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Mathematical Modeling for Human Immunodeficiency Virus (HIV) Transmission using Generating Function Approach
(Strathmore university, 2009) Waema, Rachel; Olowofeso, Olorunsola
This 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.
Water Filter Provision and Home-Based Filter Reinforcement Reduce Diarrhea in Kenyan HIV-Infected Adults and Their Household Members
(The American Journal of Tropical Medicine and Hygiene, 2014) Chaba-Omondi, Linda Akoth
Among human immunodeficiency virus (HIV) -infected adults and children in Africa, diarrheal disease remains a major cause of morbidity and mortality. We evaluated the effectiveness of provision and home-based reinforcement of a point-of-use water filtration device to reduce diarrhea among 361 HIV-infected adults in western Kenya by comparing prevalence of self-reported diarrhea before and after these interventions. After provision of the filter, 8.7% of participants reported diarrhea compared with 17.2% in the 3 months before filter provision (odds ratio [OR] = 0.39, 95% confidence interval [95% CI] = 0.23–0.66, P < 0.001). The association was similar among 231 participants who were already taking daily cotrimoxazole prophylaxis before being given a filter (OR = 0.47, 95% CI = 0.25–0.88, P = 0.019). Educational reinforcement was also associated with a modest reduction in self-reported diarrhea (OR = 0.50, 95% CI = 0.20–0.99, P = 0.047). Provision and reinforcement of water filters may confer significant benefit in reducing diarrhea among HIV-infected persons, even when cotrimoxazole prophylaxis is already being used.
Adverse information on social media will always send Kenyans to withdraw their money
(2016-04) Karoney, Carol-Noelle; Kalu, Elizabeth
In the paper “The Extent to Which Social Media Can Influence a Bank Run” Atieno,T. and Mutinda, M. (2014) provided empirical evidence that there was a huge risk of a bank run occurring in Kenya due to social media. This paper co-relates that study with the closure of Chase Bank Kenya in April 2016
Laguerre Polynomials and singular differential operators
(Indian Journal of Pure and Applied Mathematics, ) Onyango-Otieno., Vitalis
This 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 ).
On the Minimal Resolution Conjecture for P3
(International Journal of Contemporary Mathematical Sciences, ) Maingi, Damian
"Stochastic model for In-Host HIV dynamics with therapeutic intervention
(Hindawi Publishing Corporation, ) Odhiambo, John W.; Luboobi, Livingstone S.; Mbogo, Rachel Waema
Untangling 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.
A Mathematical model for bovine brucellosis incorporating contaminated environment
Robert, Godwin; Julius, Tumwiine
On the distribution of multiplicities in integer partitions
Ralaivaosaona, Dimbinaina
A Bayesian hierarchical model for correlation in microarray studies
Omolo, Bernard
Microarrays are miniaturised biological devices consisting of molecules (e.g. DNA or protein), called \probes", that are orderly arranged at a microscopic scale onto a solid support such as a nylon membrane or a glass slide.The array elements (probes) bind speci cally to labeled molecules, called "targets", into complex molecular mixtures,thereby generating signals that reveal the identity and the concentration of the interacting labeled cells.Microarray analysis has a broad range of applications that involve di erent types of probes and/or targets (cDNA or oligos)
A copula-based approach to differential gene expression analysis
Chaba, Linda Akoth; Odhiambo, John W.; Omolo, Bernard
Melanoma 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.
Conditional CAPM in financial risk management: a quantile autoregression approach
Kube, Ananda; Leo, Odongo; Mwita , Peter
The study aims to provide a comprehensive description of dependence pattern of a stock by studying a range of betas derived as quantiles of conditional return distribution using quantile regression based on moving window regression.We investigate predictability of various parts of the conditional return distribution in a linear, autoregressive framework. We also aim to capture a state of dependence at di erent quantiles of the conditional return distribution. A good (bad) state is associated with upper (lower) quantiles,thus the impact of lagged returns is di erent across quantiles. Our empirical ndings are based on daily returns of major European stocks-sample data. Lower quantiles exhibit positive dependence with past returns while upper quantiles are marked by negative dependence. Central quantiles exhibit weak dependence. Keeping the sign of returns, we discover that positive previous day's return leads to strong positive returns with today's positive return and marked negative with today's negative return. The opposite pattern is visible for past negative returns.
Enhancing mathematics research in African Universities through international collaboration
Kojoro, Peter
Managing chronic conditions through hosted medical records in Kenya
Mbogo, Rachel Waema; Mbogo, Salesio
Complex 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.
Extending genstat capability to analyze rainfall data using Markov chain model
Ster , David; Ong’ala, Jacob Otieno; Stern, Roger
Rainfall is of critical importance for many people particularly those whose livelihoods are dependent on rain fed agriculture. Methods of analysis of daily rainfall records based on Markov chain models have been available for many years and their value is widely recognized. However they are rarely used because of the complexity of their analysis. This paper describes how these models are being made more accessible through a series of specially written procedures and menus in GenStat, a widely available statistics package.
A smooth test of goodness-of-fit for the baseline hazard function in recurrent event models
Odhiambo, John W.; Odhiambo, Collins; Omolo, Bernard
In 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.
Statistical theory of integer partitions
Ralaivaosaona, Dimbinaina
Stochastic model for In-Host HIV dynamics with therapeutic intervention
Mbogo, 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.
Monads on a multiprojective space, Pa × Pb
(International Mathematical Forum, ) Maingi, Damian
Mathematical model for pneumonia dynamics among children
Ong’ala, Jacob Otieno; Mugisha , Joseph; Odhiambo, John W.
Mathematical 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.

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