Mathematical Models of STI Transmission

Modeling HIV Transmission and AIDS in the United States, By Herbert W. Hethcote and James W. Van Ark (with permission)

COVER
TABLE OF CONTENTS
FOREWORD II
PREFACE III

CHAPTER 1

BACKGROUND ON THE EPIDEMIOLOGY AND MODELING OF HIV/AIDS

1.1 HIV Transmission Mechanisms 1
1.2 Biological and Clinical Aspects of HIV Infection 2
1.3 HIV and AIDS in the United States 3
1.4 HIV and AIDS in the World 12
1.5 Three Approaches to Modeling HIV/AIDS 16
1.6 Purposes and Limitations of Epidemiological Modeling 19
1.7 Expectations of Modeling HIV Transmission Dynamics and AIDS 26

CHAPTER 2

MODELING THE PROGRESSION OF HIV INFECTED PERSONS TO AIDS 30

2.1 Staged Progression Based on Clinical Phases 30
2.2 Staged Progression Based on T4 Cell Counts 33
2.3 Staged Progression for Children 34

CHAPTER 3

FORMULATION OF THE SIMULATION MODEL FOR HOMOSEXUAL MEN 37

3.1 The Compartmental Model with Two Sexual Activity Levels 37
3.2 Modeling the Incidence of HIV Infection 41

CHAPTER 4

MATHEMATICAL ANALYSIS OF THE MODEL FOR HOMOSEXUAL MEN 44

4.1 Equilibria for the Differential-Equations Model with . One Sexual Activity Level 45
4.2 Stability of the Disease-Free Equilibrium 48
4.3 Stability of the Endemic Equilibrium 51
4.4 Stability of the Difference-Equations Model with One Sexual Activity Level 52
4.5 Stability for the Difference-Equations Model with Two Sexual Activity Levels 53

CHAPTER 5

HOMOSEXUAL MEN IN SAN FRANCISCO : ESTIMATION OF PARAMETERS AND INCIDENCES 56

5.1 Estimation of Parameters Related to the Stages 56

5.1.1 Probabilities of Transmission in the Stages 56
5.1.2 Behavioral Changes in the Stages 56

5.2 Estimation of Population Sizes and Turnover Rate Constants 57
5.3 Sexual Behavior Parameter Estimates 58

5.3.1 Probability of Transmission Per Partner 58
5.3.2 New Partners Per Month 59
5.3.3 Other Parameters 60

5.4 Estimation of HIV and AIDS Incidences 61

5.4.1 HIV Incidence in San Francisco 61
5.4.2 AIDS Incidence in San Francisco 63

CHAPTER 6

HOMOSEXUAL MEN IN SAN FRANCISCO: SIMULATIONS AND SENSITIVITY ANALYSIS 65

6.1 The Fit Criteria 66
6.2 The Baseline Parameter Set 66

6.2.1 Simulation Results 66
6.2.2 Calculations of the Contact Number 69

6.3 Modeling Zidovudine Therapy 70

6.3.1 Modification of the Simulation Model to Include Therapy 70
6.3.2 Estimates of the Therapy Percentages and Effects 71
6.3.3 Simulations Including Therapy 71

6.4 Sensitivity Analysis 74

6 .4.1 Population Structure and Dynamics 74
6 .4.2 Epidemiological Structure and Mixing 75
6.4.3 Parameters Related to the Stages 76
6.4.4 Sexual Behavior Parameters 78

6.5 Conclusions 78

CHAPTER 7

THE HIV TRANSMISSION DYNAMICS MODEL FOR FIVE MAJOR RISK GROUPS 83

7.1 The General Model 83
7.2 The Fitting Procedure 86
7.3 Discussion of the Model 87

CHAPTER 8

WEAK LINKAGE BETWEEN HIV EPIDEMICS IN HOMOSEXUAL MEN AND INTRAVENOUS DRUG USERS IN NEW YORK CITY 90

8.1 Data on HIV and AIDS in New York City 91
8.2 Parameter Estimates for New York City 93

8.2.1 Estimates of Population Sizes and Turnover 93
8.2.2 Estimates of Parameters Related to the Stages 94
8.2.3 Sexual Behavior Parameter Estimates 95
8.2.4 Needle-Sharing Behavior Parameter Estimates 95

8.3 Modified Fit Criteria for the New York City Model 96
8.4 Fitting in the New York City Population of Homosexual Men 96
8.5 Fitting in the New York City Population of IVDUs 99
8.6 Fitting in the Three New York City Risk Groups 101
8.7 Discussion of the Separate-Epidemic Theory 104

CHAPTER 9

RACIAL/ETHNIC PATTERNS OF AIDS IN THE UNITED STATES 107

9.1 Racial/Ethnic Patterns of AIDS Cases and Relative Risks 107
9.2 Exposure Categories Related by Sexual Contacts 111

9.2.1 Relating Exposure Categories 112
9.2 .2 Homosexual/Bisexual Males 113
9.2.3 Intravenous Drug Users 113
9.2.4 Other Sexually-Related Categories 114
9.2.5 Estimating HIV Transmission 115

9.3 Perinatally Related Exposure Categories 119
9.4 Racial/Ethnic Patterns of AIDS Cases in the' Northeast Region 121

9.4.1 Racial/Ethnic Patterns of AIDS Cases in Risk Groups in NE Subregions 122
9.4.2 Exposure Categoriess Related by Sexual Contacts in NE Subregions 123
9.4.3 Perinatally-Rated Exposure Categories in the NE Subregions 126

9.5 Discussion 128

CHAPTER 10

REGIONAL COMPARISONS OF HIV AND AIDS IN RISK GROUPS 132

10.1 Simplifications Based on Modeling New York City 135
10.2 The Northeast Region : Aggregation of Racial/Ethnic and Risk Groups 135
10.3 The Northeast Reg~'on: Computer Simulations of the Aggregated Groups 144
10.4 The North Central Region: Aggregation of Racial/Ethnic and Risk Groups 156
10.5 The North Central Region: Computer Simulations of the Aggregated Groups . 160
10.6 The South Region: Aggregation of Racial/Ethnic and Risk Groups 167
10.7 The South Region: Computer Simulations of the Aggregated Groups 171
10.8 The West Region: Aggregation of Racial/Ethnic an Risk Groups 175
10.9 The West Region: Computer Simulations of the Aggregated Groups 183
10.10 Discussion of Regional Comparisons 192

APPENDIX: LISTING OF COMPUTER PROGRAMS USED IN CHAPTER 10 199

REFERENCES 219