https://ir.unisa.ac.za/handle/10500/2736 2026-05-08T19:50:27Z https://ir.unisa.ac.za/handle/10500/32304 Compartmental model for the spread of infectious disease with hererogenous population: a case study of COVID-19 and Lassa fever Oluwagunwa, Abiodun Peter This study investigates the transmission dynamics of COVID-19 and Lassa fever, with particular attention to the risks and implications of co-infection. By dividing the human population into epidemiological compartments, the models capture the real course of disease spread in a structured and realistic way. The mathematical correctness of the models was validated by proving positivity, boundedness, and reliability of solutions for public health interpretation. For COVID-19, the basic SYR framework was analysed to obtain the reproduction number RY , and the model was further extended to an SEAIHR structure to include exposed, asymptomatic, infectious, and hospitalised individuals. For Lassa fever, a deterministic compartmental model was developed and subjected to stability analysis. Numerical simulations were carried out for both diseases to assess intervention strategies and transmission behaviour. The COVID–19 analysis revealed that the disease can be eliminated when RY < 1, but once RY > 1, infection becomes persistent. The extended SEAIHR model also produced the overall reproduction number R0, showing how reductions in contact rates, timely detection, effective hospital care, and faster recovery can substantially suppress transmission. For Lassa fever, the disease-free equilibrium remained stable only when the reproduction number was kept below one. Simulations highlighted the significant influence of asymptomatic carriers and showed that no single intervention— whether treatment, health education, or rodent control—can fully control the disease on its own. Instead, the most meaningful reduction in cases occurred when human-focused measures were combined with strong rodent control, leading to the elimination of infectious rodents by the 35th day. Together, these results emphasise the urgency of studying co-infections in regions such as West Africa, where both diseases circulate at the same time. Incorporating optimal control theory provides a systematic and cost-effective framework for coordinating interventions across multiple pathways of transmission. This study therefore deepens our understanding of the dynamics of both COVID– 19 and Lassa fever and offers practical insights for improving interventions, epivdemic preparedness, and public health responses. The centre-manifold analysis further shows that both models experience a forward transcritical bifurcation at R0 = 1: once transmission exceeds this threshold, a stable endemic state emerges. This reinforces a critical message—maintaining transmission below the threshold is essential for preventing long-term persistence of either disease. 2015-10-01T00:00:00Z https://ir.unisa.ac.za/handle/10500/32292 Analysis of the monthly loadshedding and unplanned power outages in South Africa: mean and quantile regression count time series models Tshuma, Sikhulile Various nations within sub-Saharan Africa are currently facing different stages of loadshedding, with South Africa being of no exception to this trend. Loadshedding has been implemented as a strategy to manage electricity consumption during peak demand periods while allowing for increased usage during off-peak times. This study examines the monthly trends of loadshedding and unplanned power outages in South Africa, utilizing mean and quantile regression count time series models. Unplanned outages can arise from multiple factors, including maintenance activities on power lines, equipment malfunctions, adverse weather events, cable theft or emergencies such as accidents. Recurrent outages impede business activities, leading to a decrease in productivity and an increase in operational expenditures. Given the profound impact of power interruptions on economic stability and social welfare, this research aims to quantify and analyze the temporal trends and seasonal patterns of outages. By leveraging a comprehensive dataset, we first apply Poisson and negative binomial regression models to assess the average frequency and duration of outages, revealing significant trends and seasonal fluctuations. Following this, we employ quantile regression techniques to explore the distributional impacts of various factors, including socioeconomic variables and weather conditions, on the occurrence of outages. The analysis considers five quantiles—10th, 25th, 50th, 75th, and 90th. While negative binomial regression adequately captures average loadshedding dynamics, quantile regression proves superior in modelling extreme outage conditions that are most relevant for electricity system risk management and policy planning. The data was diagnosed to be highly correlated. Therefore penalised models were also employed. Our findings indicate that an increase in contracted demand, along with both planned and unplanned outages, correlates with a rise in the frequency of loadshedding. This suggests that loadshedding is influenced not only by heightened demand but also by failures in generation and distribution infrastructure. The thorough methodology adopted in this research deepens our understanding of the challenges surrounding power supply in South Africa, offering critical insights for policymakers and stakeholders to formulate targeted strategies aimed at mitigating the effects of loadshedding and enhancing energy resilience. Tackling these challenges necessitates substantial investment in infrastructure, a diversification of energy sources, and enhanced management of the electricity supply chain. 2025-12-31T00:00:00Z https://ir.unisa.ac.za/handle/10500/32266 Density functional theory study of oxygen reduction reaction (ORR) products with graphene Matloga, Mahlatse The 2D crystal lattice graphene has attracted tremendous research interest due to its exceptional properties that provide interesting opportunities for many applications, including energy storage technologies. Graphene has revealed remarkable potential in electrochemical energy capacity and conversion, particularly in rechargeable metal-air batteries. However currently metal air batteries (MABs) are faced with challenges such as anode issues (corrosion, dendrite formation at the metal anode and passivation) [1]. In this study, first-principle density functional theory was employed to investigate reaction mechanisms between graphene and oxygen reduction reaction (ORR) products XxOy, where X= Li, Na, Mg and K with x,y = 1 or 2, specifically for energy storage application of the 2D graphene in an effort to address the energy crisis. The reaction mechanisms of a single atom-, double atom-, and molecules (XO-, X2O-,XO2- and X2O2-) adsorbed onto graphene was investigated. For single-atom adsorption, the three adsorption sites, i.e., top, hollow and bridge sites were considered. The calculated adsorption energies revealed that single Li atom adsorbs stronger on graphene than all the alkaline metals and oxygen, with the hollow site being the most preferred site. For double atom adsorption, the calculated adsorption energies revealed that Na2 has a strong interaction with graphene layer and as a result the hollow site being the most preferred adsorption site. Furthermore, the order of stability was found to be Na2 >K2 > Li2 > O2 > Mg2. The ORR product NaO2 was found to be the most favoured reaction product with a calculated adsorption energy of -4.209 eV, followed by KO2 with the adsorption energy of -2.808 eV The results show a stronger interaction between oxygen atom and carbon atoms, which could potentially suggest a formation of C-O bond. In addition, the study revealed that adsorbates molecules move away from graphene layer together with two neighboring carbon atoms (possibly forming CO, CO2, LiCO3, NaCO2, KCO3 and MgCO3). The electronic properties of all the systems predicted metallic behaviour along the Fermi level due to no energy band gap between the valence and conduction bands. Thus, the electronic properties of XO-, X2O-,XO2-and X2O2- adsorbed graphene systems indicated that the typical electronic model of pristine graphene remains a conductor even after adsorption. Overall Na atom adsorption as a double and reaction product was the most stable system when adsorbed onto graphene implying that graphene could be considered as a better alternative anode electrode for sodium batteries, particularly sodium air batteries (SIBs) 2025-12-01T00:00:00Z https://ir.unisa.ac.za/handle/10500/32243 Lie group analysis and conserved vectors of multidimensional nonlinear Partial differential equations Sebogodi, Motshidisi Charity This thesis studies the applications of Lie group analysis and conserved vectors to multi-dimensional nonlinear partial differential equations. Exact solutions and conservation laws are obtained for such equations. The equations which are considered in this thesis are the generalized Chaffee-Infante equation in (3+1) dimensions, the (2+1)-dimensional combined potential Kadomtsev-Petviashvili-b-type Kadomtsev- Petviashvili equation and a generalized (2+1)-dimensional generalized Korteweg-de Vries equation. The generalized Chaffee-Infante equation with power-law nonlinearity in (3+1) dimensions is analyzed. Ansatz methods are utilized to provide topological and nontopological soliton solutions of this equation. Soliton solutions to nonlinear evolution equations have several practical applications in many areas of mathematical physics such as plasma physics and diffusion process. It will be shown that for certain values of the parameters, the power-law nonlinearity Chaffee-Infante equation permits soliton solutions. The requirements and restrictions for existence of soliton solutions are mentioned. Conservation laws are derived for the aforementioned equation. The Lie symmetry method investigates a (2+1)-dimensional combined potential Kadomtsev-Petviashvili-b-type Kadomtsev-Petviashvili equation. Symmetry reduction is performed and group invariant solutions are obtained. Furthermore, the multiplier method is employed to derive conservation laws for a (2+1)-dimensional combined potential Kadomtsev-Petviashvili-b-type Kadomtsev-Petviashvili equation. Finally a generalized nonlinear (2+1)-dimensional equation is investigated from the view point of symmetry analysis in conjunction with ansatz methods and multipleexp function method. Moreover, conservation laws based on the multiplier approach will be investigated. Abstract and text in English 2025-12-01T00:00:00Z