Application of lie group analysis to mathematical models in epidemiology
- Authors: Otieno, Andrew Alex Omondi
- Date: 2013
- Subjects: Epidemiology -- Mathematical models
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:18486 , http://hdl.handle.net/11260/100
- Description: Lie group analysis is arguably the most systematic vehicle for finding exact solutions of differential equations. Using this approach one has at one's disposal a variety of algorithms that make the solution process of many differential equations algorithmic. Vital properties of a given differential equation can often be inferred from the symmetries admitted by the equation. However, Lie group analysis has not enjoyed wide-spread application to systems of first-order ordinary differential equations. This is because such systems typically admit an infinite number of Lie point symmetries, and there is no systematic way to find even a single nontrivial one-dimensional Lie symmetry algebra. In the few applications available, the approach has been to circumvent the problem by transforming a given system of first-order ordinary differential equations into one in which at least one of the equations is of order two or greater. It is therefore fair to say that the full power of Lie group analysis has not been sufficiently harnessed in the solution of systems of first-order ordinary differential equations. In this dissertation we review some applications of Lie group analysis to systems of first order ordinary differential equations. We shed light on the integration procedure for first-order systems of ordinary differential equations admitting a solvable Lie algebra. We do this via instructive examples drawn from mathematical epidemiology models. In particular we revisit the work of Nucci and Torrisi [54] and improve the exposition of the Lie-symmetry-inspired solution of a mathematical model which describes a HIV transmission. To aid implementation of the integration strategy for systems of ordinary differential equations, we have developed ad-hoc routines for finding particular types of admitted symmetries and checking if a given symmetry is indeed admitted by a system of ordinary differential equations.
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- Date Issued: 2013
Medicinal properties of some plants used for the treatment of skin disorders in the O. R. Tambo and Amathole Municipalities of the Eastern Cape Province, South Africa
- Authors: Mahachi, Josia
- Date: 2013
- Subjects: Medicinal plants -- Skin -- Diseases -- Treatment , South Africa -- Eastern Cape Province
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:18487 , http://hdl.handle.net/11260/101
- Description: The use of medicinal plants for treatment of skin infections and improvement of skin tone was assessed. The study covered Amathole and OR Tambo municipalities of the Eastern Cape Province of South Africa. The study sought to identify and document some medicinal plants which are used by the indigenous people on the skin, evaluate some biological properties which attribute to their use for therapeutic use. This report provides ethnobotanical data on some plant which were identified. Six medicinal plants (Kniphofia drepanophylla, Gnidia capitata, Hypoxis hemerocallidea, Syzgium cordatum, Macaranga capensis and Protorhus longifolia) which were implicated for treatment of skin diseases were screened for their antibacterial and antioxidant properties. Guided questionnaires were used to interview and gather ethnobotanical information from the traditional healers. Members of the communities which were indicated to be knowledgeable on use of medicinal plants in the areas were visited and interviewed. The results revealed that a total of 45 plant species distributed in 41 Genera belonging to 28 Families are used for treatment of skin infections and improvement of skin texture. The plant medicines were reported to be used as remedies against common skin problem such as wounds, pimples, acnes and itches. Some were reported to have anti-inflammatory effect on the skin while other were reported to oil dry skin and prevent skin dryness and dry eczematous conditions. Others like Cassipourea flanaganii, and Spirostachys africana were commonly used to enlighten skin and protect skin from ultra-violet radiation. The most common mode of preparation of these medicinal plants was pastes or decoctions. Sometimes crushed plant materials were put in bathing water or boiled and steamed on affected parts. It was reported that mixing pastes with oil, animal fat and milk improve medicinal properties. Water, methanol and acetone extracts of K. drepanophylla, G. capitata, H. hemerocallidea, S. cordatum, M. capensis and P. longifolia were screened against five strains of Gram negative bacteria. The results revealed that water extracts from five plant species inhibited two or more strains of bacteria with the most common minimum inhibitory concentrations (MICs) ranging between 5,0 to 10,0 mg/ml with the exception of aqueous extracts of K. drepanophylla which failed to inhibit all strains of bacteria. The screening of methanol extract of these plants for antioxidant and free radical activity revealed a significant activity with 1, 1-diphenyl-2-picryl-hydrazyl (DPPH) free radical (DPPH). The extracts of P. longifolia, G. capitata, M. capensis, S. cordutum and H. hemerocallidea showed significantly higher free radical scavenging activity with IC50 of ranging from about 11.0 to 41.2 μg/ ml while the IC50 value for K. drepanophylla could not be determined at 100 μg/ ml. Generally the study showed that medicinal plants still play a very important role in the health care delivery system, especially in the O R Tambo and Amathole municipalities of the Eastern Cape. Botanical medicine remains pivotal in the treatment of skin ailments and improvement of the skin tone.
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- Date Issued: 2013
Stable isotopes dynamics of macrophytes along Umtata River in the Eastern Cape of South Africa
- Authors: Mzamo, Sanele Caleb
- Date: 2013
- Subjects: Stable isotopes -- Macrophytes , South Africa -- Eastern Cape
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:18485 , http://hdl.handle.net/11260/d1007205
- Description: The decline of freshwater ecosystems, generally result from land use activities in the river catchment and is of great concern worldwide. This study was conducted along Umtata River in the Eastern Cape province of South Africa between May 2010 and April 2011. The study was aimed at identifying macrophytes families (to species level) and determining the stable isotope signatures (C:N ratios, δ13C and δ15N) and to relate their isotopic signatures to the land use activities along the river catchment. Analysis of variance was performed to test the effect of sites and sampling period on the C:N ratios, δ13C and δ15N signatures. There were 16 macrophyte families represented by 26 species recorded along the river. There was only a significant difference in sites and sampling period in δ15N (p< 0.05). The highest C:N ratios value (30.75±9.65‰) was recorded in the upper reaches while the lowest value (6.10±2.35‰) occurred in the lower reaches. The δ13C values varied throughout the length of the river with highest values (-19.63±5.44‰) obtained in the middle reaches. Spatial variation was evident in δ15N throughout the length of the river and showed increase from the upper reaches to middle reaches and decreased towards lower reaches. The δ15N ranged from 3.92±2.43‰ in the upper reaches to 10.02±4.56‰ in the middle reaches. Temporal variation in δ15N was also evident throughout the sampling period with highest peak in May (9.77± 4.49‰) and lowest in February (0.50±2.49‰) respectively. The highest values of isotope signatures at spatial level demonstrated the true reflection of urban development, sewage discharge and agricultural activities taking place along the river system. Continued monitoring is recommended that may ultimately come up with a better management options for the communities living within the study area, and also to better enhanced land utilization.
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- Date Issued: 2013
Response of invertebrates to alien and indigenous vegetation characteristics in Nduli and Luchaba Nature Reserves, Eastern Cape, South Africa
- Authors: Yekwayo, Inam
- Date: 2012
- Subjects: Alien and indigenous vegetation -- Invertebrates , South Africa -- Eastern Cape
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:18489 , http://hdl.handle.net/11260/d1009478
- Description: Most invertebrate species are becoming extinct due to habitat loss and alien plant invasions. Hence this study aimed at determining the response of invertebrates to alien and indigenous vegetation within protected areas in the King Sabatha Dalindyebo (KSD) Local Municipality, Eastern Cape, South Africa. Invertebrates were collected using pitfall traps, during 12 sampling occasions from May 2010 to April 2011 numbers of sampling sites. Although the sampling method was adapted to collecting ground dwelling invertebrates, opportunistic flying invertebrates were also collected. A total of 7 flying invertebrate orders, 25 families, 34 species and 248 individuals were attracted to traps while 5 orders, 19 families, 50 species and 1976 individuals of soil surface-dwelling invertebrates were collected. ANOVA test showed no significant differences (p > 0.05) in species richness and abundance across sites for soil surface-dwelling invertebrates. Bray-Curtis similarity measures in PRIMER and correspondence analysis (CA) in CANOCO showed that sampling units with alien invasive plants shared most soil surface-dwelling invertebrate species at ± 75% level of similarity. Sampling unit A from the Mix alien (MA) site shared most species with indigenous vegetation sites. Sampling units from indigenous vegetation sites shared most species at ± 65% level of similarity. Multivariate analysis using CANOCO indicated that certain site variables such litter depth influenced the distribution of soil surface-dwelling invertebrates across sites. The study provided preliminary data and information for promoting invertebrate biodiversity conservation within protected areas (Nduli and Luchaba Nature Reserves) of the KSD Local Municipality. Key words: invertebrates, indigenous vegetation, alien vegetation, Lantana camara, Acacia mearnsii, and Eucalyptus.
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- Date Issued: 2012
Microwave Mediated synthesis of cyclic compounds
- Authors: Ndebvu, Rumbidzayi
- Date: 2011
- Subjects: Cyclic compounds -- Synthesis
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:18488 , http://hdl.handle.net/11260/d1007382
- Description: The scope of microwave induced synthesis of various cyclic compounds was investigated and considerably expanded. The advantages of this synthetic method were clearly demonstrated when compared to conventional heating methods of organic synthesis. The exposure of organic compounds to continual Ultraviolet (UV) radiation damages the materials and reduces their chemical and physical properties and in most cases irreversibly and this is not only a concern for industry but for consumers as well. Particularly prevalent are incidences of skin cancer now linked to UV radiation. Research efforts are directed towards finding cheap and efficient UV-absorbers to protect such light sensitive materials. Phenyl salicylates and hydroxybenzophenones constitute families of UV-absorber compounds, and this has necessitated this research. The condensation of differently substituted phenols with salicylic acid, catalyzed by either phosphoric acid (PPA), POCl3/ZnCl2 or ZnCl2 afforded the anticipated phenolic type UV -absorber molecules such as phenyl salicylate, 4-hydroxyphenyl-2-hydroxybenzoate, 2,3-dihydroxyphenyl-2-hydroxyphenylbenzoate, 3-hydroxyphenyl-2-hydroxybenzoate, (2,4-dihydroxyphenyl)(2-hydroxyphenyl)methanone, (2,3-dihydroxyphenyl)(2-hydroxyphenyl) methanone and 1,3-dihydroxyxanthone. PPA proved to be a more efficient catalyst for the condensation of salicylic acid with phenol, hydroquinone, pyrogallol and catechol while POCl3/ZnCl2 gave higher yields for resorcinol and phloroglucinol. In all cases, ZnCl2 alone did not show significant yield enhancement. The second part of this research work describes a convenient one-pot synthesis of NMethyl-2-pyrrolidone (NMP) an important industrial solvent by a conventional heating process and by microwave irradiation. The intermediate N-Methyl-hydroxybutyramide formed from the exothermic reaction of =-butyrolactone with aqueous monomethylamine, underwent an intramolecular condensation reaction catalyzed by highly active copper powder to form the anticipated product in very good yields.
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- Date Issued: 2011
Mohair and wool fibre surface structure and lustre determination
- Authors: Ndlovu, Ntombizikhona Beaulah
- Date: 2011
- Subjects: Mohair and wool fibre -- Lustre
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:18484 , http://hdl.handle.net/11260/d1006641
- Description: Textiles have always been one of the essential materials for people and have a great variety of uses such as in clothing, agriculture, medical, automotive and aerospace applications. The sort of properties needed for any type of fabric basically depend on the structure of the fibre surface. Of many geometric attributes that can be used to describe the surface appearance of a fibre, yarn, or fabric sample, one of the more common is lustre. Mohair and wool fibre surface structure have been studied using optical microscopy and Atomic Force Microscopy (AFM). Optical microscopy was also used to take fibre diameter measurements. Another technique, goniophotometry, was used to make quantitative lustre measurements of mohair and wool fibres. The surface structure of mohair has got a faint pattern of scales where the scales are generally unpronounced or flat and relatively long. Wool has got a scaly surface structure where the scales overlap leading to interlocking of fibres. The scale configuration on the surface of mohair and wool fibres also differs. A qualitative connection between fibre lustre and the fibre surface structure was found. Because of its smooth surface relative to that of wool, mohair reflects a greater amount of incident light specularly whereas wool reflects most of the incident light diffusely. In general, mohair fibres have a higher lustre than wool due to its less prominent cuticle structure found on its surface. Furthermore, mohair fibres with the smallest diameters give an even higher lustre.
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- Date Issued: 2011
The value of remnant habitat patches for conserving butterflies (Lepidoptera) in King Sabata Dalindyebo (KSD) Local Municipality, Eastern Cape, South Africa
- Authors: Avuletey, Richard
- Date: 2011
- Subjects: Butterflies -- Research Butterflies -- Behaviour South Africa -- Transkei
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:18490 , http://hdl.handle.net/11260/d1011285
- Description: Butterflies (Lepidoptera) have attracted more attention as indicators of terrestrial ecosystems than other invertebrates. This taxon is widely used as tools or subjects for biodiversity conservation planning in the Northern and Southern Hemispheres. The study determined butterfly species turnover at a-priori selected habitat patches in a protected area (Nduli Nature Reserve) and non-formally protected areas (outside Nduli Nature Reserve) of the KSD Local Municipality and their response to measured environmental variables. Using transect survey methods, 516 butterfly individuals belonging to 22 species were caught from 16 sampling units. Species dominance curves showed more butterfly species evenness outside reserve sites than inside. Hierarchical clustering using Bray-Curtis similarity matrices and Correspondence analysis (CA) grouped sampling units according to butterfly species sampled. Site habitat patches outside the reserve were richer in butterfly and overall abundance than inside the reserve. The Canonical Correspondence analysis (CCA) results revealed that certain site variables such as percentage herb cover, area of patch size, average grass height, grazing intensity, distance to the city centre and average flower density accounted for species distribution patterns at various sampling units. The conservation implications of the study suggest that patch level management of micro-habitats with sufficient flowering herbs, structural vegetation, and patch size with minimal disturbance within and outside reserve areas can encourage rare and common butterfly species richness and diversity.
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- Date Issued: 2011