Deterministic and Stochastic Models of AIDS Epidemics and HIV Infections with Intervention


It is well recognized that AIDS is the most dangerous disease in the 21st century threatening the survival of human beings. It has been estimated by WHO (World Health Organization) that by 2003 there are at least 40 million people world-wide who are currently living with HIV/AIDS; at least 3 million people have died of AIDS and 5 million people have acquired HIV in 2003. From these statistics, obviously the most urgent challenging task is how to control HIV epidemics. Because of the complexity and seriousness of the disease, for understanding AIDS epidemics and HIV pathogenesis and for developing efficient strategies for controlling AIDS, mathematical models that take into account the dynamics of HIV epidemics and the biology of HIV pathogenesis are definitely needed. With this in mind, many mathematical models for AIDS epidemics and for HIV pathogenesis have been developed. These models have been summarized in books by Tan (2000) and in Mode and Sleeman (2000). However, few papers and models deal with drug treatments and AIDS vaccines. To fill this gap, the goal of this book is to solicit papers from world experts on HIV/AIDS treatment and vaccines. This derives basically from the following two observations:

(1) In the past ten years, important breakthroughs have been achieved in treating HIV-infected patients through the combination of Nucleoside Reverse Transcriptase Inhibitor (NRTI) drugs such as AZT and DDI with Protease Inhibitor (PI) drugs such as ritonavir and nelfinavir or Non-nucloside Reverse Transcriptase Inhibitor (NNRTI) drugs such as efavirenz, referred to as the Highly Active Anti-Retroviral Therapy (HAART). However, it is far from cure. For developing optimal treatment regimens, there are also serious problems that remain to be addressed; furthermore, to successfully control the level of HIV, life-long HAART treatments are often required. In this book we will solicit papers from world experts to present an over view on the latest advances in this aspect.

(2) Because AIDS is not curable, the best and cost-effective strategy is by prevention via AIDS vaccination. In this book we will solicit papers from world experts to provide a most recent review on the status of AIDS vaccination and newly developed models for AIDS vaccines.;

Because the HIV epidemic via IV drug becomes more important and is the major avenues for AIDS in China and Asia and because very few models in the past dealt with IV drug use, in this book we will also include some papers to present an updated review on HIV/AIDS via IV drug use. Because in Cuba every one in the country has been surveyed and under surveillance, we will also present a paper by Hsieh et al. to illustrate the effect of complete surveillance on AIDS epidemics.

This book contains 23 chapters and is organized into the following 6 parts:

  • Part I: AIDS Epidemic Models
  • Part II: HIV Vaccine Models
  • Part III: Models for HIV/Cell Dynamics and Interactions
  • Part IV: Viral Dynamics Under Antiviral Treatments
  • Part V: Modeling Drug Resistance
  • Part VI: Statistical Methods.

In Part I, extensive deterministic models, stochastic models, state space models and statistical methods as well as statistical methods for HIV epidemics involving IV drug use and HIV epidemics in homosexual populations are reviewed and discussed. In Part II, the book presents a review on the latest mathematical models for assessing effects of AIDS vaccines and provides statistical methods for analyzing clinical trial data on AIDS vaccines. In Part III, the book provides most recent biological insights into HIV pathogenesis and HIV kinetics at the cellular level and illustrates how to build up mathematical models based on these biological insights. In Part IV, extensive deterministic models, stochastic models, state space models and statistical methods on treating AIDS patients with anti-retroviral drugs and the pros and cons of these models are presented. For the first time it gives in-depth analysis of HAART treatment regimens and discusses possible improvement of the HAART treatments. It also provides a linkage between pharmacokinetics and treatment in HIV-infected individuals. In Part V, it discusses models and statistical methods for assessing drug resistance of HIV to anti-retroviral drugs. Finally in Part VI, the book provides some important statistical methods specific for the intervention and prevention of HIV epidemics.

In this book, we have solicited papers from world experts on models of AIDS epidemics and HIV pathogenesis under intervention. The topics include deterministic models, stochastic models, state space models and statistical methods for antiviral treatment and AIDS vaccines. It provides the latest information in this field. It will be a useful reference source for graduate students and researchers in biomathematics and biostatistics, as well as for HIV/AIDS epidemiologists and clinical investigators learning how to use quantitative methods to study AIDS epidemics and HIV infection.

We would like to express our sincere appreciation to all contributors who have made this book possible. We also wish to thank Dr. Sook Cheng Lim of World Scientific Publication Company for assistance in the publication of this book.

Wai-Yuan Tan
Department of Mathematical Sciences
University of Memphis
Memphis, TN, USA


Hulin Wu
Department of Biostatistics and Computational Biology
University of Rochester
Rochester, NY, USA


PART I: AIDS Epidemic Models

Chapter 1: Mathematical Models for HIV Transmission among Injecting Drug Users
----V. Capasso and D. Morale

Chapter 2: Estimation of HIV Infection and Seroconversion Probabilities in IDU and Non-IDU Populations by State Space Models
----Wai-Yuan Tan, Li-Jun Zhang, and Lih-Yuan Deng

Chapter 3: Convergence to an Endemic Stationary Distribution in a Class of Stochastic Models of HIV/AIDS in Homosexual Populations
---Charles J. Mode

Chapter 4: A Class of Methods for HIV Contact Tracing in Cuba: Implications for Intervention and Treatment
----Ying-Hen Hsieh, Hector de Arazoza, Rachid Lounes and Jose Joanes

PART II: HIV Vaccine Models

Chapter 5: Simultaneous Inferences of HIV Vaccine Effects on Viral Load, CD4 Cell Counts, and Antiretroviral Therapy Initiation in Phase 3 Trials
----Peter B. Gilbert and Yanqing Sun

Chapter 6: A Review of Mathematical Models for HIV/AIDS Vaccination
----Shu-Fang Hsu Schmitz

Chapter 7: Effects of AIDS Vaccine on Sub-populations of CD4 T Cells, CD8 T Cells and B Cells Under HIV Infection
----Wai-Yuan Tan, Ping Zhang and Xiaoping Xiong

PART III: Models for HIV/Cell Dynamics and Interactions

Chapter 8: Dynamical Models for the Course of an HIV Infection
----Christel Kamp

Chapter 9: How Fast can HIV Escape from Immune Control?
----W. David Wick and Steven G. Self

Chapter 10: CTL Action during HIV-1 Is Determined via Interactions with Several Cell Types
----Seema H. Bajaria and Denise E. Kirschner

Chapter 11: Identifiability of HIV/AIDS Models
----Annah M. Jeffrey and Xiaohua Xia

PART IV: Viral Dynamics Under Antiviral Treatments

Chapter 12: Influence of Drug Pharmacokinetics on HIV Pathogenesis and Therapy
----Narendra M. Dixit and Alan S. Perelson

Chapter 13: A Model of HIV-1 Treatment: The Latently Infected CD4+ T Cells Becomes Undetectable
----Karen O'Hara

Chapter 14: A State Space Model for HIV Pathogenesis Under Anti-Viral Drugs and Applications
----Wai-Yuan Tan, Ping Zhang and Xiaoping Xiong

Chapter 15: Bayesian Estimation of Individual Parameters in an HIV Dynamic Model Using Long-Term Viral Load Data
----Yangxin Huang and Hulin Wu

Chapter 16: Within-Host Dynamics and Treatment of HIV-1 Infection: Unanswered Questions and Challenges for Computational Biologists
----John Mittler

PART V: Modeling Drug Resistance

Chapter 17: Treatment Interruptions and Resistance: A Review
----Jane M Heffernan and Lindi M Wahl

Chapter 18: A Branching Process Model of Drug Resistant HIV
----H. Zhou and K.S. Dorman

Chapter 19: A Bayesian Approach for Assessing Drug Resistance in HIV Infection Using Viral Load
----Hua Liang, Wai-Yuan Tan and Xiaoping Xiong

PART VI: Statistical Methods

Chapter 20: Estimating HIV Incidence from a Cross-Sectional Survey with the Less Sensitive Assay
----Robert H. Byers, Jr., Dale J. Hu, Robert Janssen

Chapter 21: Design of Population Studies of HIV Dynamics
----Cong Han and Kathryn Chaloner

Chapter 22: Statistical Methods for Estimation and Inference of Parameters in Ordinary Differential Equations Models
----Sarah E. Holte

Chapter 23: A Bayesian Monte Carlo Integration Strategy for Connecting Stochastic Models of HIV/AIDS with Data
----Charles J. Mode