Department of Mathematics and Statistics

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Browsing Department of Mathematics and Statistics by Author "Ndlovu, Meshach"

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    Assessing biological control method on the progression of anaplasmosis disease in dominant cattle species in the Matabeleland north province Zimbabwe
    (arXiv, 2024-04-24) Ndlovu, Meshach
    This paper presents a compartmental (SI) model for the transmission dynamics of Anaplasmosis in resource limited farmer’s cattle subjected to a biological control method. The study seeks to evaluate the stability and control of cattle herds dynamics relative to finite agitation. Anaplasmosis disease pose a major threat in eradicating cattle population growth in resources limited communities. In gaining the insight of the disease, the following model analysis strategies were used in order to compute simulations, analysis of the model upon varying initial predator population and testing the effects of different predation rate on the disease dynamics. It is essential that the progression of Anaplasmosis be stable after the introduction of tick predators into cattle-tick system because that provides the usability of predation as a control measure. After analysing the effect of different prediction rates on the spread of the disease in resource limited communities the study asserted that tick predators like birds and bacteria have been neglected as contributors to natural mechanism of Anaplasmosis. Furthermore, the study brought to light that predictors have been neglected as major contributors to natural control mechanism of Anaplasmosis in Zimbabwe. Additional numerical simulations showed that predation method can be used in the eradication of Anaplasmosis disease thus improving rural livelihood. Investigation of natural tick enemies and predation behaviour can lead to better control of the Anaplasmosis disease efficiently and effectively. Finally, we recommend the necessity for resource limited farmers to capitalise on the use of biological disease control measures.
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    Clustering and spatial dynamics of informal trading in Zimbabwe during the COVID-19 pandemic
    (Elsevier B.V, 2025-03-22) Ndlovu, Meshach
    The COVID-19 pandemic led to significant disruptions across various sectors, with Zimbabwe's informal economy being acutely impacted. In response, the Zimbabwean government implemented measures to mitigate the economic challenges faced by informal traders, including the establishment of new trading spaces such as Nkulumane Sekusile in Bulawayo. This study investigates the spatial dynamics, understood as the clustering and grouping of different types of traders within Sekusile market during the pandemic. The research examines how the influx of traders from various regions altered the market's structure and competition. By employing advanced statistical clustering methods—such as hotspot analysis, the K-means algorithm, ordinary kriging, and persistence diagrams—this study provides critical insights into these spatial variations, informing policy recommendations aimed at enhancing the socio-economic resilience of informal traders.
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    Exploring the impact of how criminals interact with cyber-networks—a mathematical modeling approach
    (Taylor & Francis, 2024-01-11) Chikore, Tichaona; Nyirenda-Kayuni, Mwawi; Chukwudum, Queensley C.; Chazuka, Zviiteyi; Mwaonanji, John; Ndlovu, Meshach; Zhangazha, Moster; Mhlabane, Fezile; Osman, Shaibu; Nyabadza, Farai; White, K. A. Jane; Shang, Yilun
    There is a growing interest in using mathematical models to understand crime dynamics, crime pre-vention, and detection. The past decade has experienced a relative reduction in conventional crimes, but this has been replaced by significant increases in cybercrime. In this paper, we use deterministic modelling to describe the spread of cybercrime across a cyber-network by describing the hetero-geneity of interactions between individuals using a nonlinear interaction between individuals in the network, and we allow criminals to operate either internally or externally to the cyber-network. We are able to determine the impact of the location of the criminal relative to the cyber-network which is being attacked. The model structure incorporates key elements of a social network structure thereby allowing for limited rates of victimisation. Both model structure and our observations are novel and provide a new contribution to the theoretical discussion of cybercrime dynamics, offering potential avenues to consider control strategies. Using steady-state analysis and extensive numerical simu-lations, we find that the location of criminals relative to the network does not impact the system qualitatively, although there are quantitative differences. Cyber-networks that are more clustered are likely to experience greater levels of cybercrime, but there is also a saturation effect that limits the level of victimisation as the number of criminals attempting to undertake crimes on given network increases. We discuss model limitations and describe how the model might be used with datasets to translate the theoretical findings into a useful tool in the fight to detect and eradicate cybercrime activity.
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    Nutrition and work efficiency as a strategic variable necessary in a mining environment for high productivity: A case of Filabusi mining community
    (Qeios, 2023-06-09) Ndlovu, Meshach; Zulu, Eldon
    Work has a central role in the lives of big share of mine employees and meals they eat during the workday comprise an important factor in their nutrition, health, and wellbeing. The objective of this study was to examine the contribution of agricultural dimension, vegetable markets enhancing nutrition and work efficiency as a strategic necessity in a mining environment for high productivity during the COVID 19 pandemic. The study employed a Quasi –experiment quantitative research paradigm and a questionnaire was distributed to the mentioned population. Also of note, are the socio-demographic, socio- economic and work-related factors to the eating patterns of 150 mine employees from 6 different mines around Filabusi community during the working day and how their eating patterns influence dietary intake and productivity? The study revealed that, all the variables in the pre-test analysis indicated no significant difference in each of the listed variables between the two groups then the evidence in the post-test analysis point out that the two variables with a significant difference between the two group is strongly as a result of the treatment (eating habits, nutrition and diet) during this COVID-19 pandemic that has led to better emotional strength and improved productivity at work place.
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    Rational homotopy type of projectivization of the tangent bundle of certain spaces
    (Emerald, 2024-08-22) Gastinzi, Jean Baptiste; Ndlovu, Meshach
    Purpose The paper aims to determine the rational homotopy type of the total space of projectivized bundles over complex projective spaces using Sullivan minimal models, providing insights into the algebraic structure of these spaces. Design/methodology/approach The paper utilises techniques from Sullivan’s theory of minimal models to analyse the differential graded algebraic structure of projectivized bundles. It employs algebraic methods to compute the Sullivan minimal model of and establish relationships with the base space. Findings The paper determines the rational homotopy type of projectivized bundles over complex projective spaces. Of great interest is how the Chern classes of the fibre space and base space, play a critical role in determining the Sullivan model of P(E). We also provide the homogeneous space of P(E) when n = 2. Finally, we prove the formality of P(E) over a homogeneous space of equal rank. Research limitations/implications Limitations may include the complexity of computing minimal models for higher-dimensional bundles. Practical implications Understanding the rational homotopy type of projectivized bundles facilitates computations in algebraic topology and differential geometry, potentially aiding in applications such as topological data analysis and geometric modelling. Social implications While the direct social impact may be indirect, advancements in algebraic topology contribute to broader mathematical knowledge, which can underpin developments in science, engineering, and technology with societal benefits. Originality/value The paper’s originality lies in its application of Sullivan minimal models to determine the rational homotopy type of projectivized bundles over complex projective spaces, offering valuable insights into the algebraic structure of these spaces and their associated complex vector bundles.