Stochastic Modeling of AIDS Epidemiology and HIV Pathogenesis

The following sections are included:

• PREFACE

• CONTENTS

• ERRATA: STOCHASTIC MODELING OF AIDS EPIDEMIOLOGY AND HIV PATHOGENESIS

The following sections are included:

• The Role and the Importance of Mathematical Models for AIDS

• Different Modeling Approaches for Modeling the AIDS Epidemic and the HIV Pathogenesis in HIV-infected Individuals
  • Deterministic Models of the HIV Epidemic
  • Stochastic Models of the HIV Epidemic
  • Statistical Models of the HIV Epidemic
  • The State Space Model (Kalman Filter Model of the HIV Epidemic

• An Illustrative Example From the AIDS Epidemic
  • The Deterministic Model
  • The Stochastic Model
  • The Statistic Model
  • The State Space Model (The Kalman Filter Model)

• The Scope of the Book

• Complements and Exercises

• References

• Appendices

The following sections are included:

• Stochastic Processes And Examples From AIDS

• Markov Processes vs Non-Markovian Processes and Examples From AIDS

• Binomial Distributions, Poisson Distributions And Multinomial Distributions
  • The Binomial Distribution
  • The Chain Binomial Model in the HIV Epidemic
  • The Poisson Distribution
  • The Multinomial Distribution

• The Negative Binomial Distributions And The Delayed Negative Binomial Distributions
  • Probability of S → I in a Homosexual Population With One Sexual Activity Level
  • Probability of S → I in Homosexual Populations Under Complex Situations

• Some Stochastic Birth-Death Processes and Applications to AIDS
  • Some General Theories of Stochastic Birth-Death Processes
  • An Alternative Approach Through Stochastic Differential Equations

• Some First Passage Times in AIDS and the HIV Incubation Distributions
  • A Stochastic Model for the HIV Incubation
  • Some General Results of First Passage Times in Markov Chains
  • The HIV Incubation Distribution Under a Markov Model
  • The HIV Incubation Distribution under Non-Markovian Models

• Complements and Exercises

• References

The following sections are included:

• Some Basic Procedures for Developing HIV Stochastic Models
  • The Mixing Pattern and the Transmission of HIV
  • The Probability of HIV Infection of S People
  • The Progression of HIV

• A General Stochastic Model of the HIV Epidemic in Homosexual Populations
  • The Probability p_S(i, t) of HIV Infection of S People
  • The Chain Multinomial Model and the Stochastic Difference Equations
  • The Probability Distribution of the State Variables
  • The Mean Numbers
  • The Variance and the Covariances

• Some Features of the Model Via Monte Carlo Studies

• Some Deterministic Models and the Mean Behavior of the HIV Epidemic
  • The Steady State Solutions
  • Some Asymptotic Behavior of the Epidemic

• Some Stochastic Staged Models of the HIV Epidemic in Homosexual Populations
  • Model Formulation
  • Some Applications

• Extensions of Stochastic Models of HIV Epidemic to Models Under Complex Situations
  • The Probability of HIV Infection in Populations of IV Drug Users
  • A Selective Mixing Pattern for Complex Models

• Some Applications of the Stochastic Models

• Complements and Exercises

• References

The following sections are included:

• Some General Waiting–Time Distributions for the HIV Epidemic

• The Infection Distribution and the Seroconversion Distribution
  • The Poisson Arrival as Infection Distributions in AIDS From Blood Transfusion
  • The Spline Approximation
  • Estimating the HIV Infection and Seroconversion Distributions

• Some Statistical Methods For Estimating the HIV Seroconversion Distribution
  • Non-parametric Methods
  • Some Parametric Methods

• Characterization of the Infection Distribution and the Seroconversion Distribution

• The Fourier Transform Method

• The HIV Incubation Distribution
  • Some Exact HIV Incubation Distributions
  • Some Statistical Methods for Estimating the HIV Incubation Distribution

• Some Statistical Methods for Estimating the HIV Incubation Distribution by Using Blood Transfusion Data
  • Parametric Estimation of Unknown Parameters
  • Nonparametric Method for Estimating the Unknown Parameters

• Characterization of the HIV Incubation Distribution

• Effects of Risk Factors on the HIV Infection, the HIV Seroconversion and the HIV Incubation Distributions
  • Risk Factors Which Affect the HIV Infection and Seroconversion
  • Risk Factors Which Affect the HIV Incubation

• Complements and Exercises

• References

The following sections are included:

• Limitations and Assumptions of the Method

• The Model and the Likelihood Function
  • Some Limitations and Procedures
  • The Complete Likelihood Function

• Estimating the HIV Infection Distribution by Backcalculation
  • The EMS Method
  • The Penalized Likelihood Method
  • The Linear Regression and Spline Method

• Estimating the HIV Incubation Distribution by Backcalculation

• Estimating the Number of People at Risk for AIDS by Backcalculation

• The Bayesian Method for Estimating the HIV Infection and the Incubation By Backcalculation
  • The Prior Distributions
  • The Posterior Distribution of the Parameters
  • Bayesian Estimation of the HIV Infection Distribution and the Incubation Distribution in the San Francisco Homosexual Population

• Short Term Projection of Future AIDS Cases by Backcalculation

• Simultaneous Estimation of the HIV Infection Distribution and the HIV Incubation Distribution

• Complements and Exercises

• References

The following sections are included:

• Some HIV Epidemic Models as Discrete-Time Linear State Space Models

• Some General Theories For Discrete-Time Linear State Space Models

• Estimation of HIV Prevalence and AIDS Cases in the San Francisco Homosexual Population
  • Estimation of p_S(i, t) and γ_i(u, t) = γ(u, t) in the San Francisco Homosexual Population
  • The Initial Distribution
  • The Kalman Filter Estimates of the HIV Prevalence and AIDS Cases

• Some General Procedures for Estimating Simultaneously the Unknown Parameters and the State Variables By State Space Models
  • Generating Data From P(X|Y, θ)
  • Generating θ From P(θ|Y, X)

• Simultaneous Estimation of the HIV Infection, the HIV Incubation and the State Variables in the San Francisco Homosexual population
  • A State Space Model for the San Francisco Homosexual Population
  • The Initial Size
  • The Prior Distribution
  • Generating X From the Conditional Density P(X|θ, Y)
  • Generating θ From the Conditional Density P(θ|X, Y)

• Simultaneous Estimation of the HIV Infection, the HIV Incubation, the Immigration rate, the Death Rate and the State Variables in the Swiss Homosexual population
  • A State Space Model for the Swiss Homosexual and Bisexual Population
  • The Initial Size
  • The Prior Distributions and the Conditional Posterior Distributions of the Parameters
  • Generating X From the Conditional Density P(X|θ, Y)
  • Generating θ From the Conditional Density P(θ|X, Y)

• Complements and Exercises

• References

• Appendices
  • Appendix (6A)
  • Appendix (6B): Some Basic Ideas of Gibb Sampler Method
  • Appendix (6C): The Weighted Bootstrap Method for Generating Random Samples

The following sections are included:

• Some Biological Background and Observations

• A Simple Stochastic Model of HIV Pathogenesis in HIV-infected Individuals
  • Stochastic Differential Equations
  • The Mean Numbers of X(t)
  • An Illustrative Example

• Stochastic Models of HIV Pathogenesis Under Complex Situations in HIV-infected Individuals
  • Model Formulation
  • Stochastic Equations for the Numbers of Different Types of CD4⁽⁺⁾ T-Cells and Free HIV
  • The Expected Numbers of T Cells, Macrophage and Free HIV

• Some Specific Features of HIV Pathogenesis Via Monte Carlo Studies
  • Choice of the Parameter Values
  • Generation of Monte Carlo Data
  • Results and Features From Monte Carlo Studies

• Complements and Exercises

• References

The following sections are included:

• Some Biological Background of Treatment by Anti-Retroviral Drugs
  • Modeling Effects of Category 1 drugs
  • Modeling Effects of Category 2 drugs
  • Modeling Development of Drug Resistance of HIV
  • Modeling Net Flow of HIV From Lymph Nodes to Plasma

• Some Stochastic Models Under Treatment by Anti-Retroviral Drugs in the Absence of Drug Resistance
  • Stochastic Equations of HIV Pathogenesis Under Combination Therapy or HAART
  • Some Special Cases
  • The Mean Numbers
  • An Example From Some Real Data

• Some Stochastic Models Under Treatment by Anti-Retroviral Drugs in the Presence of Drug Resistance
  • Modeling Effects of Treatment and Drug Resistance
  • Modeling Net Flow of Free HIV From Lymph Nodes to Plasma
  • Stochastic Equations of the State Variables Under Treatment by HAART and Development of Drug Resistance
  • The Mean Values

• Stochastic Models of HIV Pathogenesis Under Treatment by a RT Inhibitor and Development of Drug Resistance

• Stochastic Models of HIV Pathogenesis Under Treatment by a Protease Inhibitor and Development of Drug Resistance

• Some Features of Drug Resistance Via Monte Carlo Studies

• Compliments and Exercises

• References

The following sections are included:

• Some State Space Models of HIV Pathogenesis as Nonlinear State Space Models
  • A State Space Model of HIV Pathogenesis Involving Interaction Between CD4 T cells and HIV
  • A State Space Model of HIV Pathogenesis Under Treatment by A Protease Inhibitor
  • A State Space Model of HIV Pathogenesis Under Treatment With Lymph Nodes

• Some General Theories For Continuous Time-Discrete Time Linear State Space Models
  • Estimating Given Data
  • Estimating X(t) Given

• Estimation of the Numbers of Different Types of CD4(+) T Cells and Free HIV in Blood By State Space Models
  • Estimation of the Numbers of T Cells and Free HIV By Using a State Space Model
  • An Illustrative Example
  • Some Monte Carlo Studies

• Assessing Effects of Treatment By Anti-retroviral Drugs By State Space Models
  • Estimation of the Numbers of T Cells and Free HIV Under Treatment By Using a State Space Model
  • An Illustrative Example

• Some General Comments

• References

• Appendix

The following sections are included:

• SUBJECT INDEX