SIMC 2019
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- ItemConducting and communicating classroom-close research that makes an impact(Strathmore University, 2019) Dr Jennie, GoldingThese two sessions will complement Professor Jaworskis by focusing on two strands in research on mathematics teaching and learning: >As an insider in ones own institution, whether school, college or university >As an outsider and guest in other classrooms. At least the first is likely to be quite small-scale — but it can still have impact. Throughout, I hope we can all benefit by drawing on participants own experiences. In Session 1 we shall consider the rationale and audience for such research, its potential and limitations, and the implications of those for research planning and structure. I shall share my experiences and some of my learning from studies of both kinds, and participants will work in small groups to analyse the issues in relation to research they are doing, or would like to do. The particular methods adopted will depend on the context and research questions, but for all of them, ethics are key, so we shall work together to analyse the ethical and practical challenges associated with such work. In Session 2 we shall first consider the challenges associated with being an insider researcher. We shall then focus on the theoretical framings and tools that can be used to analyse and interpret classroom-close research, considering the ways those can be used to make meaning of a range of (often subjective) data and relate findings to existing literature. We shall also discuss means and benefits of developing interpretation collaboratively, including with participants. The second part of the session will focus on the purposes and form of dissemination: how can we communicate our findings to the range of audience we would want to know about them?
- ItemA Model-based approach to genetic association testing in Malaria studies(Strathmore University, 2019) Akoth, Morine; Odhiambo, John; Omolo, BernardIn human genetics, heterozygote advantage (heterosis) has been detected in studies that focused on specific genes, but not in genome-wide association studies (GWAS). For example, heterosis is believed to confer resistance to certain strains of malaria in patients heterozygous for the sickle-cell gene HbS. Yet the power of allele-based tests can be substantially diminished by heterosis. Since GWAS (and haplotype-associations) also utilize allele-based tests, it is unclear to what degree GWAS could underachieve because heterosis is ignored. In this study, we propose a two-step approach to genetic association testing in malaria studies in a GWAS setting that may enhance the power of the tests, by identifying the underlying genetic model first before applying the association tests. We fit generalized linear models for the dominant, recessive, additive and heterotic effects and perform tests of significance using the MAX and the allelic tests, noting the minimum p-values across all the models and the proportion of tests that a given genetic model was deemed the best, using simulated data. Case-control genotype data on malaria from Kenya and the Gambia are used for validation. Results show that the allelic test returned a number of false negatives under the heterosis model, suggesting reduced power in testing genetic association. Thus, GWAS and haplotype associations should be treated with caution, unless the underlying genetic model had been determined.
- ItemSpatiotemporal patterns of successful TB treatment outcomes among HIV co-infected patients in Kenya(Strathmore University, 2019) Otiende, Verrah A.; Achia, Thomas N. O.; Mwambi, Henry GConvergence of the Tuberculosis (TB) and HIV epidemics threatens the management of TB treatment. These has been evidenced by various studies describing how HIV cc-infection propagates unsuccessful TB treatment outcomes. Information on the spatiotemporal patterns of successful TB treatment outcomes remain less understood despite the multi-organizational TB treatment efforts. This study uses case notification data to evaluate the spatiotemporal patterns of successful TB treatment outcomes for HIV co-infected patients in Kenya. This study used the case notification data from the Kenya National TB control program to investigate successful TB treatment outcomes in forty-seven counties in the period 2012 - 2017. The population of study was HIV co-infected cases with known TB treatment outcome. Achi-squre test was performed to determine the association between treatment outcomes and risk factors; TB- type, age, gender, ART therapy and patient type. The study also assessed the geographic patterns and temporal trends by mapping the TB treatment success rate in each county for the six-year period. Using the Integrated Nested Laplace Approach (INLA), the TB treatment success of HIV co-infected patients was modeled. The spatial parameters assumed the BesagYork-Mollie (BYM) specification. The temporally structured effect was represented through a neighboring structure and the temporally unstructured effects using a Gaussian exchangeable prior. Among the 172233 HIV co-infected cases included in the analysis, 135973 (78.9%) achieved successful TB treatment outcomes. Female cases registered higher treatment success rates (80.1%) compared to the male cases (77.8%). The cases on Anti-Retroviral Therapy (ART) recorded a success rate of 79.9% against 69.1% for their counterpart not on ART. The spatial trend depicted increased treatment success in some parts of the country with a relatively high level of associated certainty, characterized by a spatial relative success above 1 and posterior probabilities above 0.8. The temporal trend of treatment success showed an increase in the treatment success of TB in HIV coinfected cases. Overall, the success rate was still below 85% particularly for Homabay, Siaya, Kisumu, Migori and Busia counties in western Kenya. The successful TB treatment outcomes for HIV coinfected cases in Kenya were slightly below the 85% standard threshold set by the World Health Organization. Our study showed that even though co-infected cases have an increased risk of unsuccessful treatment outcomes, enhanced treatment monitoring improved the treatment outcome in most counties for the six-year period.
- ItemCoverage probability of a non-parametric estimator for a finite population total using edgeworth expansion(Strathmore University, 2019) Okungu, Jacob; Orwa, George; Odhiambo, RomanusIn survey sampling, the main objective is more often than not to establish information about any population parameter using the sample statistics. A nonparametric estimator of the finite population total is proposed. The nonparametric estimator of finite population total by Dorfman (1992) is developed and the coverage probabilities explored using the Edgeworth. The asymptotic properties; unbiasedness, efficiency and coverage rates of the estimator are analytically explored. In literature, a lot of work has been done on analyzing unbiasedness and efficiency of the estimators and more particularly for the population total estimators. This study departs from these studies by studying the tail properties using the confidence interval in more detail as opposed to just the unbiasedness, efficiency and mean squared error. An empirical analysis is done on three artificial functions; linear, quadratic and exponentially. It is observed that the coverage probabilities from Edgeworth expansion have higher coverage probabilities compared to design-based Horvitz-Thompson and Ratio estimators of the finite population total. The Edgeworth expansion also gave a tighter confidence interval length.
- ItemDependence modelling of financial returns using generalised normal mixtures(Strathmore University, 2019) Maina, CalvinIt has long been known that financial returns are often not normally distributed, but the technical difficulties of dealing with non-normal distributions have often stood on the way of using them in financial modeling. In particular, in dependence modelling of financial returns, using copulas and Normal Mixtures as marginal, for the practical value of risk management, the choice of marginal distribution is key. In this work, generalized normal mixtures are constructed, their properties studied, parameter estimation is achieved using the EM algorithm and application in Risk Management and portfolio optimization considered.
- ItemModeling and stability analysis of the African swine fever epidemic model(Strathmore University, 2019) Byamukama, Michael; Tumwiine, JuliusIn this paper, a mathematical model for the transmission dynamics and control of African swine fever with recruitment of susceptible, exposed and infective domestic pigs into the population is studied using a system of ordinary differential equations. The basic reproduction number Ro for the model was obtained and its dependence on model parameters discussed. Without the inflow of exposed and infective pigs into the population, the model exhibits the disease-free equilibrium Eo and the endemic equilibrium El. The disease-free equilibrium Eo is globally stable if the basic reproduction number Ro < 1 and the disease will be wiped out of the population. If Ro > 1, the endemic equilibrium El is asyrnptotically globally stable and the disease persists in the population. With the influx of exposed and infective domestic pigs, the model has only a unique endemic equilibrium Ee that is globally asymptotically stable and the disease persists. Numerical simulation is carried out to verify the analytical results. It is revealed that with the influx of the exposed and infected pigs, the disease is maintained at endemic equilibrium.
- ItemResponse surface regression modelling for the quality characteristics of wheat-plantain composite Flour bread containing gum Arabic from Acacia Senegal Var Kerensis(Strathmore University, 2019) Shitandi, Anakalo; Soibe|, Lilian; Agasa, Lameck Ondieki; Monari, FredThis paper is based on a study on the quality characteristics of wheat - plantain composite flour bread containing gum Arabic from acacia Senegal var kerensis using response surface methodology. In the study the effect of partial replacement of wheat with 10- 40% plantain and the subsequent effect of gum Arabic on composite bread quality attributes was investigated. The characteristics of bread tested included hardness, springiness, cohesiveness, gumminess and chewiness. Wheat- plantain composites produced dough that took longer than the control to breakdown thus stronger dough. Plantain composites had a higher peak viscosity which indicated that the composites had a higher swelling index than the wheat (control). The model p-values were significant for both linear and quadratic models. The parameter estimates for hardness, springiness, cohesiveness, gumminess and chewiness were all statistically significant at a = 0.05 level of significance. The results indicated that low levels of plantain substitution may have no adverse effect on gluten functionality since composites bread volume did not differ significantly from the control. Gum Arabic as used in this study was found to improve the breads textural qualities such as reducing bread hardness and chewiness and increasing bread springiness.
- ItemCreating equitable environments through ethno-mathematics on a worldwide voyage(Strathmore University, 2019) Prof.Furuto, LindaEthno mathematics is a pathway to real-world problem solving that empowers locally minded, global citizens through a sense of purpose and a sense of place. Over the past decade, the Ethno mathematics and STEM Institute has explored learning and teaching practices via the design, implementation, and assessment of culturally sustaining work aligned with state and federal standards. Research has led to policy and practice implications including becoming institutionalized as a new academic program at the University of Hawaii. In this presentation I will highlight some of that research and also share the mission, vision and values that inspire the Ethno mathematics Graduate Certificate/M.Ed Curriculum Studies Math Education at University of Hawaii.
- ItemConservation laws and exact solutions of a generalized (3+1)-dimensional mKdV-ZK equation(Strathmore University, 2019) Adeyemo, Oke Davies; Masood, KhaliqueiIn this talk we investigate conservation laws and exact solutions of a generalized SBS (3+1)-dimensional mKdV-ZK equation that describes the behavior of weakly nonlinear ion-acoustic waves contained in magnetized electron-positron plasma which also comprises equal hot and cool components of each species. The use of the reductive perturbation procedure yields a mKdV-ZK equation that simply governs the oblique propagation of nonlinear electrostatic modes.
- ItemA Study of a nonlinear derivative Schrodinger equation(Strathmore University, 2019) Karabo, Plaatjie; Chaudry, Masood KhaliqueIn this talk we present symmetry reductions and group-invariant solutions for the SBS derivative nonlinear Schrodinger equation. This equation is used to describe the evolution of some signal in lossless discrete nonlinear transmission line made of circuits that contains constant inductors and voltage-dependent capacitors. We then derive the conservation laws for this equation through the use of a direct method.
- ItemMathematical model of global warming effect on Malaria transmission(Strathmore University, 2019) Benjamin, Peter; Ogunsola, AmosIn the recent times malaria is one of the top leading, most predominant and significant communicable diseases in Kampala, Uganda. The endemic health hazard is approximately 95 percent in the country. This paper presents a mathematical model of malaria transmission with the effect of climate change due to increase in temperature on the increase of conveyor dependent infectious diseases and probably alter the region transmission potential of malaria. A deterministic compartmental model is proposed and analyzed. This study presents both qualitative and quantitative approaches of the model. The numerical simulation is employed using Excel micro software to and support the qualitative results. The next generation matrix is employed to determine the common fundamental reproduction number. The basic reproduction number implies that the force of malaria transmission in Kampala is high. From the analysis of the result, the optimal temperature for the transmission of the infectious malaria is The result also shows that increase in temperature due to climate change give rise to development of parasite which consequently leads to an increase in the wide spread of malaria transmission in Kampala. It is also seen from the results that increase in temperature leads to an increase in the number of infectious human host and mosquitoes. However as temperatures approaches exposed human and mosquito populations decline asymptotically to low levels.
- ItemA Stochastic hierarchical system steady-state availability model(Strathmore University, 2019) Musiga, LydiaStochastic models are adept at modeling the dependability attributes of critical systems. The dependability attributes include availability, reliability, safety, integrity, maintainability, survivability, performance and confidentiality. This paper presents a novel method of computing the steady-state availability of a system using the closed form approach. Continuous Time Markov Chain models are instrumental in deriving the steadystate availability balance equations of the system modules from which the closed form solutions are obtained. Imperfect coverage and switch-over are incorporated into the Continuous Time Markov Chain models where applicable.
- ItemLesson study approach for teachers' professional growth in mathematics education and comparison of three examples(Strathmore University, 2019) Prof. Takuya, BabaTeachers' growth is one of the most important factors to consider in each country where the quality of education is directly connected to the level of intelligence and thus level of economy. It is, however, regarded as a lifelong continuing process and not easy to grow in a short period. Teaching Gap (Stigler et al 1999) has caught attention on the lesson study from educators all over the world. With such a trend, the lesson study approach is a unique approach to address the issue of lifelong continuing process and collective aspect of professional growth. This lesson study approach was born and has been grown in Japan more than one hundred years. It has certainly become a part of the Japanese education culture, and on the other hand, Stigler et al. (1999) clearly has pointed out that the lesson study has a potential to influence culture of teachers and classrooms with time. While JICA has introduced the lesson study approach since 2003 in various countries, the cultural aspect of the lesson study is not well paid attention to. Thus this paper is to address the cultural and contextual factors of the lesson study through comparison of three cases in Japan, Bangladesh and Zambia.
- ItemLaplace-transform asymptotics of longest gaps in Poisson processes(Strathmore University, 2019) Okello Omwonylee, Joseph; Opaka Awichi, RichardIn a Poisson process with constant rate (also known as homogeneous Poisson process) with exponential inter-arrival (waiting time to the next event) time, the longest/largest gap, L(t) which is the maximal inter-arrival time is considered in this paper. The aim was to establish the Laplace transform asymptotic and the large deviation principles related to the longest gap L(t) between epochs of arrival in a homogeneous Poisson process. The result of the investigation suggest two natural and different large deviation principles for the longest gap with two distinct rate functions and speeds.
- ItemGeneralization and classes of probability distributions(Strathmore University, 2019) Omukami, Howard; Ottieno, JarnHighlights of various methods for constructing probability distributions are given. The distributions are based on : power series, transformations, mixtures, sums of independent random variables, recursive relations, differential equations, geometry, generators, lifetime, special functions and weighted functions . Distributions arising from stochastic processes are also discussed. Some of the distributions are generalizations of other distributions while others form classes. In this paper we shall present work done on constructions, properties, estimations and applications of these distributions in the School of Mathematics University of Nairobi.
- ItemOn the operating characteristics of queuing system for an NNPC mega station in Nigeria(Strathmore University, 2019) Evans, Evans; Nyor, Ngutor; Inyang, GloryIn this work, an understanding is sought of Queuing characteristics at an NNPC Mega station in Nigeria when petrol is easily available so as to compare with the queuing characteristics when there is petrol scarcity which is a recurring decimal in the country. The Mega station with queuing discipline of First-In First-Out, a service mechanism of single-queue multiple-channels and a system capacity of an infinite source has distinct operating characteristic of traffic intensity being 0.77. Further analysis of the queuing characteristics revealed that, the average number of vehicles in queue is from 2 to 3 while the average time a vehicle spends in queue is 1.58 minutes. The probability of vehicle queuing on arrival is 0.5993 while there is a 0.4007 probability that a vehicle may not queue on arrival. It was concluded that with 1.8 minutes, a vehicle spends more time in service than on the queue and since the number of vehicles on the queue is < the number of active servers, there is no queue at NNPC Mega station Minna when there is no fuel scarcity country.
- ItemMathematical model for the infectiology of Brucellosis with some control strategies(Strathmore University, 2019) Nyerere, Nkuba; Luboobi, Livingstone; Mpeshe, Saul; Shirima, GabrielBrucellosis is a zoonotic infection caused by gram-negative bacteria of genus brucella. In this paper, a deterministic mathematical model for the infectiology of brucellosis with vaccination of ruminants, culling of seropositive animals through slaughter, and proper environmental hygiene and sanitation is formulated and analyzed. A positive invariant region of the formulated model is established using the Box Invariance method, the effective reproduction number, Re of the model is computed using the standard next generation approach. We proved that the brucellosis free equilibrium exists, locally and globally asymptotically stable if Re < 1 while the endemic equilibrium point exists, locally and globally asymptotically stable if Re > 1. Sensitivity analysis of the effective reproductive number shows that, natural mortality rate of ruminants, recruitment rate, ruminant to ruminant transmission rate, vaccination rate, and disease induced mortality rate are the most sensitive parameters and should be targeted in design of the control strategies for the disease. Numerical simulation shows that the combination of more than two control strategies reduces/eliminates the disease from the livestock population.
- ItemFinite population total estimation with measurement errors(Strathmore University, 2019-08) Tinega, RichardWe consider measurement errors on linear regression estimates of the finite population total. A general case of the linear regression estimates with unbiased measurement errors where the effect of biases on the simple and correlated response variances is analyzed. A simulation study to investigate the effect of these biases on the variance of the finite population total is done. From the results, the variance of the finite population total increases as the proportion of the systematic errors increase.
- ItemA Dynamic predictive model for efficient emergency health care center placement and resource allocation: a case of Kenyan healthcare system(Strathmore University, 2019-08) Tunduny, TitusHealth is one of the cardinal areas of focus for a functioning society and is one of Kenya’s goals for the Vision 2030 goal. Kenya lacks an effective healthcare system, falling way below the recommended ratio of 23 healthcare practitioners for 10,000 people, with the current ratio of 17 per 100,000. Limited resourcing and poor placement of hospitals further compounds to the marginalization of some communities, some of whom are greatly disadvantaged and make great candidates for terror sympathizers. The constitution of Kenya (2010) devolved healthcare management to the county governments, but there is lack of an efficient framework/ model that can aid in the placement of the healthcare centers and first level POC for emergency situation, coupled with the resource allocation to operationalize them. This proposed research aims to develop a neural network model that can identify and place healthcare centers to areas of need, while also identifying the resourcing needs and capacitation for the healthcare centers.
- ItemA Comparative analysis of rural and urban students’ performance in an Interactive Mathematics supported classroom(Strathmore University, 2019-08) Uwineza, Innocent; Uworwabayeho, AlphonsePerformance in education is a key characteristic of effective teaching and learning SBS and a criteria which is mostly used to classify schools from the best to the least. However, it depends on different factors including teaching resources and facilities. The current educational era is promoting the use of ICT in education as an instructional material with the purpose to raise the quality of education. After adopting the Competence Based Curriculum (CBC) which is now under its early implementation phase, the Rwandan education system is now seeking to find all the means to maximize the benefits of CBC to education. The development of the Interactive Mathematics (1M) content software for Rwanda is in this regard expected to bring the effectiveness of teaching and learning of mathematics in basic education by making mathematics enjoyable and accessible to children. After the testing of 1M in a bootcamp setting that had shown the 1M software potentiality to influence student’s motivation and performance, it had been necessary to analyse the situation in a real class setting. This paper provide the results of pre-test, post-test and comparison tests conducted in primary schools of rural and urban areas.