Meshach Ndlovu | Searcharxiv

arXiv2025

The biquotient model of the total space of the projectivization quaternionic bundles over certain manifolds

In this paper, we compute the rational homotopy type of the quaternionic projective bundle $P(\tau): \mathbb{H}P^{n-1} \rightarrow P(E) \rightarrow M$ obtain from the quaternionic tangent bundle $\tau: \mathbb{H}^{n} \rightarrow E \rightarrow M$ over quaternionic manifold $M$. If the base space $M$ is the quaternionic projective space $\mathbb{H}P^{2}$, then the rational homotopy type of the total space $P(E)$ of the quaternionic projective bundle $P(\tau)$ is given by a biquotient model $Sp(1)\backslash Sp(3) / Sp(1) \times Sp(1)$.

math.AT↗

arXiv2025

A note on the rational homotopy type of the projectivization of the tangent bundle of complex projective spaces

In this paper, we determine the rational homotopy type of the total space of the projectivization of the complex tangent bundle $\tau : \mathbb{C}^n \longrightarrow E \longrightarrow \mathbb{C}P^{n}$. We show that the total space $P(E)$ of the projectivization bundle $P(\tau): \mathbb{C}P^{n-1} \longrightarrow P(E) \longrightarrow \mathbb{C}P^{n}$ has the rational homotopy type of $\mathrm{U}(n+1)/\mathrm{U}(1)\times \mathrm{U}(1)\times \mathrm{U}(n-1)$.

math.AT↗

arXiv2024

Assessing biological control method on the progression of anaplasmosis disease in dominant cattle species in the Matabeleland north province Zimbabwe

This paper presents a compartmental model for the transmission dynamics of Anaplasmosis in resource limited farmers 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.

q-bio.PE↗