Browsing by Author "Witten, G"

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    An analysis of spatial percolation structures using a network approach
    (2006) Fadul, Mohammed Altaj Mohammed; Witten, G; Perrier, E
    In this thesis we analyse several spatial structures, built from percolation models, by means of an approach used so far in the field of network science. In the first chapter we summarize the major network concepts and characterizations that have been obtained as regards the statistical properties of several data sets or theoretical models, We also give a brief introduction to percolation theory and its applications, adding details in two particular cases where mathematical results are available. In the second chapter we then study one particular application of percolation theory to the modelling of distribution and species abundance at different seales. We mainly focus on the way percolation theory was used to compare two diffcrcnt spatial patterns, particularly the random and the aggrergated distribution.
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    Mathematical models of coreceptor usage and a dendritic cell-based vaccine during HIV-1 infection
    (2005) Mugwagwa, Tendai; Witten, G
    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 in 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 development 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 repeated. 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.