[theory.bio.uu.nl]

Mathematical models of coreceptor
usage and a dendritic cell-based
vaccine during HIV-1 infection.
Tendai Mugwagwa
Master of science
Department of mathematics and applied mathematics
University of Cape Town
2005
I

Abstract
While most of Europe is affected by HIV-1 subtype B, sub-Saharan African
is dominated by HIV-1 subtype C. Due to costs, most vaccine development
is carried out Europe rather than sub-Saharan countries. However since the
mechanisms of disease progression in HIV-1 subtype B may be different from
those in HIV-1 subtype C, it is interesting to investigate if and how a dendritic
cells based vaccine such as the one developed France and tested on Brazilians
(Lu et al, Nature; 2004) can be used on individuals in sub-Saharan Africa.
To investigate this, mathematical models and sensitivity analysis techniques
are used to understand the mechanisms of disease progression in two HIV-1
subtypes. These models are then extended to explore the ways in which the
vaccine could be used to treat these different HIV-1 subtypes. It is found
that the level of immune activation plays a large role in determining the
mechanism of disease progression and can itself be a means to the develop-
ment of AIDS. Furthermore, it is also shown that the dendritic cells based
vaccine could reduce the viral load but not eliminate the virus resulting in a
viral rebound. To maintain a low viral load, vaccination would have to be re-
peated. Unfortunately, repeated vaccination may lead to the overproduction
of proinflamatory cytokines resulting in severe side effects however this could
be avoided by using a carefully planned treatment schedule. We conclude
that the dendritic cells based vaccine can be used in individuals in either
subtype B or subtype C region as long as the correct treatment schedule is
followed.
II

Acknowledgements
Many thanks to my supervisor Dr Gareth Witten for guidance and advice
as I started my journey through the field of mathematical biology. Many
thanks also to the AIMS family and everyone who helped me through.
To Judith Mugwagwa and Nneoma Ogbonna
III

Contents
Acknowledgements II
1 Introduction. 1
1.1 Motivation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Introduction to HIV biology. . . . . . . . . . . . . . . . . . . . 3
1.3 Thesis organisation. . . . . . . . . . . . . . . . . . . . . . . . . 7
2 Literature review 9
3 Factors affecting the choice of coreceptor usage. 15
3.1 Model development. . . . . . . . . . . . . . . . . . . . . . . . . 17
3.2 Model outcomes. . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.3 Model analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.3.1 Methodology of model analysis. . . . . . . . . . . . . . 26
3.3.2 Results of model analysis. . . . . . . . . . . . . . . . . 29
IV

3.4 Chapter summary and conclusion. . . . . . . . . . . . . . . . . 38
4 The role of dentritic cells in viral dynamics 45
4.1 Model Development . . . . . . . . . . . . . . . . . . . . . . . . 50
4.2 Model outcomes . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.2.1 Analysis of equilibrium points . . . . . . . . . . . . . . 54
4.3 Extension of model to include vaccination. . . . . . . . . . . . 60
4.3.1 Extended model results. . . . . . . . . . . . . . . . . . 61
4.4 The dynamics of repeated vaccination. . . . . . . . . . . . . . 68
4.4.1 Designing of repeated treatment schedules. . . . . . . . 72
4.5 Chapter summary and conclusion. . . . . . . . . . . . . . . . . 74
5 Vaccination of subtype B and C infected individuals. 79
5.1 Effect of vaccination on coreceptor switching. . . . . . . . . . 82
5.2 Conclusions and recommendations. . . . . . . . . . . . . . . . 83
5.3 Limitations and future work. . . . . . . . . . . . . . . . . . . . 85
5.4 Papers submitted for publication. . . . . . . . . . . . . . . . . 86
Bibliography 86
A Results tables 101
V