Stochastic Modeling of AIDS Epidemiology and HIV Pathogenesis

by Tan, W. Y.; Wai-Yuan, Tan

• ISBN13: 9789810241223
• ISBN10: 9810241224
• Format: Hardcover
• Copyright: 2001-01-01
• Publisher: World Scientific Pub Co Inc

Table of Contents

Preface	vii
Introduction	1	(32)
The Role and Importance of Mathematical Models for AIDS	2	(1)
Different Modeling Approaches for Modeling the AIDS Epidemic and the HIV Pathogenesis in HIV-infected Individuals	2	(3)
An Illustrative Example from the AIDS Epidemic	5	(12)
The Scope of the Book	17	(3)
Complements and Exercises	20	(1)
References	20	(7)
Appendices	27	(6)
Some Basic Concepts and Stochastic Processes for Modeling the AIDS Epidemic and the HIV Pathogenesis	33	(42)
Stochastic Processes and Examples from AIDS	33	(1)
Markov Processes vs Non-Markovian Processes and Examples from AIDS	34	(2)
Binomial Distributions, Poisson Distributions and Multinomial Distributions	36	(9)
The Negative Binomial Distributions and the Delayed Negative Binomial Distributions	45	(7)
Some Stochastic Birth-Death Processes and Applications to AIDS	52	(8)
Some First Passage Times in AIDS and the HIV Incubation Distributions	60	(7)
Complements and Exercises	67	(3)
References	70	(5)
Some Stochastic Transmission Models of the HIV Epidemic	75	(62)
Some Basic Procedures for Developing HIV Stochastic Models	76	(6)
A General Stochastic Model of the HIV Epidemic in Homosexual Populations	82	(11)
Some Features of the Model via Monte Carlo Studies	93	(7)
Some Deterministic Models and the Mean Behavior of the HIV Epidemic	100	(8)
Some Stochastic Staged Models of the HIV Epidemic in Homosexual Populations	108	(7)
Extensions of Stochastic Models of HIV Epidemic to Models under Complex Situations	115	(8)
Some Applications of the Stochastic Models	123	(1)
Complements and Exercises	124	(3)
References	127	(10)
Statistical Modeling of the HIV Epidemic	137	(62)
Some General Waiting-Time Distributions for the HIV Epidemic	137	(3)
The Infection Distribution and the Seroconversion Distribution	140	(6)
Some Statistical Methods for Estimating the HIV Seroconversion Distribution	146	(15)
Characterization of the HIV Infection Distribution and the Seroconversion Distribution	161	(2)
The Fourier Transform Method	163	(2)
The HIV Incubation Distribution	165	(7)
Some Statistical Methods for Estimating the HIV Incubation Distribution by Using Blood Transfusion Data	172	(6)
Characterization of the HIV Incubation Distribution	178	(6)
Effects of Risk Factors on the HIV Infection, the HIV Seroconversion and the HIV Incubation Distributions	184	(2)
Complements and Exercises	186	(2)
References	188	(11)
The Backcalculation Method for the HIV Epidemic	199	(42)
Limitations and Assumptions of the Method	199	(1)
The Model and the Likelihood Function	200	(4)
Estimating the HIV Infection Distribution by Backcalculation	204	(8)
Estimating the HIV Incubation Distribution by Backcalculation	212	(3)
Estimating the Number of People at Risk for AIDS by Backcalculation	215	(1)
The Bayesian Method for Estimating the HIV Infection and the Incubation by Backcalculation	216	(10)
Short Term Projection of Future AIDS Cases by Backcalculation	226	(3)
Simultaneous Estimation of the HIV Infection Distribution and the HIV Incubation Distribution	229	(2)
Complements and Exercises	231	(1)
References	232	(9)
Some State Space Models of the HIV Epidemic and Applications	241	(52)
Some HIV Epidemic Models as Discrete-Time Linear State Space Models	241	(4)
Some General Theories for Discrete-Time Linear State Space Models	245	(3)
Estimation of HIV Prevalence and AIDS Cases in the San Francisco Homosexual Population	248	(9)
Some General Procedures for Estimating Simultaneously the Unknown Parameters and the State Variables by State Space Models	257	(4)
Simultaneous Estimation of the HIV Infection, the HIV Incubation and State Variables in the San Francisco Homosexual Population	261	(7)
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	(7)
Complements and Exercises	275	(7)
References	282	(4)
Appendices	286	(7)
Some Stochastic Models of HIV Pathogenesis in HIV-Infected Individuals in the Absence of Anti-Viral Treatment	293	(52)
Some Biological Background and Observations	295	(4)
A Simple Stochastic Model of HIV Pathogenesis in HIV-Infected Individuals	299	(6)
Stochastic Models of HIV Pathogenesis under Complex Situations in HIV-Infected Individuals	305	(14)
Some Specific Features of HIV Pathogenesis via Monte Carlo Studies	319	(14)
Complements and Exercises	333	(4)
References	337	(8)
Stochastic Models of HIV Pathogenesis Under Treatment by Anti-Viral Drugs	345	(40)
Some Biological Background of Treatment by Anti-Retroviral Drugs	345	(5)
Some Stochastic Models under Treatment by Anti-Retroviral Drugs in the Absence of Drug Resistance	350	(12)
Some Stochastic Models under Treatment by Anti-Retroviral Drugs in the Presence of Drug Resistance	362	(8)
Stochastic Models of HIV Pathogenesis under Treatment by a RT Inhibitor and Development of Drug Resistance	370	(1)
Stochastic Models of HIV Pathogenesis under Treatment by a Protease Inhibitor and Development of Drug Resistance	370	(1)
Some Features of Drug Resistance via Monte Carlo Studies	371	(5)
Complements and Exercises	376	(3)
References	379	(6)
Some State Space Models of HIV Pathogenesis in HIV-Infected Individuals	385	(34)
Some State Space Models of HIV Pathogenesis as Nonlinear State Space Models	385	(3)
Some General Theories of Continuous Time-Discrete Time Linear State Space Models	388	(8)
Estimation of the Numbers of Different Types of CD4(+) T Cells and Free HIV in Blood by State Space Models	396	(12)
Assessing Effects of Treatment by Anti-Retroviral Drugs by State Space Models	408	(5)
Some General Comments	413	(1)
References	413	(3)
Appendix	416	(3)
Subject Index	419