Submitted in fulfillment of the requirements of Doctor of Engineering, Durban University of Technology, Durban, South Africa, 2017. / The need to quantify and model transformations that have taken place in the cities of South Africa is one of the grand challenges linked to country’s transition to Democracy. Given the complexities associated with different stages of city transformation, it is imperative that models used to unpack processes of city transformation are novel. In this study it emerged that statistical methods alone are not adequate to fully present, in a comprehensible way, all facets of drivers of city transformation. As a result, statistical methods have been combined with mathematical and system dynamics models. Results revealed that city transformations derive from a number of triggers. Underlining these are income, migration and houses. The empirical data collected through questionnaire survey that was later incorporated into mathematical models demonstrated that income is a primary driver that fuels city migration. System Dynamic Models demonstrated that the availability of houses or accommodation serve as constraints that keep the city population within the limits of the carrying capacity of a city. In addition it was further confirmed, through mathematical models that income has varying effects on the attractiveness of cities. This was found to be linked to the shape of the distribution of income in the city. A normally distributed income with a peak in the middle results in a city being more attractive than an evenly distributed income that peaks either at very low or high income levels. This observation brought forth a need to test heterogeneity when analyzing city transformation using income as an index. Mathematical Models that incorporated heterogeneity demonstrated the usefulness of systems analysis in unpacking the mechanism of city transformation, a component of city management that requires serious consideration for planning, budgeting and provision of limited resources like houses in the cities. Success of methods used in this study led to a conclusion that these can be enhanced through other techniques like agent based models. With this call, improvements on this study that can be attained through these techniques are recommended. This will enrich the understanding of the transformation and dynamics of cities under different conditions than those that exist in South Africa. / D