Doctoral Degrees (Applied Mathematics)

Permanent URI for this collectionhttps://hdl.handle.net/10413/7094

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Diffuse radio emission in ACTPol clusters.
(2021) Sikhosana, Sinenhlanhla Precious.; Moodley, Kavilan.; Knowles, Kenda Leigh.; Hilton, Matthew James.
Low-frequency radio observations of galaxy clusters reveal cluster-scale diffuse emission that is not associated with individual galaxies. Studying the properties of these diffuse radio sources gives insight into astrophysical processes such as cosmic ray transportation in the intracluster medium (ICM). Observations have linked the formation of radio halos and relics with turbulence caused by cluster mergers and the formation of mini-halos to gas sloshing in cool-core clusters. Statistical studies of large galaxy cluster samples have been used to determine how the radio properties of diffuse emission scale with the mass and X-ray luminosity of the host clusters. Such studies are crucial for refining the formation theories of diffuse emission. New generation telescopes with wide bandwidths and high sensitivity such as the upgraded Giant Metrewave Radio Telescope (uGMRT) andMeerKAT are advantageous for the study of faint extended emission in large cluster samples. The main aim of this thesis was to do an in-depth study of the diffuse radio emission using a cluster sample that spans a wider mass and redshift range compared to the currently studied parameter space. We developed data reduction techniques for calibrating data from telescopes such as uGMRT and MeerKAT. The wide bandwidth of these telescopes introduces directional dependent effects (DDEs) that make the calibration process extremely complicated. However, such observations are excellent for studies of the faint diffuse emission and in-band spectral indices of this emission. In the first part of this thesis, we focused on the study of diffuse radio emission in a Sunyaev- Zeldovich (SZ) selected sample of clusters. These clusters were observed by the Atacama Cosmology Telescope’s Polarimetric extension (ACTPol). We used archival and new GMRT observations for the radio analysis of this sample. We reported newly detected diffuse emission in the following clusters: a radio halo and revived fossil plasma in ACT-CL J0137.4 0827, a radio relic in ACT-CL J2128.4+0135, and a candidate relic in ACT-CL J0022.2 0036. The radio analysis of the full sample revealed that the fraction of clusters in the sample hosting diffuse emission is 26.7% excluding candidate emission and 30% when it is included. The detection rate of the diffuse emission over all categories is lower than the detection rates reported in literature. We note that this may be because the sample comprised high redshift (z ¡ 0.5) and low mass clusters (M500c;SZ 5 1014 Md), though future more sensitive observations of these clusters could reveal fainter diffuse emission structures. We compared our results to the most recent radio halo and radio relic scaling relations. The radio halo P1:4GHz M500 scaling relation plot indicates that a few flatter spectrum radio halos are located in the region previously known to be populated by ultrasteep spectrum radio halos (USSRHs). Finally, we presented preliminary results of the uGMRT wideband backend (GWB) data reduction for ACT-CL J0034.4+0225, ACT-CL J0137.4 0827, and ACT-CL J2128.4+0135. We prioritised these clusters because the narrowband data revealed that they host diffuse emission. However, once the data reduction algorithm is improved, we will reduce the remaining clusters with non-detections. Comparing the GWB results to the narrowband GMRT data, we note that the radio halo observed in ACT-CL J0137.4 0827 is more extended in the GWB data. The diffuse emission is detected at a higher signal-to-noise ratio in the GWB images for the three clusters. We note that an improvement in the GWB reduction algorithm might reveal diffuse emission that was not detected in the narrowband data. In the second part of the thesis, we used MeerKAT observations to study diffuse emission in the Bullet Cluster (1E0657 56), RXCJ1314.4 2515, Abell 3562, and Abell 3558. We detected new extended features in the radio halos hosted by the Bullet cluster and Abell 3562. We assume that the decrement feature in the Bullet cluster might be an indication of a second wave of merger activity. The ridge feature in the peripheral region of the radio halo in Abell 3562 overlaps with the edge of the X-ray emission. Hence, we assume that the feature might be related to a shock region. We also reported the detection of a new mini-halo in Abell 3558. MeerKAT’s sensitivity and wide bandwidth enabled us to perform in-band spectral index studies and produce spectral index maps for the Bullet cluster, RXCJ1314.4 2515, and Abell 3562. The spectral index maps of the relics in the Bullet cluster and RXCJ1314.4 2515 indicate a spectral steepening towards the cluster center, while the spectral index map of the radio halo in the Bullet cluster indicates radial spectral steepening. The spectral index map of Abell 3562 indicates that the radio halo and ridge have similar spectral index variations, which suggests that the ridge feature is related to the radio halo.
Mathematical modelling of the Ebola virus disease = I-Model yeziBalo yesifo Segciwane Le-Ebola.
(2024) Abdalla, Suliman Jamiel Mohamed.; Govinder, Keshlan Sathasiva.; Chirove, Faraimunashe.
Despite the numerous modelling efforts to advise public health physicians to understand the dynamics of the Ebola virus disease (EVD) and control its spread, the disease continued to spread in Africa. In the current thesis, we systematically review previous EVD models. Further, we develop novel mathematical models to explore two important problems during the 2018-2020 Kivu outbreak: the impact of geographically targeted vaccinations (GTVs) and the interplay between the attacks on Ebola treatment centres (ETCs) and the spread of EVD. In our systematic review, we identify many limitations in the modelling literature and provide brief suggestions for future work. Our modelling findings underscore the importance of considering GTVs in areas with high infections. In particular, we find that implementing GTVs in regions with high infections so that the total vaccinations are increased by 60% decreases the cumulative cases by 15%. On the other hand, we need to increase the vaccinations to more than 1000% to achieve the 15% decrease in EVD cases if we implement GTVs in areas with low infections. On the impact of the attacks on ETCs, we find that due to the attacks on ETCs, the cumulative cases increased by more than 17% during the 2018-2020 Kivu outbreak. We also find that when 10% of the hospitalised individuals flee the attacks on ETCs after spending only three days under treatment, the cumulative cases increased by more than 30% even if these individuals all returned to the ETCs three days later. On the other hand, if only half of these individuals returned to ETCs for treatment, the cumulative cases increase by approximately 50%. Further, when these patients spend one more day in the community, after which they all return to ETCs, the cumulative cases rise by an additional 10%. Global sensitivity analysis also confirmed these findings. To conclude, our literature systematic review is used to identify many critical factors which were overlooked in previous EVD models. Our modelling findings show that the attacks on ETCs can be destructive to the efforts of EVD response teams. Hence, it is important for decision-makers to tackle the reasons for community distrust and address the roots of the hostility towards ETCs. We also find that GTVs can be used to contain the spread of EVD when ring vaccinations, contact tracing and antiviral treatments cannot successfully control the spread of EVD. Iqoqa. Naphezu kwemizamo eminingi yokumodela okuhloswe ngayo ukweluleka izikhulu zezempilo zomphakathi ukuthi ziqonde amandla egciwane lesifo se-Ebola (EVD) futhi zilawule ukusakazeka kwaso, lesi sifo saqhubeka nokusabalala e-Afrikha. Kulo mbhalo weziqu zobudokotela, sibuyekeza ngokuhlelekile amamodeli angaphambilini e-EVD futhi sithuthukise amamodeli ezibalo amasha ukuze sihlole izinkinga ezimbili ezibalulekile ngesikhathi sokubheduka kwesifo eKivu ngonyaka wezi-2018-2020: umthelela wemigomo eqondiswe ngokwendawo (GTVs) kanye nokuhlangana phakathi kokuhlaselwa kwezindawo ezelapha i-Ebola (ETCs) kanye ukusabalala kwe-EVD. Ukubuyekeza kwethu okuhlelekile kuveza imikhawulo embalwa ezincwadini zokumodela ezikhona futhi kunikeza iziphakamiso zomsebenzi wesikhathi esizayo. Okutholakele kugcizelela ukubaluleka kokucabangela ama-GTV ezindaweni ezinamazinga aphezulu okutheleleka. Ngokukhethekile, sithola ukuthi ukusebenzisa ama-GTV ezifundeni ezinamazinga aphezulu okutheleleka—njengokuthi isamba sokugoma sikhuphuke ngo-60%—kwehlisa isibalo sezifo ngo-15%. Ngokuphambene, imigomo idinga ukukhuphuka ngaphezu kuka-1000% ukuze kuzuzwe ukwehla okungu-15% ezimweni ze-EVD uma ama-GTV esetshenziswa ezindaweni ezinamazinga aphansi okutheleleka. Mayelana nomthelela wokuhlaselwa kwama-ETC, sithola ukuthi lokhu kuhlasela kwenyuse amacala anqwabelene ngaphezu kuka-17% ngesikhathi sokubheduka kwesifo e-Kivu ngo-2018-2020. Ukwengeza, lapho u-10% wabantu abasesibhedlela bebalekela ukuhlaselwa kwama-ETC ngemva kokuchitha izinsuku ezintathu kuphela belashwa, amacala anqwabelene akhuphuka ngaphezu kuka-30%, ngisho noma laba bantu bebuyela kuma-ETC ezinsukwini ezintathu kamuva. Uma ngabe uhhafu walaba bantu ubuyela kuma-ETC ukuze bathole ukwelashwa, izimo ezikhulayo zikhuphuka cishe ngo-50%. Ngaphezu kwalokho, lapho lezi ziguli zichitha usuku olulodwa ngaphezulu emphakathini, ngemva kwalokho zonke zibuyela kuma-ETC, amacala akhulayo akhuphuka ngo-10%. Ukuphetha, ukubuyekezwa kwezincwadi zethu kukhomba izici ezimbalwa ezibalulekile ezinganakwa kumamodeli angaphambilini e-EVD. Okutholakele kokumodela kwethu kubonisa ukuthi ukuhlaselwa kwama-ETC kungakhinyabeza kakhulu imizamo yamaqembu okuphendula e-EVD. Ngakho-ke, kubalulekile ukuthi abenzi bezinqumo babhekane nezizathu zokungathembeki komphakathi kanye nezimpande zobutha kuma-ETC. Ngaphezu kwalokho, sithola ukuthi ama-GTV angaqukatha ngempumelelo ukusabalala kwe-EVD lapho ukugonywa okuzungezile, ukulandelelwa kokuthintana, kanye nokwelashwa ngezidambisigciwane kunganele ukulawula ukusabalala kwesifo.
Modeling the effectiveness of control measures from the within-host dynamics to the population dynamics of sleeping sickness.
(2024) Mulalo, Makhuvha.; Mambili-Mamboundou, Hermane.
This study addresses the persistent health challenge of sleeping sickness in sub-Saharan Africa by comprehensively exploring its transmission dynamics. The primary focus is on developing, studying, and analyzing mathematical models spanning from within-host dynamics to multiscale interactions of sleeping sickness. The thesis begins by investigating the dynamics within a single sleeping sickness-infected human host. The model considers the interplay between parasite types, macrophages, and cytokines within the human host. Findings suggest that the immune response play a pivotal part in regulating parasite growth, and the absence of switching enables effective immune system intervention. Two distinct optimal control problems emerge, emphasizing the need to identify the disease stage for effective drug application, thereby preventing parasite persistence and reducing drug toxicity. The study’s second phase focuses on developing an epidemiological model of sleeping sickness transmission among humans, non-human hosts, and tsetse flies. Sensitivity analysis reveals that parameters such as biting rate and death rate are particularly influential. The examination of bifurcation concerning the effective reproductive number (Re) indicates the presence of a backward bifurcation within the system which signifies that the traditional condition of Re < 1 is no longer adequate for achieving effective disease elimination. Disease dynamics are strongly scale dependent, so we propose a multi-temporal scale model that incorporates within-host and between-host disease dynamics. Results are compared with the single-scaled models. Furthermore, the numerical solutions for susceptible humans in both the between-host and multiscale models demonstrated a similar pattern: a rapid reduction in susceptible human populations within the first 50 days in the absence of intervention. The vector profiles in both the multiscale and between-host models showed similar trends, with intervention initially applied at maximum intensity and rapidly reduced within the first 50 days of use. However, a notable distinction arose regarding treatment profiles: whereas within-host results indicated that drugs needed to be administered at maximum dosage to reduce the burden of infection effectively, the opposite was observed in the between-host model. In conclusion, this thesis offers valuable insights into the disease transmission dynamics of sleeping sickness, highlighting the significance of comprehending both within host and between-host interactions. Essentially, our models proved to be more mathematically, numerically, and biologically tractable compared to most standard models used for projecting sleeping sickness.
Overlapping grid spectral collocation methods for solving unsteady MHD nanofluid flow over stretching surfaces.
(2024) Jamiu, Folarin Oluwaseun.; Goqo, Sicelo Praisegod.; Mondal, Hiranmoy.
This study comprehensively explores diverse magneto-hydrodynamic (MHD) nanofluid flow phenomena over various stretching surfaces with distinctive physical and mathematical attributes. Firstly, we investigated the entropy generation of an unsteady MHD nanofluid flow over a porous inclined stretching surface, incorporating velocity slip and viscous dissipation. Then, the solution methodology utilizing spectral quasilinearization method (SQLM) on overlapping grids for analyzing electromagnetic MHD tangent hyperbolic nanofluid flow over an inclined stretchable Riga surface was considered. This study considers the Dufour effect, activation energy, and heat generation, enriching the understanding of complex fluid dynamics. Next, we explored the unsteady squeezing flow and heat transport involving silicon SiO2/kerosene oil nanofluid around radially stretchable parallel rotating disks. Particularly, the upper disk oscillates, adding an extra layer of dynamism to the system that develops a negative pressure situation, which has vast applications in modern-day engineering and medical sciences. Moving on, we employed the bivariate simple iteration method on overlapping grids to analyze unsteady ternary hybrid nanofluid flow with a magnetic dipole over an oscillatory stretching surface. This investigation offers insights into the intricate interplay of magnetic effects and oscillatory stretching, contributing to the broader field of magnetohydrodynamics. Lastly, the thesis explores the numerical analysis of unsteady Casson ternary hybrid nanofluid flow over a bidirectionally stretching sheet. This study incorporates motile gyrotactic microorganisms and nanoparticle shape factors. This collective body of work contributes to the fundamental understanding of nanofluid dynamics and showcases the versatility of numerical methods in solving complex fluid flow problems across diverse geometries. The findings presented in this thesis pave the way for future advancements in nanofluid research and hold significant implications for various engineering applications. Overall, the inclusion of overlapping grids in the regular SQLM, BSIM and BSQLM greatly improve their performances in terms of accuracy, computational efficiency, robustness, and ability to effectively tackle complex fluid flow problems.

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Browsing Doctoral Degrees (Applied Mathematics) by SDG "SDG4"