SIMs Scholarly Articles
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- ItemA copula-based approach to differential gene expression analysisChaba, Linda Akoth; Odhiambo, John W.; Omolo, BernardMelanoma is a major public health concern in the developed world. Melanoma research has been enhanced by the introduction of microarray technology, whose main aim is to identify genes that are associated with outcomes of interest in melanoma biology and disease progression. Many statistical methods have been proposed for gene selection but so far none of them is regarded as the standard method. In addition, none of the proposed methods have applied copulas to identify genes that are associated with quantitative traits. In this study, we developed a copula-based approach to identify genes that are associated with quantitative traits in the systems biology of melanoma. To assess the statistical properties of model , we evaluated the power, the false-rejection rate and the true-rejection rate using simulated gene expression data . The model was then applied to a melanoma dataset for validation. Comparison of the copula approach with the Bayesian and other parametric approaches was performed, based on the false discovery rate (FOR) , the value of R-square and prognostic properties. It turned out that the copula model was more robust and better than the others in the selection of genes that were biologically and clinically significant.
- ItemA Mathematical model for bovine brucellosis incorporating contaminated environmentRobert, Godwin; Julius, Tumwiine
- ItemA smooth test of goodness-of-fit for the baseline hazard function in recurrent event modelsOdhiambo, John W.; Odhiambo, Collins; Omolo, BernardIn this paper, we formulate a smooth test of goodness-of-fit for a simple hypothesis about the baseline hazard function in recurrent-event models. The formulation is an extension of Neyman' s goodness-of-fit approach, whose score tests are obtained by embedding the null hypothesis in a larger class of hazard rate functions. Since the application is in recurrent event models , the data is dynamic.A useful feature about this test is the parametric approach that makes inference about the hazard function more efficient. To examine the finite-sample properties of this test, we used simulated data . For validation, we applied the test to a real-life recurrent event data. Results show that the test possesses better power over wide range of alternatives, when compared with similar tests of the chi-square type in the literature.
- ItemLaguerre Polynomials and singular differential operators(Indian Journal of Pure and Applied Mathematics, ) Onyango-Otieno., VitalisThis paper is concerned with the connections between the orthogonal polynomials and the differential operators generated by the Laguerre differential equation of Ten in the space L' (0, w ). However, for the left definite case, a suitably w determined resolvent function Q is used to define a bounded self-adjoint operator A, whose inverse is the required self-adjoint “differential” operator 5m in the space H 2M1 (0, 00). In both cases the spectra of Tat and Sm are shown to be discrete and the corresponding eigenvectors turn out to be the orthogonal polynomials of Laguerre. These results provide an alternative proof of the completeness of the Laguerre polynomials in the spaces L‘: (0,00) and ).
- ItemManaging chronic conditions through hosted medical records in KenyaMbogo, Rachel Waema; Mbogo, SalesioComplex medical conditions are rising in developing countries at very alarming rates. E.g. projections from the World Health Organization’s global burden of disease and risk factors report chronic diseases are responsible for up to 50% of disease burden in selected countries. Diseases hitherto associated with the developed countries like diabetes, cancer and Hypertension are in the increase in developing countries. Management of these medical conditions calls for a new way of delivering health care services in these countries. Long term therapeutic management of these diseases requires availability of medical records to a provider when a patient presents him/herself at a medical facility. Advances in technology present opportunities for informing systematic management of these chronic conditions within constraints of resources that these countries face.
- ItemMathematical model for HIV and CD4+ cells dynamics in vivo(IJAPM, ) Mbogo, Rachel Waema; Luboobi, Livingstone S.; Odhiambo, John W.Mathematical models are used to provide insights into the mechanisms and dynamics of the progression of viral infection in vivo. Untangling the dynamics between HIV and CD4+ cellular populations and molecular interactions can be used to investigate the effective points of interventions in the HIV life cycle. With that in mind, we develop and analyze a stochastic model for In-Host HIV dynamics that includes combined therapeutic treatment and intracellular delay between the infection of a cell and the emission of viral particles. The unique feature is that both therapy and the intracellular delay are incorporated into the model. We show the usefulness of our stochastic approach towards modeling combined HIV treatment by obtaining probability generating function, the moment structures of the healthy CD4+ cell, and the virus particles at any time t and the probability of virus clearance. Our analysis show that, when it is assumed that the drug is not completely effective, as is the case of HIV in vivo, the predicted rate of decline in plasma HIV virus concentration depends on three factors: the initial viral load before therapeutic intervention, the efficacy of therapy and the length of the intracellular delay.
- ItemMathematical Modeling for Human Immunodeficiency Virus (HIV) Transmission using Generating Function Approach(Strathmore university, 2009) Waema, Rachel; Olowofeso, OlorunsolaThis study is concerned with the mathematical modeling for human immunodeficiency virus (HIV) transmission epidemics. The mathematical models are specified by stochastic differential equations that are solved by use of Generating Functions (GF). Models based on Mother to child transmission (MTCT) (age group 0-5 years), Heterosexual transmission (age group 15 and more years) and combined case (incorporating all groups and the two modes of transmission) were developed and the expectations and variances of Susceptible (S) persons, Infected (I) persons and AIDS cases were found. The S$_{1}$(t) Susceptible model produces a constant expectation and increasing variance. It was shown that Mother to Child transimission and Heterosexual models are special cases of the Combined model.
- ItemMaximal rank for ΩPn(International Mathematical Forum, ) Maingi, Damian; Dieudonne, Laboratoir´e J. A.
- ItemModel-Assisted Estimation of Finite Population Mean in Two-stage Cluster SamplingBii, Nelson Kiprono; Onyango, Christopher OumaEstimation of finite population parameters has been an area of concern to statisticians for decades. This paper presents an estimation of the population mean under a model-assisted approach.Dorfman (1992), Breidt and Opsomer (2000) and Ouma et al(2010) carried out theestimation of finite population total on the assumption that the sample size is large and the sampling distribution is approximately normal. Unlike their researches, this paper considered a case when the sample size is small under a model-assisted approach. A model-assisted regression model was considered in a case where the cluster sizes are known only for the sampled clusters in order to predict the unobserved part of the population mean. Under mild assumptions, the proposed estimator is asymptotically unbiased and its conditional error variance tends to zero. Simulation studies show that model assisted estimation performs better than model based estimation of a finite population mean in a case where the sample size is small.
- ItemOn the Minimal Resolution Conjecture for P3(International Journal of Contemporary Mathematical Sciences, ) Maingi, Damian
- ItemOn the pattern recognition of verhulst-logistic Itô processes in market price data.Onyango, Silas N.We introduce a highly error resistant method of extracting Itô processes as applied to market data. This method is inspired by an AI method known as Hough transforms (HT). The HT method has been used in extracting geometric shape patterns from noisy and corrupted image data. We use this method to extract simultaneously logistic geometric Brownian motion trends from simulated price histories data. It turns out that this approach is an effective method of extracting market processes for both simulated and real-world market price data.
- ItemOn unconditional banach space ideal propertyAywa, Shem; Muthengi, Fredrick; Musundi, SammyLet denote the assignment which associates with each pair of Banach spaces the vector space and be the space of all compact linear operators from . Let and suppose converges in the dual weak operator topology Denote by the finite number given by. The u-norm on is then given by. It has been shown that is a banach operator ideal. We find conditions for to be an unconditional ideal in
- ItemPricing European convertible bonds: geometric brownian motion vs. CGMYLabuschagne, Coenraad; Offwood, Theresa
- ItemSemi-Markov model for evaluating the HIV patient treatment costMbogo, Rachel Waema; Luboobi, Livingstone S.; Odhiambo, John W.The aim of this study is to model the progression of HIV/AIDS disease and evaluate the cost of the anti-retroviral therapy for an HIV infected patient under ART follow-up using Non homogeneous semi-Markov processes. States of the Markov process are defined by the seriousness of the sickness based on the clinical scores. The five states considered are: Asymptomatic (CD$^{+}_{4}$ count > 500 cells/microliter); Symptomatic 1 (350 < CD$^{+}_{4}$ count ≤ 500 cells/microliter); Symptomatic 2 (200 < CD$^{+}_{4}$ count ≤ 350 cells/microliter); AIDS (CD$^{+}_{4}$ count ≤ 200 cells/microliter) and Death (Absorbing state). The first four states are named as good or alive states. The models formulated can be used to gain insights on the transition dynamics of the HIV patient given the follow-up time. The transition probability Model, when fitted with data will give insights on the conditional probability of a patient moving from one disease state to another, given the current state and the follow-up time. This model will also give the probability of survival for the HIV patient under treatment given the current state and follow-up time. The total Lifetime Treatment Cost model obtained, when applied to real data will give the cost of managing an HIV patient given the starting state, the treatment combination which incurs minimum cost and which treatment combination is most effective at each state. The treatment reward model also when applied to real data will give the state, which a patient should be maintained so that they remain healthy, noninfectious and productive to the society. Also the model will show the optimal/effective time to initiate treatment, which can be used to give advice on how to handle the HIV infecteds given their states.
- ItemStatistical theory of integer partitionsRalaivaosaona, Dimbinaina
- Item"Stochastic model for In-Host HIV dynamics with therapeutic intervention(Hindawi Publishing Corporation, ) Odhiambo, John W.; Luboobi, Livingstone S.; Mbogo, Rachel WaemaUntangling the dynamics between HIV and CD4 cellular populations and molecular interactions can be used to investigate the e fective points of interventions in the HIV life cycle. With that in mind,we propose and show the usefulness of a stochastic approach towards modeling HIV and CD4 cells Dynamics in Vivo by obtaining probability generating function, the moment structures of the healthy CD4 cell and the virus particles at any time t and the probability of HIV clearance. The unique feature is that both therapy and the intracellular delay are incorporated into the model. Our analysis show that, when it is assumed that the drug is not completely eff ective, as is the case of HIV in vivo, the probability of HIV clearance depends on two factors: the combination of drug effi cacy and length of the intracellular delay and also education to the infected patients. Comparing simulated data for before and after treatment indicates the importance of combined therapeutic intervention and intracellular delay in having low, undetectable viral load in HIV infected person.
- ItemStochastic model for In-Host HIV dynamics with therapeutic interventionMbogo, Rachel Waema; Odhiambo, John W.; Luboobi, Livingstone S.;Mathematical models are used to provide insights into the mechanisms the dynamics between HIV and CD4+ cellular populations and molecuar interactions can be used to investigate the eff ective points of interventions in the HIV life cycle. With that in mind, we develop and analyze a stochastic model for In-Host HIV dynamics that includes combined therapeutic treatment and intracellular delay between the infection of a cell and the emission of viral particles, which describes HIV infection of CD4+ T-cells during therapy. The unique feature is that both therapy and the intracellular delay are incorporated into the model. Models of HIV infection that include intracellular delays are more accurate representations of the biological data. We show the usefulness of our stochastic approach towards modeling combined HIV treatment by obtaining probability distribution, variance and co-variance structures of the healthy CD4+ cell, and the virus particles at any time t. Our analysis show that, when it is assumed that the drug is not completely eff ective, as is the case of HIV in vivo, the predicted rate of decline in plasma HIV virus concentration depends on three factors: the death rate of the virons, the e cacy of therapy and the length of the intracellular delay.
- ItemStochastic Model for Langerhans cells and HIV Dynamics in VivoMbogo, Rachel Waema; Luboobi, Livingstone S.; Odhiambo, John W.Many aspects of the complex interaction between HIV and the human immune system remain elusive. Our objective is to study these inter-actions, focusing on the speci c roles of langerhans cells (LCs) in HIV infection. In patients infected with HIV, a large amount of virus is as-sociated with LCs in lymphoid tissue. To assess the influence of LCs on HIV viral dynamics during anti-retroviral therapy, we present and analyse a stochastic model describing the dynamics of HIV, CD4+ T-cells, and LCs interactions under therapeutic intervention in vivo. We per-form sensitivity analyses on the model to determine which parameters and/or which interaction mechanisms strongly affect infection dynamics.