Mathematical Theory and Modeling
http://www.iiste.org/Journals/index.php/MTM
<p><span id="internal-source-marker_0.04939836589619517"><span id="internal-source-marker_0.04939836589619517">Mathematical Theory and Modeling </span>is a peer reviewed journal published by IISTE. The journal publishes original papers at the forefront of mathematical theories, modelings, and applications. The journal is published in both printed and online versions. The online version is free access and download.</span></p><p><span>IISTE is member of <a href="http://www.crossref.org/01company/17crossref_members.html">CrossRef</a>.<br /></span></p>en-USMathematical Theory and Modeling2224-5804A Predator-prey Model With Transition Two Infectious Diseases in Prey and Harvesting of The Predator
http://www.iiste.org/Journals/index.php/MTM/article/view/15606
<p>In this paper, we proposed and study prey-predator model involving effect of transition different infectious diseases in prey population with the optimal harvesting for metapopulation, especially predator population, using dynamics programming. Sufficient conditions on the system parameters are derived which guarantee that the equilibrium points of the system are globally asymptotically stable while the harvesting which has an effect on the stability of this system satisfies certain conditions. Also, we discuss the existence of local bifurcation at each equilibrium point. Finally the effects both of the disease and harvest on the dynamical behavior the model are discussed numerically.</p> <p><strong>Keywords:</strong> SIS epidemics disease, Predator-prey model, Harvest management; Global stability; Lyaponov function; local bifurcation.</p>Rasha Majeed Yaseen4An Epidemiological Model of Malaria at Techiman Municipality, Ghana
http://www.iiste.org/Journals/index.php/MTM/article/view/15607
<p>The study examined the prevalence of Malaria in the Techiman Municipality of Ghana. We used model to analyze, model and predict the prevalence of Malaria disease in the municipality. The study is made up of two sections. An model without the vital dynamics and an with vital dynamics were used to explain the spread of the Malaria in the Techiman Municipality followed by the Fred Brauer simple treatment model ( ) to determine whether the treatment of malaria in the municipality is beneficial. The model has two equilibrium states: the disease-free equilibrium and the endemic equilibrium states respectively. The stability condition of each equilibrium point is discussed. The basic reproductive number of Malaria without the vital dynamics is estimated to be and the basic reproductive number of Malaria with the vital dynamics is estimated to be in the Techiman Municipality. The basic reproductive numbers of the model and the modified malaria model were also estimated to be and respectively. Our work shows that the reproductive number () of Malaria infection at Techiman Municipality is less than 1(). Our work also shows that malaria treatment is beneficial in the municipality. According to the results of this study whenever the transmission rate coefficient in any of the models is increased, , but when the transmission rate coefficient is reduced, . We recommend that Malaria control measures should be intensified in the municipality so as to decrease the rate of transmission.</p> <p><strong>Keywords: </strong>SIRS model, Stability analysis, Equilibrium points, Mathematical model, Epidemiological model.</p>Isaac Kwasi AduDouglas Kwasi BoahFrancis Julius Gyebil4Analysis of the Behaviour of Stocks of Dar es Salaam Stock Exchange (DSE)
http://www.iiste.org/Journals/index.php/MTM/article/view/15608
<p>A stock market is a place where investors trade certificates that indicate partial ownership in businesses for a set price. Different countries in the world have stock markets where other countries started their stock markets long time ago like the USA and they have investigated the trend of their market if it is normally distributed or not. Also they have strong models that assist them in making predictions and also help the investors on the choice of the stocks to invest so as to gain the profit in the future. On the other hand other countries just started few years ago. Tanzania is among the countries where stock markets has just started recently and hence there is a need to study the nature of the stocks distribution and see whether the Dar-Es-Salaam Stock of Exchange (DSE) market do follow the theoretical conclusions or not. Thus in this study we adapt the Markowitz modern portfolio theory (MPT) and using the mean variance analysis theory together with the DSE data to investigate if the DSE stock market follows a normal distribution or not. The analysis shows that the DSE stocks log returns are reasonably normally distributed and its prices do change according to the change in other factors like the inflation rate, consumers (investors) interest, the policy of the country, and other exogenous factors.</p> <p><strong>Keywords: </strong>portfolio, stock market, volatility (risk), expected return, covariance matrix.</p>Phares KabonekaWilson C. MaheraSilas Mirau4Application of paired student t-test on impact of Anti-retroviral therapy on CD4 cell count among HIV Seroconverters in serodiscordant heterosexual relationships: A case study of Nyanza region, Kenya.
http://www.iiste.org/Journals/index.php/MTM/article/view/15626
<p>Human immunodeficiency virus (HIV) infection leads to rise in HIV-RNA resulting in CD4 T-cell decline leading to AIDS-related illness. Knowing the effect of Antiretroviral Therapy (ART) on CD4 cell count is vital in assessing the progression of the disease and treatment planning for treatment. This study sought to apply paired t-test distribution to assess the effect of CD4 cell count just before and after initiation of ART among HIV infected individuals. The target populations were HIV sero-converters enrolled in a prospective randomized placebo controlled trial in Nyanza region, Kenya. CD4 cell count was measured at the time of sero-conversion and subsequently after very six months of follow up. Participants were referred for initiation of ART at patient support centre once the criteria for initiation was met and report back the ART regime they were put on and the date they were started on . We applied paired t-test to assess the change in CD4 cell count after initiating ART. Use of ART within a median time of 9 months resulted rise in CD4 cell count by 241 cells per ul, 95% CI (60-422) which confirms the effect of ART in protecting depletion of CD4 cell count.</p> <p><strong>Keywords: </strong>Sero-converters, Progression, ART, HIV, CD4 cells, t-test.</p>Bernard K. RonoGeorge OrwaJoseph MungatuAntony Wanjoya4Structural Equation Modelling: Confirmatory Factor Analysis To Construct Measurement Model & Mediator Check Among Formed Factors.
http://www.iiste.org/Journals/index.php/MTM/article/view/15627
<p>The study aimed to build a measurement model, to describe satisfaction of students towards the quality of service provided at their hostel. A measurement model out of the hypothesized SERVPERF Model, was build for this purpose, using Confirmatory Factor Analysis. A number of 313 respondents were used in this data set. Study found that the hypothesized model with some modifications fits the data well. As the hypothesized model fits the data well, study was also done to investigate if the Working Style factor act as a mediator for the relationship of Empathy factor towards Tangible factor in the modified SERVPERF Model. Study found that Working Style factor act as a partial mediator for this relationship.</p> <p><strong>Keywords</strong>: Measurement Model, Confirmatory Factor Analysis, SERVPERF Model, Mediator, Working Style, Empathy, Tangible</p>Loshini ThiruchelvamSabri Ahmad4On Two Tests for Main Effects in A Balanced Two-Way Interactive Model
http://www.iiste.org/Journals/index.php/MTM/article/view/15628
<p>Two methods of removing interaction in a two-way balanced design were considered. Removing interaction from the model/ data will result to a reduced model and data which consequently violates the assumptions of analysis of variance (ANOVA). To resolve this problem, a linear combination method approach was used which does not violates the assumptions of ANOVA and completely makes the presence of interaction to be zero.</p> <p><strong>Keywords:</strong> Additive effects, Homogeneity of variance, Normal distribution</p>F.C. EzeAdimonye F.0Urama K. U4On the Use of Posterior Probabilistic Clustering
http://www.iiste.org/Journals/index.php/MTM/article/view/15629
<p>Bayesian approach to mixture models makes use of Gibbs sampler, the most common of Markov Chain Monte Carlo (MCMC), for estimation of posterior density and subsequent classification of objects into components of mixture, especially for conjugate priors. In practice conjugacy may not exist and when it does, the time required calculating the posterior density will be far too high for the Bayesian approach to be applied in practice (McLachlan and Peel, 2000). Therefore, we developed a clustering procedure that is a result of using non-conjugate prior distribution of product multinomial to obtain posterior distribution that is hypergeometric, for cross-classifying categorical data. The performance of the scheme was examined through a simulation study of observed tables of counts compared with expected generated by assuming product multinomial to obtain posterior distribution under variety of parameter distributions and loadings. We observed that the approach performed well when the component proportions are properly distinguishable. The approach was illustrated using real life data from social science.</p>S.S. AbdulkadirE. T. Jolayemi4Time series modeling of tourist accommodation demand in Kenya
http://www.iiste.org/Journals/index.php/MTM/article/view/15631
<p>Tourism is a very important sector in the world economy and contributes significantly to foreign exchange earnings. Earnings from tourism in Kenya increased annually from Kenya Shillings 24.3 billion in 2001 to 73.7 billion in 2010 (ROK, 2012). The number of tourists coming into the country increased from 1,146,102 in the year 2003 to 1,822,885 in the year 2011. The major tourist zones in Kenya are: Nairobi, Beach, Mombasa, Coast Hinterland, Maasailand, Nyanza basin, Western, Central and North (ROK, 2012). These can further be reduced to three: Nairobi, Coastal and Others. Tourism in Kenya relies on many other sectors and industries, one of which is the hotel and accommodation. In order to enable these related industries match the specific accommodation needs for the tourists arriving in the country, there is needed a model that can forecast the accommodation demands by the tourists. This will make it possible for the hotel industry players to respond in good time to the anticipated changes in demand over time and also to maximize returns on investments.</p> <p>Seasonal variations are important in tourism and hospitality demands. The Box-Jenkins models for time series analysis allow the analyst to forecast future values of a series with only the past period’s data, without having some related variable’s data (Shumway and Stoffer, 2011). The authors therefore focused on the Box-Jenkins models to generate a forecasting model using quarterly data on bed occupancy by tourists visiting Kenya from 1974 to 2011. The SARIMA (1,1,2)(1,1,1)[4] model was found to be suitable for forecasting future quarterly demand on tourist accommodation in Kenya. This model shall therefore be useful to the tourism and related industries in forecasting future demands and maximize their returns on investment.</p> <p><strong>Keywords: </strong>Tourist Accommodation Demand, Kenya Tourism Accommodation, Tourism Accommodation Modeling</p>George OtienoJoseph Mung’atuGeorge Orwa4Some Results on the Group of Lower Unitriangular Matrices L(3,zp)
http://www.iiste.org/Journals/index.php/MTM/article/view/15632
<p>The main objective of this paper is to find the order and its exponent, the general form of all conjugacy classes, Artin characters table and Artin exponent for the group of lower unitriangular matrices L(3,?<em><sub>p</sub></em>), where p is prime number.</p>Asmaa Abd AswhadNiran Sabah JasimAhmed Rasim Hameed4Bayesian One- Way Repeated Measurements Model as a Mixed Model
http://www.iiste.org/Journals/index.php/MTM/article/view/15633
<p>In the Bayesian approach to inference, all unknown quantities contained in a probability model for the observed data are treated as random variables. Specifically, the fixed but unknown parameters are viewed as random variables under the Bayesian approach. In this paper, Bayesian approach is employed to making inferences on the one- way repeated measurements model as mixed model , and we prove some theorems about posterior.</p> <p class="Default"><strong>Keywords:</strong><strong> </strong>Mixed models, One- way repeated measurements model , Bayesian inference, Prior density, Posterior density.<strong></strong></p>Ameera Jaber MohaisenKhawla Abdul Razzaq Swadi4Optimal Production Planning For Patsol’s Venture Company Limited Using Integer Programming
http://www.iiste.org/Journals/index.php/MTM/article/view/15634
<p>Industrial Production and the flow of resources in an economy are all complexes. Therefore, careful planning and control are required in the production process especially when the real situations being considered are to be integer values. The Various Problems facing industrialists today are as a result of inadequate and improper production planning techniques. This article determines the optimal production schedule of products for the PATSOL’S Furniture Company Limited. A mathematical model was used to represent the real situations based on the data collected. The model was analyzed and solution developed using the Integer Programming Algorithm. The result gives an optimum monthly profit of <span style="text-decoration: line-through;">N</span>132, 120.00 with the production of 15 dinning chairs, 485 half upholsteries, 2 full upholsteries and 73 church pews.</p> <p><strong>Key Words: </strong>Industrial Production; Integer Programming, Planning.</p>Abam, Ayeni OminiNsien, Edwin Frank4Numerical Solution of Airy Differential Equation by Using Haar Wavelet
http://www.iiste.org/Journals/index.php/MTM/article/view/15636
<p>Haar wavelet is exceedingly simple and optimized completely for computers, so that it can be used for solving ordinary differential equations and partial differential equations without a hassle. In this paper, numerical solutions of Airy differential equations have been obtained by using the Haar Wavelet Method . Comparisons with exact solutions make clear that the Haar Wavelet Method is a powerful candidate for solving the Airy differential equation. Moreover the use of Haar wavelets is found to be accurate, uncomplicated, speedy, adaptable and convenient with very small computation costs and the extra perk of being computationally attractive.</p> <p><strong>Key Words:</strong> Orthogonal Wavelet, Airy Equation, Function Approximation, Operational Matrix</p>M. KhalidMariam SultanaFaheem Zaidi4Temperature and Rainfall Effects on Spice Crops Production and Forecasting the Production in Bangladesh: An Application of Box-Jenkins ARIMAX Model
http://www.iiste.org/Journals/index.php/MTM/article/view/15637
<p>The objective of this study is to develop the best Box-Jenkins Auto-Regressive Integrated Moving Average with External Regressor, that is, ARIMAX model for measuring the temperature and rainfall effects on major spice crops productions in the Bangladesh and forecasting the production using the same model. Due to time sequence dataset, ARIMAX model is considered as a measuring tool of cause-effect relation among the spice crops and climatic variables (temperature and rainfall) under study. From the study, it is found that ARIMAX(2,1,2), ARIMAX(2,0,1) and ARIMAX(2,1,1) are the best model for Chili, Garlic and Ginger crop respectively. From the comparison between original series and forecasted series, it shows that these fitted model are well representative of the practical situations and both series shows the same manner indicating good forecasting. <strong></strong></p> <p><strong>Keywords: </strong>Temperature, Rainfall, Species Production, Forecasting, ARIMAX Model.</p>Mohammed Amir Hamjah4An Inventory Model For Non – Instantaneous Deteriorating Products With Price And Time Dependent Demand
http://www.iiste.org/Journals/index.php/MTM/article/view/15638
<p>Many inventory models have been developed by many researchers for deteriorating products. But certain products do not deteriorate immediately. In fact the deterioration starts after certain period of time. This kind of deterioration is known as non – instantaneous deterioration. In the present paper an inventory model for non – instantaneous deteriorating products with price and time dependent demand have been given. Shortages are allowed and completely backlogged. Numerical examples have been considered to demonstrate the effectiveness of the model.</p> <p><strong>Keywords: </strong>Price and time dependent demand, non – instantaneous deterioration, inventory, shortages<strong></strong></p>Shalu Kapoor4Enumeration of Hamiltonian Cycles on a Complete Graph using ECO method
http://www.iiste.org/Journals/index.php/MTM/article/view/15639
<p>ECO is a method for enumerating classes of combinatorial objects based on recursive constructions of such classes. A construction for a class of Hamiltonian cycles in a complete graph consisting of n nodes is constructed based on ECO method. Here, a <em>Hamiltonian cycle is represented as a permutation cycle of length n whose permutation and its corresponding inverse permutation are not distinguished. </em>Later, this construction is translated into a succession rule. The final goal of this paper is to determine the generating function of Hamiltonian cycles and it is achieved by making use of the ordinary generating function of a permutation class and the exponential generating function of the infinite sequences of 1s.</p> <p><strong>Keywords: </strong><em>ECO method, Hamiltonian cycle, cycle permutation, generating function, succession rule.</em></p>Retno maharesi4The Retention Rates of Students In Public Secondary Schools Using The Cox Proportional Hazard Model: A Case of Kisumu County, Kenya
http://www.iiste.org/Journals/index.php/MTM/article/view/15641
<p>The study sought to propose a statistical model for the public Secondary School students' retention rates for Kisumu County. We used survival regression analysis in which students were grouped according to the their performance in KCSE, mean school fee payment, school category, sex, mean age and teacher - student ratio using a desirable survival function. The model was of interest because the study sought to address a life testing experience mostly restricted to survival models and most of the existing models on student retention addressed Universities and tertiary colleges' trend and were particularly developed outside the country. This was in spite of the fact that Kenya suffers from high dropout rates at the Secondary level. The annual Secondary School students data traced from a cohort in form one in the year 2010 to form four in the year 2013 were obtained from the Kisumu County Ministry of Education headquarters and analyzed using survival regression. The variables which were insignificant were dropped to get the desirable function. Survival rates of students in the Secondary Schools were traced at the end of each and every level. It was found out that dropping out of students was influenced by; the category of the school, average fee payment, performance in KCSE and sex, with more girls dropping out than boys and the dropping out mostly rampant at form two. The model will be of relevance to the concerned Secondary education stakeholders in improving the quality of education for it will inform the planning of necessary educational interventions to ensure enhanced retention rate and transition.</p> <p><strong>Keywords: </strong> Retention, Cox Regression, Drop-out rate, Probability Density function, Kaplan Meier.</p>Jacob Oketch OkunguGeorge OrwaJoseph Mung’atu4