Department of Mathematical Sciences

Recent Submissions

  • Investigating tumour micro environment dynamics based on cytokine-mediated innate-adaptive immunity 

    Amima, Innocenter Moraa (Stellenbosch : Stellenbosch University, 2018-03)
    ENGLISH ABSTRACT : Cancer is a leading cause of death worldwide, yet much is still unknown about its mechanism of establishment, recurrence cycle and destruction. It is known that the successive alterations that occur ...

  • Refinable vector splines and multi-wavelets with shortest matrix filters 

    Ranirina, Dinna (Stellenbosch : Stellenbosch University, 2018-03)
    ENGLISH ABSTRACT : A widely used class of basis functions in signal analysis is obtained from the dilation and integer shifts of a given (compactly supported) wavelet ψ : R → R, by means of which a (scalar) signal can ...

  • Assessment of a measles outbreak response vaccination campaign, and two measles parameter estimation methods 

    Azam, James Mba (Stellenbosch : Stellenbosch University, 2018-03)
    ENGLISH ABSTRACT : Measles is highly transmissible, and is a leading cause of vaccine-preventable death among children. Consequently, it is regarded as a public health issue worldwide and has been targeted for elimination ...

  • Enumeration of tanglegrams 

    Ravelomanana, Jean Bernoulli (Stellenbosch : Stellenbosch University, 2018-03)
    ENGLISH ABSTRACT : Tanglegrams are graphs obtained by taking two binary rooted trees with the same number of leaves and a perfect matching between the leaves of the two trees. Tanglegrams appear in biology in the study ...

  • Modelling the effects of temperature change on the dynamics of tsetse flies and trypanosomiasis disease transmission 

    Mthombothi, Zinhle Emily (Stellenbosch : Stellenbosch University, 2018-03)
    ENGLISH ABSTRACT : Global temperatures have increased over recent decades. This is expected to have an impact on vector-borne diseases, raising questions such as: Will the increased temperature result in changing disease ...

  • Oriented 123-TQFTs via String-Nets and State-Sums 

    Goosen, Gerrit (Stellenbosch : Stellenbosch University, 2018-03)
    ENGLISH ABSTRACT :In a series of papers Bartlett, Douglas, Schommer-Pries, and Vicary discovered a finite generators-and-relations presentation of the oriented bordism bicategory. This simplifies the task of finding ...

  • Contributions to projective group theory 

    Van Niekerk, Francois Koch (Stellenbosch : Stellenbosch University, 2017-12)
    ENGLISH ABSTRACT : Projective Group Theory (PGT for short) provides a self-dual axiomatic context that allows one to establish homomorphism theorems for (non-abelian) group-like structures. The present thesis has two ...

  • Towards projective set theory 

    van Zyl, Phillippus Johannes III (Stellenbosch : Stellenbosch University, 2017-12)
    ENGLISH ABSTRACT : In this thesis an axiomatic framework is presented which extends the projective group theory introduced by Z Janelidze to also hold for sets. The isomorphism theorems are reformulated so that they hold ...

  • Contributions to the theory of near-vector spaces 

    Sanon, Sogo Pierre (Stellenbosch : Stellenbosch University, 2017-12)
    ENGLISH ABSTRACT : The purpose of this thesis is to give an exposition and expand the theory of near-vector spaces. Near-vector space theory is a new and rich field of mathematics and has been used in several applications, ...

  • A meta-analysis of the association between intimate partner violence and age disparity in sub-Saharan Africa 

    Otieno, Fanuel Omondi (Stellenbosch : Stellenbosch University, 2017-12)
    ENGLISH ABSTRACT : Intimate partner violence (IPV) is the most common form of violence against women and a worldwide human rights and public health problem. IPV against women can be emotional, physical, and sexual in ...

  • Analysis of partner turnover rate and the lifetime number of sexual partners in Cape Town using generalized linear models 

    Olojede, Christianah Oyindamola (Stellenbosch : Stellenbosch University, 2017-12)
    ENGLISH ABSTRACT :A large number of analyses have been carried out to investigate how sexually active people contracted human immunodeficiency virus (HIV) by using common indicators like the number of new sexual partners ...

  • Centrality in random trees 

    Durant, Kevin (Stellenbosch : Stellenbosch University, 2017-12)
    ENGLISH ABSTRACT : We consider two notions of centrality—namely, the betweenness centrality of a node and whether or not it is a centroid—in families of simply generated and increasing trees. Both of these concepts are ...

  • Properties of graph polynomials and related parameters 

    Misanantenaina, Valisoa Razanajatovo (Stellenbosch : Stellenbosch University, 2017-12)
    ENGLISH ABSTRACT : In this thesis, we investigate various problems related to graph polynomials. We first define two-variable polynomials for rooted trees and specific posets, which are motivated by the Tutte polynomial. ...

  • Random walk hitting times in random trees 

    Oosthuizen, Joubert (Stellenbosch : Stellenbosch University, 2017-12)
    ENGLISH ABSTRACT : The hitting time Hxy, between two vertices x and y of a graph, is the average time that the standard simple random walk takes to get from x to y. We start by giving a recursive formula for higher moments ...

  • A simulation age-specific tuberculosis model for the Cape Town metropole 

    Nyabadza, Farai; Winkler, Dieter (Academy of Science of South Africa, 2013-09-18)
    Tuberculosis (TB) continues to present an insurmountable health burden in the Western Cape Province of South Africa. TB dynamics in adults is different from that in children, with the former determining the latter. Because ...

  • Generalised sequences and compactness notions in point-free topology 

    Masuret, Jacques (Stellenbosch : Stellenbosch University, 2017-12)
    ENGLISH ABSTRACT : While sequences and naturally associated notions like convergence and clustering have received extensive attention in classical topology, the same cannot be said for the point-free setting. The aim of ...

  • Invading a mutualistic network : to be or not to be similar 

    Minoarivelo, Henintsoa Onivola; Hui, Cang (Wiley Open Access, 2016)
    Biological invasion remains a major threat to biodiversity in general and a disruptor to mutualistic interactions in particular. While a number of empirical studies have directly explored the role of invasion in mutualistic ...

  • A geometrical model for testing bilateral symmetry of bamboo leaf with a simplified Gielis equation 

    Lin, Shuyan; Zhang, Li; Reddy, Gadi V. P.; Hui, Cang; Gielis, Johan; Ding, Yulong; Shi, Peijian (Wiley Open Access, 2016)
    The size and shape of plant leaves change with growth, and an accurate description of leaf shape is crucial for describing plant morphogenesis and development. Bilateral symmetry, which has been widely observed but poorly ...

  • The seesaw effect of winter temperature change on the recruitment of cotton bollworms Helicoverpa armigera through mismatched phenology 

    Reddy, Gadi V. P.; Shi, Peijian; Hui, Cang; Cheng, Xiaofei; Ouyang, Fang; Ge, Feng (John Wiley & Sons Ltd., 2015)
    Knowing how climate change affects the population dynamics of insect pests is critical for the future of integrated pest management. Rising winter temperatures from global warming can drive increases in outbreaks of some ...

  • An optimal proportion of mixing broad-leaved forest for enhancing the effective productivity of moso bamboo 

    Cheng, Xiao-Fei; Shi, Pei-Jian; Hui, Cang; Wang, Fu-Sheng; Liu, Guo-Hua; Li, Bai-Lian (John Wiley & Sons Ltd., 2015-03-17)
    Moso bamboos (Phyllostachys edulis) are important forestry plants in southern China, with substantial roles to play in regional economic and ecological systems. Mixing broad-leaved forests and moso bamboos is a common ...

  • Ultraproducts and Los’s Theorem: A Category-Theoretic Analysis 

    Chimes, Mark Jonathan (Stellenbosch : Stellenbosch University, 2017-03)
    ENGLISH ABSTRACT : Ultraproducts are an important construction in model theory, especially as applied to algebra. Given some family of structures of a certain type, an ultraproduct of this family is a single structure ...

  • Imaginaries in dense pairs of real-closed fields 

    Rakotonarivo, Tsinjo Odilon (Stellenbosch : Stellenbosch University, 2017-03)
    ENGLISH ABSTRACT : Imaginaries are definable equivalence classes, which play an important role in model theory. In this thesis, we are interested in imaginaries of dense pairs of real-closed fields. More precisely, we ...

  • Immune biomarker reference range estimation for healthy paediatric patients in South Africa 

    Bicko, Steve Cygu (Stellenbosch : Stellenbosch University, 2017-03)
    ENGLISH ABSTRACT : Understanding and quantifying human peripheral blood T-lymphocyte immunophenotypes is necessary for the diagnosis and treatment of immune and haematological disorders. This is only possible if comparison ...

  • Thermodynamics analysis of variable viscosity hydromagnetic Couette flow in a rotating system with Hall effects 

    Makinde, Oluwole D.; Eegunjobi, Adetayo S.; Tshehla, M. Samuel (MDPI, 2015-11-20)
    In this paper, we employed both first and second laws of thermodynamics to analyze the flow and thermal decomposition in a variable viscosity Couette flow of a conducting fluid in a rotating system under the combined ...

  • Whole body modelling of glucose metabolism in malaria patients 

    Green, Kathleen (Stellenbosch : Stellenbosch University, 2017-03)
    ENGLISH ABSTRACT : Diagnosing a patient with a disease is typically done by considering a list of clinical symptoms. For severe malaria two of the key pathophysiological indicators for poor chances of survival are ...

  • Social and genetic networks of HIV-1 transmission in New York City 

    Wertheim, Joel O.; Kosakovsky Pond, Sergei L.; Forgione, Lisa A.; Mehta, Sanjay R.; Murrell, Ben; Shah, Sharmila; Smith, Davey M.; Scheffler, Konrad; Torian, Lucia V. (PLoS, 2017-01-09)
    Background Sexually transmitted infections spread across contact networks. Partner elicitation and notification are commonly used public health tools to identify, notify, and offer testing to persons linked in these ...

  • Modelling the trends of inpatient and outpatient rehabilitation for methamphetamine in the Western Cape province of South Africa 

    Mushanyu, J.; Nyabadza, F.; Stewart, A. G. R. (BioMed Central, 2015-12-18)
    Background: Dependence on methamphetamine remains one of the major health and social problem in the Western Cape province of South Africa. We consider a mathematical model that takes into account two forms of rehabilita ...

  • On the transmission dynamics of Buruli ulcer in Ghana : insights through a mathematical model 

    Nyabadza, Farai; Bonyah, Ebenezer (BioMed Central, 2015-11-06)
    Background: Mycobacterium ulcerans is know to cause the Buruli ulcer. The association between the ulcer and environmental exposure has been documented. However, the epidemiology of the ulcer is not well understood. ...

  • The double Heston model via filtering methods 

    Namundjebo, Elia N (Stellenbosch : Stellenbosch University, 2016-12)
    ENGLISH ABSTRACT : Stochastic volatility models are well-known for their ability to generate a volatility smile for financial securities. The development of the stochastic volatility models followed shortly after the ...

  • An integrated framework modelling susceptibility to tuberculosis in homogeneous and admixed populations 

    Gebremariam, Zoe Zerihun (Stellenbosch : Stellenbosch University, 2016-12)
    ENGLISH ABSTRACT : In spite of the wide variety of anti-tuberculosis drugs, tuberculosis (TB), caused by mycobacterium tuberculosis (MTB), is the second leading infectious disease after Human Immunode ciency Virus (HIV) ...

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