Stochastic modeling of AIDS epidemiology and HIV pathogenesis / Tan Wai-yuan.

Format:

Book

Author/Creator:

Tan, W. Y., 1934-

Language:

English

Subjects (All):

AIDS (Disease)--Epidemiology.

AIDS (Disease).

HIV (Viruses).

HIV infections--Pathogenesis.

HIV infections.

Stochastic analysis.

Physical Description:

xiv, 431 pages : illustrations ; 23 cm

Place of Publication:

Singapore ; River Edge, N.J. : World Scientific, [2000]

Summary:

It is widely accepted that AIDS is one of the most dangerous diseases currently threatening the human species. As such, there has been a wealth of effort invested into developing mathematical models for the AIDS epidemic and for the HIV pathogenesis. Thus far, a number of studies have utilized deterministic models, in which the state variables have been treated as deterministic functions of time, ignoring completely the randomness of the epidemic. Or, statistical models have been used, ignoring completely the dynamics of the epidemic. This book take a different approach, using stochastic models, something Wai-yuan (mathematical science, U. of Memphis) hopes will provide a superior model. He begins the book with an argument as to why a stochastic approach is suited to this scenario, and then explains how this method could be applied. Annotation copyrighted by Book News, Inc., Portland, OR

Contents:

1.1. The Role and Importance of Mathematical Models for AIDS 2

1.2. Different Modeling Approaches for Modeling the AIDS Epidemic and the HIV Pathogenesis in HIV-infected Individuals 2

1.3. An Illustrative Example from the AIDS Epidemic 5

1.4. The Scope of the Book 17

Chapter 2 Some Basic Concepts and Stochastic Processes for Modeling the AIDS Epidemic and the HIV Pathogenesis 33

2.1. Stochastic Processes and Examples from AIDS 33

2.2. Markov Processes vs Non-Markovian Processes and Examples from AIDS 34

2.3. Binomial Distributions, Poisson Distributions and Multinomial Distributions 36

2.4. The Negative Binomial Distributions and the Delayed Negative Binomial Distributions 45

2.5. Some Stochastic Birth-Death Processes and Applications to AIDS 52

2.6. Some First Passage Times in AIDS and the HIV Incubation Distributions 60

Chapter 3 Some Stochastic Transmission Models of the HIV Epidemic 75

3.1. Some Basic Procedures for Developing HIV Stochastic Models 76

3.2. A General Stochastic Model of the HIV Epidemic in Homosexual Populations 82

3.3. Some Features of the Model via Monte Carlo Studies 93

3.4. Some Deterministic Models and the Mean Behavior of the HIV Epidemic 100

3.5. Some Stochastic Staged Models of the HIV Epidemic in Homosexual Populations 108

3.6. Extensions of Stochastic Models of HIV Epidemic to Models under Complex Situations 115

3.7. Some Applications of the Stochastic Models 123

Chapter 4 Statistical Modeling of the HIV Epidemic 137

4.1. Some General Waiting-Time Distributions for the HIV Epidemic 137

4.2. The Infection Distribution and the Seroconversion Distribution 140

4.3. Some Statistical Methods for Estimating the HIV Seroconversion Distribution 146

4.4. Characterization of the HIV Infection Distribution and the Seroconversion Distribution 161

4.5. The Fourier Transform Method 163

4.6. The HIV Incubation Distribution 165

4.7. Some Statistical Methods for Estimating the HIV Incubation Distribution by Using Blood Transfusion Data 172

4.8. Characterization of the HIV Incubation Distribution 178

4.9. Effects of Risk Factors on the HIV Infection, the HIV Seroconversion and the HIV Incubation Distributions 184

Chapter 5 The Backcalculation Method for the HIV Epidemic 199

5.1. Limitations and Assumptions of the Method 199

5.2. The Model and the Likelihood Function 200

5.3. Estimating the HIV Infection Distribution by Backcalculation 204

5.4. Estimating the HIV Incubation Distribution by Backcalculation 212

5.5. Estimating the Number of People at Risk for AIDS by Backcalculation 215

5.6. The Bayesian Method for Estimating the HIV Infection and the Incubation by Backcalculation 216

5.7. Short Term Projection of Future AIDS Cases by Backcalculation 226

5.8. Simultaneous Estimation of the HIV Infection Distribution and the HIV Incubation Distribution 229

Chapter 6 Some State Space Models of the HIV Epidemic and Applications 241

6.1. Some HIV Epidemic Models as Discrete-Time Linear State Space Models 241

6.2. Some General Theories for Discrete-Time Linear State Space Models 245

6.3. Estimation of HIV Prevalence and AIDS Cases in the San Francisco Homosexual Population 248

6.4. Some General Procedures for Estimating Simultaneously the Unknown Parameters and the State Variables by State Space Models 257

6.5. Simultaneous Estimation of the HIV Infection, the HIV Incubation and State Variables in the San Francisco Homosexual Population 261

6.6. Simultaneous Estimation of the HIV Infection, the HIV Incubation, the Immigration Rate, the Death Rate and the State Variables in the Swiss Homosexual Population 268

Chapter 7 Some Stochastic Models of HIV Pathogenesis in HIV-Infected Individuals in the Absence of Anti-Viral Treatment 293

7.1. Some Biological Background and Observations 295

7.2. A Simple Stochastic Model of HIV Pathogenesis in HIV-Infected Individuals 299

7.3. Stochastic Models of HIV Pathogenesis under Complex Situations in HIV-Infected Individuals 305

7.4. Some Specific Features of HIV Pathogenesis via Monte Carlo Studies 319

Chapter 8 Stochastic Models of HIV Pathogenesis Under Treatment by Anti-Viral Drugs 345

8.1. Some Biological Background of Treatment by Anti-Retroviral Drugs 345

8.2. Some Stochastic Models under Treatment by Anti-Retroviral Drugs in the Absence of Drug Resistance 350

8.3. Some Stochastic Models under Treatment by Anti-Retroviral Drugs in the Presence of Drug Resistance 362

8.4. Stochastic Models of HIV Pathogenesis under Treatment by a RT Inhibitor and Development of Drug Resistance 370

8.5. Stochastic Models of HIV Pathogenesis under Treatment by a Protease Inhibitor and Development of Drug Resistance 370

8.6. Some Features of Drug Resistance via Monte Carlo Studies 371

Chapter 9 Some State Space Models of HIV Pathogenesis in HIV-Infected Individuals 385

9.1. Some State Space Models of HIV Pathogenesis as Nonlinear State Space Models 385

9.2. Some General Theories of Continuous Time-Discrete Time Linear State Space Models 388

9.3. Estimation of the Numbers of Different Types of CD4(+) T Cells and Free HIV in Blood by State Space Models 396

9.4. Assessing Effects of Treatment by Anti-Retroviral Drugs by State Space Models 408.

Notes:

Errata slip inserted.

Includes bibliographical references and index.

ISBN:

9810241224

OCLC:

45686800