Browsing by Author "Ngari, Cyrus, G"

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    Decomposition of Riemannian Curvature Tensor Field and Its Properties
    (Science Domain, 2018-11-22) Gicheru, James,G; Ngari, Cyrus, G
    Decomposition of recurrent curvature tensor fields of R-th order in Finsler manifolds has been studied by B. B. Sinha and G. Singh [1] in the publications del’ institute mathematique, nouvelleserie, tome 33 (47), 1983 pg 217-220. Also Surendra Pratap Singh [2] in Kyungpook Math. J. volume 15, number 2 December, 1975 studied decomposition of recurrent curvature tensor fields in generalised Finsler spaces. Sinha and Singh [3] studied decomposition of recurrent curvature tensor fields in a Finsler space. In this paper we study the Riemannian Curvature tensor with its properties its decomposition of the Riemannian curvature tensor and its properties. This raises important question: in Riemannian manifold , is it possible to decompose Riemannian curvature tensor of rank four, get another tensor of rank two and study its properties?
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    A Deterministic Model Of HIV Transmission Between Two Closed Patches Incorporating The Monod Equation
    (IISTE, 2019-11-06) Ngari, Cyrus, G; Mirgichan, James, K; Karanja, Stephen
    Among other factors, migration has significantly contributed to the spread of HIV. Recent studies have revealed that new infections occur along major transport corridors and truck-drivers have overall higher prevalence rates of HIV and sexually transmitted infections than non-truck drivers’ counterparts. Therefore, there exist a link between population mobility and HIV infection, as populations along transport corridors remain substantial contributors of new infections. This research work documents a deterministic model of the dynamics of HIV transmission between two closed patches that incorporates the Monod equation in migration with truck drivers being the agents of HIV transmission. Migration is considered as a social determinant to health and have a significant impact on health‐ related vulnerabilities and access to services. We assumed that susceptible individuals become infected via sexual intercourse with HIV infected truck drivers and all the infected individuals ultimately developed AIDS exponentially. The model also assumed that the patches have different infection and susceptibility rates. The patches basic reproduction number, 𝑅0 was determined using the Next Generation Matrix. The results revealed that 𝑅0 should be kept below unity to eradicate the transmission of the virus. The Disease-Free Equilibrium Point was obtained based on the signs of the Eigen values of the Jacobian matrix. In the absence, the Disease-Free Equilibrium Point is both Locally Asymptotically and Globally Asymptotically Stable. It was further proved that the model did not display Endemic Equilibrium Point under a special property for epidemic models. The model findings are vital in guiding health practitioners, governmental and non-governmental health agencies in the development of effective mitigation strategies to reduce the spread of HIV.
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    Parameters And State Estimates Of Sex Based Covid-19 Model Using Kenya Data, Nonlinear Least Square And Interpolating Polynomials
    (International Journal of Scientific and Research Publications, 2021-05-05) Kitavi, Dominic, M; Ngari, Cyrus, G; Ngari, Paul, M; Muchangi, David, M
    COVID-19 spread in Kenya has been growing at a very high rate in the recent past. According to the Kenya’s ministry of health, the confirmed COVID-19 infections as of 19th July 2020 was 13,353 with recorded 5,122 recoveries and 234 deaths. Based on quarantine data, there is media speculation about COVID-19 manifesting gender dimension, however, no studies have been carried out to establish the gender-based dimension in the community. This paper aimed at: formulating gender based Mathematical model, estimate gender-based disease burden in the community using quarantine data and using estimated parameters and states to predict dynamics of the disease in the quarantine centers. Mathematical compartment model was developed using characteristic and status of disease. Daily number of infectious and exposed in the community was estimated using interpolating polynomials. Nonlinear least square was used to fit observed data in the developed model. Prediction of the initial value problem was carried out using MATLAB inbuilt ode solver. Daily estimate of states in Figures 8 and 9 confirms that COVID-19 is also burdening more males in the community than females. Simulation using MATLAB indicated that the number of individuals who will remain constantly infected after disease induced deaths and recoveries ranges between (567 − 219) and (363 − 116) for males and females respectively. Future studies should focus on Mathematical model analysis and predictions of disease burden in the community.