Research Publications (Applied Sciences)
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Item Development of the RCUSP model for the purpose of improving the curriculum evaluation(Green Publication, 2024) Mazibuko, Godfrey Nkululeko; Maharaj, AneshkumarThe current study presents the development of the new curriculum evaluation model, that resulted from improving the previously developed model called Susceptible-vaccinated-healthy-infected-recovered (SVHIR) model. The previous model was presented as an exploratory study, which means it was a study open for improvement. In the new model the compartments categorization would more relevant to the context of teaching and learning than of the previous model, since it does not categorize students who lack High order thinking skilled (HOTS) as being sick. Also, the basic mathematical details that were omitted in the previous model, are now included to enable a better model understanding by a reader. Further on, the current study elaborates the importance of the evaluation model and some parameters such as reproductive ratio. It is also discovered that the newly developed model is not limited only to HOTS, but is open a wider range of curriculums and skills. Lastly, the new model is found to be simpler than the previous model, given it has less compartments to be predicted. Hence, it is more accessible to any reader for better understanding and application.Item On AI-iteration process for finding fixed points of enriched contraction and enriched nonexpansive mappings with application to fractional BVPs(SCIK Publishing Corporation, 2024) Oboyi, J.; Orim, R. E.; Ofem, A. E.; Maharaj, A.; Narain, O. K.In this article, we consider the AI-iteration process for approximating the fixed points of enriched contraction and enriched nonexpansive mappings. Firstly, we prove the strong convergence of the AI-iteration process to the fixed points of enriched contraction mappings. Furthermore, we present a numerical experiment to demonstrate the efficiency of the AI-iterative method over some existing methods. Secondly, we establish the weak and strong convergence results of AI-iteration method for enriched nonexpansive mappings in uniformly convex Banach spaces. Thirdly, the stability analysis results of the considered method is presented. Finally, we apply our results to the solution of fractional boundary value problems in Banach spacesItem A new relaxed inertial Ishikawa-type algorithm for solving fixed points problems with applications to convex optimization problems(SCIK Publishing Corporation, 2024) Orim, R. E.; Ofem, A. E.; Maharaj, A.; Narain, O. K.In this research, we present a new relaxed intertial algorithm without viscosity for solving common solution of countable family of nonexpansive mappings in real Hilbert spaces. We obtain the strong convergence results of the proposed method under some wild conditions on the control parameters. Weapply our main results to solve convex bilevel optimization problems. Finally, we present a numerical example to illustrate the efficiency of our method over some existing methods in the literature.Item Survival analysis of patients with multidrug-resistant tuberculosis in KwaZulu-Natal, South Africa : a comparison of cox regression and parametric models(Common Ground Research Networks, 2024-06-21) Mbona, Sizwe Vincent; Mwambi, Henry; Ramroop, Shaun; Chifurira, RetiusResearchers in medical sciences often prefer the Cox semi-parametric model instead of parametric models because of its restrictive distributional assumptions, but under certain circumstances, parametric models estimate the parameters more efficiently and powerful than the Cox model. The objective of this study was to compare the Cox and parametric models by studying a dataset of patients diagnosed with multidrug-resistant tuberculosis (MDR-TB). A total of 1 542 patients were included in the study from four decentralised sites located in rural areas and one centralised hospital in KwaZulu-Natal, South Africa from 1 July 2008 to 30 July 2012. Out of 1 542 patients with MDR-TB, 886 (57.5%) were cured and 245 (15.9%) died. According to the AIC, the Lognormal and Weibull regression models were the best fitting to data and the Cox regression model was the weakest. According to the results from parametric models, baseline weight of patients had an increased risk of death in both univariate and multivariate analysis. Patients with ages 31 – 40, 41 - 50 and >50 years at diagnosis had an increased risk for death in Cox proportional hazards model. In univariate analysis the data strongly supported the Lognormal regression among parametric models, while in multivariate analysis Weibull and Lognormal are approximately similar, according to Akaike Information Criterion. Although it seems that there may not be a single model that is substantially better than others, Lognormal is the most favorable as an alternative to Cox for identifying risk factors for patients with MDR-TB.Item An inertial iterative method for solving split monotone inclusion problems in Hilbert spaces(American Institute of Mathematical Sciences (AIMS), 2024) Mebawondu, Akindele Adebayo; Sunday, Akunna Sunsan; Narain, Ojen Kumar; Maharaj, AdhirThe purpose of this work is to introduce and study a new type of a relaxed extrapolation iterative method for approximating the solution of a split monotone inclusion problem in the framework of Hilbert spaces. More so, we establish a strong convergence theorem of the proposed iterative method under the assumption that the set-valued operator is maximal monotone and the single-valued operator is Lipschitz continuous monotone which is weaker assumption unlike other methods in which the single-valued is inverse strongly monotone. We emphasize that the value of the Lipschitz constant is not re- quired for the iterative technique to be implemented, and during computation, the Lipschitz continuity was not used. Lastly, we present an application and also some numerical experiments to show the e ciency and the applicability of our proposed iterative method.Item A new fixed point approximation method for solving third-order BVPs based on Green's function(SCIK Publishing Corporation, 2024) Orim, R. E.; Udo, M. O.; Maharaj, A.; Narain, O. K.This study presents an interesting method based on Picard-Ishikwa fixed point iterative method to solve nonlinear third-order boundary value problems. We develop a sequence called Picrad-Ishikawa Green’s iterativeItem An inertial Tseng algorithm for solving quasimonotone variational inequality and fixed point problem in Hilbert spaces(Kyungnam University Press, 2024-02) Kajola, Shamsudeen Abiodun; Narain, Ojen Kumar; Maharaj, AdhirIn this paper, we propose an inertial method for solving a common solution to fixed point and Variational Inequality Problem in Hilbert spaces. Under some standard and suitable assumptions on the control parameters, we prove that the sequence generated by the proposed algorithm converges strongly to an element in the solution set of Variational Inequality Problem associated with a quasimonotone operator which is also solution to a fixed point problem for a demimetric mapping. Finally, we give some numerical experiments for supporting our main results and also compare with some earlier announced methods in the literature.Item The performances of the Cox, Andersen-Gill, Prentice- Williams-Peterson-total time and Wei-Lin-Weissfeld- total-time models in Identifying risk factors in patients with recurrent diseases : a kidney infections example(2024-07-19) Mbona, Sizwe Vincent; Ananth, Anisha; Mzamane, Tsepang Patrick; Ndlovu, Bonginkosi, DuncanIn many longitudinal studies, when subjects are followed over a period of time, recurrent event frequently occur. However, some analysis focusses only on time to the first event, ignoring the subsequent events. The main objective of this paper was to compare the extended standard Cox models, such as Andersen-Gill (AG), Prentice-Williams-Peterson total time (PWP-TT), PWP-Gap time model, Wei Lin-Weissfeld total time (WLW-TT), and Cox frailty model, to identify risk factors associated with kidney re-infection. Empirical evaluation and comparison of these different models were performed. The better model was assessed based on the goodness of fit criteria (AIC, BIC and likelihood ratio test). Kidney data that was downloaded from the R statistical software using the command data(“kidney”) was used to perform analyses in this study. The PWP-TT model had lower standard errors, AIC and BIC values compared to other models, therefore fitted data better and was used to interpret results. The results showed that 81% (HR = 0.19; 95% CI: 0.09-0.39) of the female patients were less likely to experience kidney reinfection than male patients. The risk of recurrent kidney infection was significantly high (HR = 2.32; 95% CI: 1.25-4.29) to patients having an Acute Neptiritis (AN) disease compared to patients with other diseases. While the prevalence of kidney infection remains the public health problem, intervention strategies and awareness campaigned are needed to in order to minimize risk factors behind the recurrent of the disease.Item A metagenomic investigation of the faecal RNA virome structure of asymptomatic chickens obtained from a commercial farm in Durban, KwaZulu-Natal province, South Africa.(Springer Science and Business Media LLC, 2024-06) Nwokorogu, Vivian C.; Pillai, Santhosh; San, James E.; Pillay, Charlene; Nyaga, Martin M.; Sabiu, SaheedVirome studies on birds, including chickens are relatively scarce, particularly from the African continent. Despite the continuous evolution of RNA viruses and severe losses recorded in poultry from seasonal viral outbreaks, the information on RNA virome composition is even scantier as a result of their highly unstable nature, genetic diversity, and difficulties associated with characterization. Also, information on factors that may modulate the occurrence of some viruses in birds is limited, particularly for domesticated birds. Viral metagenomics through advancements in sequencing technologies, has enabled the characterization of the entire virome of diverse host species using various samples.Methods
The complex RNA viral constituents present in 27 faecal samples of asymptomatic chickens from a South African farm collected at 3-time points from two independent seasons were determined, and the impact of the chicken's age and collection season on viral abundance and diversity was further investigated. The study utilized the non-invasive faecal sampling method, mRNA viral targeted enrichment steps, a whole transcriptome amplification strategy, Illumina sequencing, and bioinformatics tools.Results
The results obtained revealed a total of 48 viral species spanning across 11 orders, 15 families and 21 genera. Viral RNA families such as Coronaviridae, Picornaviridae, Reoviridae, Astroviridae, Caliciviridae, Picorbirnaviridae and Retroviridae were abundant, among which picornaviruses, demonstrated a 100% prevalence across the three age groups (2, 4 and 7 weeks) and two seasons (summer and winter) of the 27 faecal samples investigated. A further probe into the extent of variation between the different chicken groups investigated indicated that viral diversity and abundance were significantly influenced by age (P = 0.01099) and season (P = 0.00099) between chicken groups, while there was no effect on viral shedding within samples in a group (alpha diversity) for age (P = 0.146) and season (P = 0.242).Conclusion
The presence of an exceedingly varied chicken RNA virome, encompassing avian, mammalian, fungal, and dietary-associated viruses, underscores the complexities inherent in comprehending the causation, dynamics, and interspecies transmission of RNA viruses within the investigated chicken population. Hence, chickens, even in the absence of discernible symptoms, can harbour viruses that may exhibit opportunistic, commensal, or pathogenic characteristics.Item Junction conditions for composite matter in higher dimensions(IOP Publishing, 2021-10-07) Maharaj, Sunil D.; Brassel, Byron P.We derive the junction conditions for a general higher dimensional spherically symmetric radiating star across a comoving surface with an electromagnetic field. The charged composite interior consists of barotropic matter, a null dust and a null string fluid. The higher dimensional generalised Vaidya geometry describes the exterior radiating atmosphere of the charged composite star. We show at the stellar surface that the pressure is determined by the interior heat flux, anisotropy, null string density, charge distribution and the exterior null string density. The charge distribution affects the stellar pressure in general; the higher dimensional charged Vaidya spacetime is special and does not exhibit this feature. The number of dimensions appears explicitly in the surface pressure showing that the dimensions affect the gravitational dynamics. All previous treatments, for matter which is neutral or charged, emerge as special cases in our treatment.