Department of Mathematical Sciences

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Browsing Department of Mathematical Sciences by browse.metadata.advisor "Cang, Hui"

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    Computational and analytical methods for constructing a multilevel model for human glucose metabolism
    (Stellenbosch : Stellenbosch University, 2022-03) Green, Kathleen Alice; Snoep, Jacob Leendert; Van Niekerk, David Douglas ; Cang, Hui; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences.
    ENGLISH ABSTRACT: Glucose metabolism is carefully regulated in humans to ensure that homeosta- sis is maintained. Disruptions in the multiple processes involved, or the inabil- ity to sustain adequate glucose concentrations, can cause various metabolic complications that can become life threatening. These complications can present as a result of diseases such as Type 2 diabetes (hyperglycaemia), or severe malaria (hypoglycaemia). In the context of malaria, two key metabolic indicators for poor chance of survival are hypoglycaemia (low plasma glu- cose concentrations) and lactic acidosis (high plasma lactate concentrations). Currently, it is understood that these conditions are the result of various clin- ical complications, and the extent to which the malaria parasite Plasmodium falciparum contributes to them is unknown. This contribution could be a consequence of the accelerated glycolytic flux, brought about by the parasite increasing the glucose demand and lactate production, once it has invaded the host’s red blood cells, a hypothesis that is tested in this thesis using a mathematical modelling approach. We used a new approach to building a whole body glucose metabolism model that is well-grounded in a large number of clinical studies following a thorough literature review to obtain clinical data on glucose metabolism. This model is parametrised using data from 49 different studies, and 74 figures that have been successfully reproduced between different softwares. The model construction is performed using a specialised package for model merging called Hierarchical Model Composition [1]. This model consists of several different organs that contribute to glucose metabolism in humans with a specific compartment that was incorporated to describe red blood cell metabolism. In addition to the reference model built for glucose metabolism in a healthy individual, we extend the model to represent malaria patients by explicitly modelling parasitaemia via the inclusion of a detailed mathematical model for Plasmodium falciparum into the red blood cell compartment. The multilevel model for malaria reveals that a 13% parasite burden leads to hypoglycaemia, but lactic acidosis as is observed in malaria patients, is not induced. Patient data and sensitivity analysis is used for initial model validations and identification of potential treatment targets in the parasite’s glycolytic pathway. The multilevel model is large (303 variables) which makes it difficult to anal- yse. Therefore we developed a flexible model reduction technique that can aid in the simplification of the multilevel model through selection of the relevant enzyme mechanisms, while retaining the whole body descriptions on the higher level. This reduction method applies a combination of structural and kinetic modification to the original model, and was tested on different modelling struc- tures and kinetics occurring in biochemical pathways. Thereafter, the method is extended to biological applications which show how multiple model simpli- fications for different inhibitor titration studies can be investigated starting from a single model description and performing various selections of reactions or species. During model merging we encountered logistical challenges such as unit con- version and the use of unique identifiers that are generic for merging different modules into a single model. Our solution was to use automated approaches as much as possible as developed in the Systems Biology community, and to code additional solutions for our automated workflow. This work highlights the benefits of utilising automated approaches, as well as combining differ- ent computational and analytical techniques from different disciplines, during model construction, validation and analysis. By making these models, all datasets, and simulation experiment descriptions available on JWS Online [2], FAIRDOMHub [3], and PK database [4], we envisage that future improve- ments and extensions can be implemented in a systematic way owing to the modular structure of the model, and the transparency and reproducibility of the construction process.
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    Modelling multi-species co-occurrence patterns and processes
    (Stellenbosch : Stellenbosch University, 2022-04) Lagat, Vitalis Kimutai; Cang, Hui; Guillaume, Latombe; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences.
    ENGLISH ABSTRACT: The structure of ecological communities is determined by the interplay among a range of processes, such as biotic interactions, abiotic filters, and disper- sal. Their effects can be detected by examining patterns of co-occurrence between different species. Using species-by-site matrices, null models that are based on permutations under constraints on row or column sums, have been widely used for comparing the observed values of co-occurrence met- rics (e.g., C-score and the natural metric) against null model expectations. This allows to detect significant signals of species association or dissocia- tion, from which the type of biotic interactions between species (e.g., facil- itative or antagonistic) can be inferred. In such a permutation-based null model test, the levels of co-occurrence between randomly paired species are often pooled to obtain a sampling distribution. However, the level of co-occurrence for three or more species are ignored, which could reflect functional guilds or motifs composed of multiple species within the com- munity. Null model tests without considering multi-species co-occurrence could often lead to false negatives (Type II error) in detecting non-random forces at play. Moreover, variations of co-occurrence have been explored by many models with covariates reflecting between-site environmental filters and distance decay of similarity. This, however, does not allow us to explic- itly explore the role of biotic interactions that could give rise to the observed co-occurrence patterns. An R software package for performing null model testing of multi-species co-occurrence patterns is currently lacking. This dis- sertation focuses on addressing all the above challenges. First, we propose a multi-species co-occurrence index that measures the number of sites jointly occupied by three or more species simultaneously, with the pairwise metric of co-occurrence as a special case for order two. We identify nine archetypes of species co-occurrence and show the majority of real communities con- form to six of these archetypes. Second, we develop a statistical model (gen- eralised B-spline modelling) that can use trait variations among species as a niche-based force and encounter rate as a neutral force to explain the la- tent interaction strength structure. This method decomposes each predictor into a linear combination of B-splines that allow to measure the local sen- sitivity of joint occupancy along the full range of the predictor’s variation. The generalised B-spline modelling can explain the observed co-occurrence and joint occupancy at different orders of joint occupancy. Finally, we im- plement the proposed multi-species co-occurrence index and the associated generalised B-spline modelling in the multi-species co-occurrence (msco) R package for null model testing of multi-species interactions and interference with covariates.
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    Modelling the transmission of Buruli ulcer in fluctuating environments
    (Stellenbosch : Stellenbosch University, 2015-12) Assan, Belthasara; Nyabadza, Farai; Cang, Hui; Stellenbosch University. Faculty of Science. Department Mathematical Sciences (Mathematics)
    ENGLISH ABSTRACT : Buruli ulcer is a disease caused by Mycobacterium ulcerans. The transmission dynamics of this disease largely depends on environmental changes. In this thesis a deterministic model for the transmission converge to the disease free and endemic equilibrium respectively. A very good synergy was obtained between the deterministic model and STELLA model. The STELLA model however, provided flexibility through its ability to accommodate more social dynamics without adding mathematical intractability. The model provides useful insights in the dynamics of Buruli ulcer and has significant implication to the management of disease. of Buruli ulcer in fluctuating environments is proposed. The model incorporates periodicity in the disease transmission pathways and the Mycobacterium ulcerans density, that are thought to vary seasonally. Two reproduction numbers, time-averaged reproduction number [R0] and the basic reproduction number R0, are determined and compared. The time-averaged reproduction number obtained shows that Buruli ulcer epidemic is driven by the dynamics of the environments. It shows inaccuracy in predicting the number of infections. Numerical simulations confirmed that if R0 > 1 the infection is sustained seasonally. The model outcome suggests that environmental fluctuation should be taken into consideration in designing policies aimed at Buruli ulcer control and management. In addition to the deterministic model, a systems dynamic model for the transmission of Buruli ulcer by using STELLA is also proposed with and without periodicity in the disease transmission pathways and the Mycobacterium ulcerans density. The model simulations confirm that when R0 < 1 and R0 > 1 the solutions converge to the disease free and endemic equilibrium respectively. A very good synergy was obtained between the deterministic model and STELLA model. The STELLA model however, provided flexibility through its ability to accommodate more social dynamics without adding mathematical intractability. The model provides useful insights in the dynamics of Buruli ulcer and has significant implication to the management of disease.