie ram Epidémiologie jussieu Foetussen gtt Infectieziekten gtt Maladies infectieuses - Transmission - Modèles mathématiques ram Modèle différence jussieu Modèle différentiel jussieu Modèle retard jussieu Ouder-kind-relaties gtt Pasgeborenen gtt Populatiedynamica gtt Statistiek gtt Mathematisches Modell Statistik Communicable Diseases transmission Communicable diseases in newborn infants Forecasting Communicable diseases in newborn infants Mathematical models Communicable diseases in the fetus Forecasting Communicable diseases in the fetus Mathematical models Infant, Newborn, Diseases epidemiology Models, Statistical Pregnancy Complications, Infectious epidemiology Vertikal übertragbare Krankheit (DE-588)4311530-5 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Epidemiologie (DE-588)4015016-1 gnd rswk-swf Vertikale Übertragung (DE-588)4376600-6 gnd rswk-swf Vertikal übertragbare Krankheit (DE-588)4311530-5 s Epidemiologie (DE-588)4015016-1 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Vertikale Übertragung (DE-588)4376600-6 s Cooke, Kenneth Verfasser aut Biomathematics 23 (DE-604)BV000894631 23 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003696968&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Busenberg, Stavros N. 1941-1993 Cooke, Kenneth Vertically transmitted diseases models and dynamics Biomathematics Disease Transmission cabt Mathematical Models cabt Biologie - Modèles mathématiques ram Biomathématiques ram Biométrie ram Epidémiologie jussieu Foetussen gtt Infectieziekten gtt Maladies infectieuses - Transmission - Modèles mathématiques ram Modèle différence jussieu Modèle différentiel jussieu Modèle retard jussieu Ouder-kind-relaties gtt Pasgeborenen gtt Populatiedynamica gtt Statistiek gtt Mathematisches Modell Statistik Communicable Diseases transmission Communicable diseases in newborn infants Forecasting Communicable diseases in newborn infants Mathematical models Communicable diseases in the fetus Forecasting Communicable diseases in the fetus Mathematical models Infant, Newborn, Diseases epidemiology Models, Statistical Pregnancy Complications, Infectious epidemiology Vertikal übertragbare Krankheit (DE-588)4311530-5 gnd Mathematisches Modell (DE-588)4114528-8 gnd Epidemiologie (DE-588)4015016-1 gnd Vertikale Übertragung (DE-588)4376600-6 gnd |
| subject_GND | (DE-588)4311530-5 (DE-588)4114528-8 (DE-588)4015016-1 (DE-588)4376600-6 |
| title | Vertically transmitted diseases models and dynamics |
| title_auth | Vertically transmitted diseases models and dynamics |
| title_exact_search | Vertically transmitted diseases models and dynamics |
| title_full | Vertically transmitted diseases models and dynamics Stavros Busenberg ; Kenneth Cooke |
| title_fullStr | Vertically transmitted diseases models and dynamics Stavros Busenberg ; Kenneth Cooke |
| title_full_unstemmed | Vertically transmitted diseases models and dynamics Stavros Busenberg ; Kenneth Cooke |
| title_short | Vertically transmitted diseases |
| title_sort | vertically transmitted diseases models and dynamics |
| title_sub | models and dynamics |
| topic | Disease Transmission cabt Mathematical Models cabt Biologie - Modèles mathématiques ram Biomathématiques ram Biométrie ram Epidémiologie jussieu Foetussen gtt Infectieziekten gtt Maladies infectieuses - Transmission - Modèles mathématiques ram Modèle différence jussieu Modèle différentiel jussieu Modèle retard jussieu Ouder-kind-relaties gtt Pasgeborenen gtt Populatiedynamica gtt Statistiek gtt Mathematisches Modell Statistik Communicable Diseases transmission Communicable diseases in newborn infants Forecasting Communicable diseases in newborn infants Mathematical models Communicable diseases in the fetus Forecasting Communicable diseases in the fetus Mathematical models Infant, Newborn, Diseases epidemiology Models, Statistical Pregnancy Complications, Infectious epidemiology Vertikal übertragbare Krankheit (DE-588)4311530-5 gnd Mathematisches Modell (DE-588)4114528-8 gnd Epidemiologie (DE-588)4015016-1 gnd Vertikale Übertragung (DE-588)4376600-6 gnd |
| topic_facet | Disease Transmission Mathematical Models Biologie - Modèles mathématiques Biomathématiques Biométrie Epidémiologie Foetussen Infectieziekten Maladies infectieuses - Transmission - Modèles mathématiques Modèle différence Modèle différentiel Modèle retard Ouder-kind-relaties Pasgeborenen Populatiedynamica Statistiek Mathematisches Modell Statistik Communicable Diseases transmission Communicable diseases in newborn infants Forecasting Communicable diseases in newborn infants Mathematical models Communicable diseases in the fetus Forecasting Communicable diseases in the fetus Mathematical models Infant, Newborn, Diseases epidemiology Models, Statistical Pregnancy Complications, Infectious epidemiology Vertikal übertragbare Krankheit Epidemiologie Vertikale Übertragung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003696968&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000894631 |
| work_keys_str_mv | AT busenbergstavrosn verticallytransmitteddiseasesmodelsanddynamics AT cookekenneth verticallytransmitteddiseasesmodelsanddynamics |