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Applied Mathematics

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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.
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    Mathematical modelling of the Ebola virus disease.
    (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.