Deterministic And Stochastic Models Of Aids Epidemics And Hiv Infections With Intervention

610 Pages·2005·6.94 MB·English

by  Tan Wai-Yuan

Deterministic and Stochastic Models of
AIDS Epidemics and HIV Infections
with Intervention
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Deterministic and Stochhastic Models of
AIDS Epidemics and HIV Infections
with Intervention
WAI-YUAN TAN
University of Memphis, USA
HULIN WU
University of Rochester, USA
WeWorld Scientific
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British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
DETERMINISTIC AND STOCHASTIC MODELS OF AIDS EPIDEMICS
AND HIV INFECTIONS WITH INTERVENTION
Copyright © 2005 by World Scientific Publishing Co. Pte. Ltd.
All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means,
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CONTENTS
Chapter 1
Mathematical Models for HIV Transmission Among
Injecting Drug Users 1
Vincenzo Capasso and Daniela Morale
Chapter 2
Estimation of HIV Infection and Seroconversion
Probabilities in IDU and Non-IDU Populations by State
Space Models 31
Wai-Yuan Tan, Li-Jun Zhang and Lih-Yuan Deng
Chapter 3
A Bayesian Monte Carlo Integration Strategy
for Connecting Stochastic Models of HIV/AIDS
with Data 61
Charles J. Mode
Chapter 4
A Class of Methods for HIV Contact Tracing
in Cuba: Implications for Intervention and Treatment 77
Ying-Hen Hsieh, Hector de Arazoza, Rachid Lounes
and Jose Joanes
Chapter 5
Simultaneous Inferences of HIV Vaccine Effects
on Viral Load, CD4 Cell Counts, and Antiretroviral
Therapy Initiation in Phase 3 Trials 93
Peter B. Gilbert and Yanqing Sun
v
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vi Contents
Chapter 6
A Review of Mathematical Models for HIV/AIDS
Vaccination 121
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 139
Wai-Yuan Tan, Ping Zhang and Xiaoping Xiong
Chapter 8
Dynamical Models for the Course of an HIV Infection 173
Christel Kamp
Chapter 9
How Fast Can HIV Escape from Immune Control? 189
W. David Wick and Steven G. Self
Chapter 10
CTL Action During HIV-1 Is Determined VIA
Interactions with Multiple Cell Types 219
Seema H. Bajaria and Denise E. Kirschner
Chapter 11
Identifiability of HIV/AIDS Models 255
Annah M. Jeffrey and Xiaohua Xia
Chapter 12
Influence of Drug Pharmacokinetics on HIV
Pathogenesis and Therapy 287
Narendra M. Dixit and Alan S. Perelson
Chapter 13
A Model of HIV-1 Treatment: The Latently Infected
CD4+ T Cells becomes Undetectable 313
Karen O’Hara
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Contents vii
Chapter 14
A State Space Model for HIV Pathogenesis Under
Anti-Viral Drugs and Applications 333
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 361
Yangxin Huang and Hulin Wu
Chapter 16
Within-Host Dynamics and Treatment of HIV-1
Infection: Unanswered Questions and Challenges for
Computational Biologists 385
John Mittler
Chapter 17
Treatment Interruptions and Resistance: A Review 423
Jane M Heffernan and Lindi M Wahl
Chapter 18
A Branching Process Model of Drug Resistant HIV 457
H. Zhou and K. S. Dorman
Chapter 19
A Bayesian Approach for Assessing Drug Resistance
in HIV Infection Using Viral Load 497
Hua Liang, Waiyuan Tan and Xiaoping Xiong
Chapter 20
Estimating HIV Incidence from a Cross-Sectional
Survey with the Less Sensitive Assay 513
Robert H. Byers, Jr., Dale J. Hu and Robert S. Janssen
Chapter 21
Design of Population Studies of HIV Dynamics 525
Cong Han and Kathryn Chaloner
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viii Contents
Chapter 22
Statistical Estimation, Inference and Hypothesis Testing
of Parameters in Ordinary Differential Equations
Models of HIV Dynamics 549
Sarah Holte
Chapter 23
Convergence to an Endemic Stationary Distribution
in a Class of Stochastic Models of HIV/AIDS in
Homosexual Populations 569
Charles J. Mode
Index 593
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CHAPTER 1
MATHEMATICAL MODELS FOR HIV TRANSMISSION
AMONG INJECTING DRUG USERS
VincenzoCapasso and Daniela Morale
Inthispaper,weproposeasurveyofmathematicalmodelsforthespread
of HIV/AIDS through shared drug injection equipment in groups of
injecting drug users. We extend the expression for the force of infec-
tion by including the mechanism of exchange of a drug injecting equip-
ment (DIE) in a friendship group. The classical models based on the
lawofmassactionfordirecttransmissionareobtainedaslimitingcases.
We analyze models for a homogeneous population; for multiple stages
of infectivity of HIV-infected individuals, and for stratified populations
and multiple stages of infectivity by providing threshold theorems and
possible stability results for nontrivial endemic states.
Keywords: HIV/AIDS, transmission models, injecting drug users,
multistage-multigroup models.
1. Introduction
A large amount of literature is available about the mathematical model-
ing of HIV/AIDS epidemics. Most of the proposed models may be seen as
extensions of classical epidemic models, by the inclusion of various modi-
fications in order to take into account relevant peculiarities of the mecha-
nismoftransmissionofHIV.Amongthose,wemaymentionthesubstantial
variabilityofthe infectionrates fordifferent subpopulationsatrisk (homo-
sexuals, heterosexuals, intravenous drug users, etc.); the long incubation
period before the exhibition of symptoms; the variability of the infection
with respect to the evolution of the infection in each individual; etc. As
a consequence, the mathematical modeling of the dynamics of HIV/AIDS
infections cannot avoid including “structures” in the population. In order
toreducethelevelofcomplexity,mostoftheauthorshaveproposedtostart
from simplified models in order to obtain some first information about the
macroscopic qualitative behavior of the system.
1