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Item Double-layered anisotropic stellar model of embedding class I with gaseous envelope(Elsevier, 2023) Mathias, Amos Vincent; Mkenyeleye, Jason Maombi; Sunzu, Jefta M.The current paper presents a double-layered neutral anisotropic stellar model in general relativistic setting. The model is developed by using Einstein field equations and class I embedding condition. We consider the core with quark matter obeying linear equation of state and envelope layer with gaseous matter admitting Chaplygin gas equation of state. The interior and exterior metric coefficients match smoothly at the interface of core and envelope layers and at the stellar surface. The profiles for matter variables, stability and energy conditions show acceptable trend for physical stellar models. In this model, stellar masses and radii consistent with compact stars HerX-1, 4U1538-52, SAXJ1808.4-3658, CenX-3 and SMCX-1 are generated. We note that studies of multi-layered stars with gaseous envelope and embedding class I condition are missing in investigations conducted in the past.Item Analysis and investigation of logical flaw of Zeno’s Achilles-Tortoise paradox(Informa UK Limited, 2024-03-16) Mayila, Shega; Mpimbo, Marco; Rugeihyamu, Sylvester; Hari M. SrivastavaIn this paper, we analyze the Achilles-Tortoise paradox, which denies the overtaking of the slowest runner (Tortoise) by the quickest runner (Achilles) because the pursuer must first reach the point whence the pursued started, so the slower must always hold the lead. The paradox translates into a requirement for the quicker to complete one by one an infinite sequence of distinct runs in a finite time to overtake the slower. This feat is impossible because the infinite sequence of distances contains no final distance to run, and the time to complete such a feat is not enough. However, we know better that in a race, the quickest always overtakes the slowest. Then why does the argument say otherwise? There should be logical flaws in its argumentation. Therefore, after an analysis of the paradox, we investigate the existence of such a flaw that exists in the argument itself or in the inferences its premises make. In addition to this, we present the new mathematical solution based on open balls in real Euclidean space, which shows that only a finite number of runs are needed by the quickest to overtake the slowest.Item Influence of induced magnetic field and chemically reacting on hydromagnetic Couette flow of Jeffrey fluid in an inclined channel with variable viscosity and convective cooling: A Caputo derivative approach(Elsevier, 2024-05) Chillingo, Kidney Josiah; Mng’ang’a, Jumanne; Onyango, Edward Richard; Matao, Paul M.In this study, the influence of induced magnetic field and chemically reacting on hydromagnetic generalized Couette flow of Jeffrey fluid in an inclined channel through a porous medium with variable viscosity and convective cooling has been investigated using the Caputo fractional order derivative operator. The mathematical formulation used for the hydromagnetic Couette flow of Jeffrey fluid takes into account the effects of viscous dissipation, Soret, and Dufour. The system of nonlinear partial differential equations governing the flow were solved numerically using the explicit finite difference method. The numerical results for the behavior of various physical parameter on the flow variables are obtained and represented graphically. Moreover, effects of the flow parameters on heat and mass transfer rates are obtained and discussed numerically through tabular forms. The graphical findings show that velocity, concentration, induced magnetic field, and thermal field profiles decline with progressively increment of Jeffrey parameter. The velocity, and temperature of the fluid decline with higher values of fluid viscosity parameter. An increase in the chemical reaction parameter recede the concentration field profiles while increase with raises the values of Soret number. Increasing Biot, and Dufour numbers significantly grows the thermal field profiles. Induced magnetic field grows with larger values of fluid viscosity parameter. The findings of this study are important due to its application in magnetohydrodynamics pumps, polymer manufacturing, fins designs, and food processing.Item Application of Odd Lomax log-logistic distribution to cancer data(Elsevier, 2024-03) Kailembo, Benson Benedicto; Gadde, Rao Srinivasa; Kirigiti, Peter JosephatThe effectiveness of the parental distribution is modified in this article by adding flexibility, allowing it to capture all characteristics of the provided real-world data sets. This is accomplished by using the T-X class of distributions to generalize the parental distribution. Odd Lomax loglogistic distribution or OLLLD in short, is the name of the generalized parental distribution. The fundamental statistical properties of OLLLD are explicitly expressed. The maximum likelihood estimation approach is used to estimate the unidentified OLLLD parameters. In order to investigate the fit of the approach employed in estimating the parameters of OLLLD, the data are generated and an investigation done. Again, the ability of OLLLD is evaluated by fitting it to the real survival time data set of breast cancer.Item Designing of multiple dependent state sampling plan for Type-II generalized half logistic distribution(Informa UK Limited, 2024-03-22) Jilani, Sd.; Rao, Gadde Srinivasa; Rao, A. Vasudeva; Yilun ShangIn this study, we propose the multiple dependent state (MDS) sampling plan for a time truncated life test when the lifetime of product follows the Type-II Generalized Half Logistic Distribution (TGHLD). The quality of the product is considered in terms of percentile lifetime. The optimal plan parameters of the our proposed MDS sampling plan, such as the sample size, the acceptance and rejection numbers, and the number of preceding lots needed for making the decision whether to accept or reject the current lot, are determined using the approach of two points on the operating characteristic curve. Tables are obtained for various values of shape parameter and results are discussed. The real data analysis is given to illustrate the applicability of the proposed in the industry. Comparison is also made with the existing plans.Item Charged anisotropic composite stellar object with strange, polytropic and gaseous matter(Elsevier, 2024-08) Olengeile, Lilian; Sunzu, Jefta M.; Mkenyeleye, Jason M.In this study, we build a charged star model with three layers with distinct equations of state. The core, intermediate layer, and envelope layer obey linear, polytropic, and Chaplygin equations of state, respectively. The model satisfies the physical requirements for the matter variables, gravitational potentials, and stability conditions. We have generated within-acceptable range masses and radii for stars. We also recover the masses and radii for the stars PSRJ1903+0327, PSRJ1614-2230, SAXJ1808.4-3658, Vela X-1, and EXO1785-248 from earlier investigations which shows astrophysical significance of our model.Item A finite difference study of radiative mixed convection MHD heat propagating Casson fluid past an accelerating porous plate including viscous dissipation and Joule heating effects(Elsevier, 2024-04) Reddy, B. Prabhakar; Matao, P.M.; Sunzu, J.M.A finite difference numerical simulation scrutiny is executed to evaluate the combined impacts of heat generation, buoyancy forces, viscous dissipation and Joule heating in unsteady hydromagnetic mixed convective chemically reactive and radiative Casson fluid flowing along an exponentially accelerating permeable vertical plate engrossed in a porous media by considering ramp surface concentration and temperature. The dimensionless non-linear coupled PDEs describing the flow model are dealt numerically by adopting the competent implicit Crank-Nicolson finite difference procedure. The variance of velocity, temperature, and concentration distributions are exposed via graphical representations due to the dissimilarity of the flow restrained parameters. Computational outcomes of the skin-friction, Nusselt and the Sherwood numbers are portrayed in the tabular pattern. The final outcomes of the research exposed that the impacts of thermal radiation, viscous dissipation, and heat production parameters enlarges the temperature and velocity distributions. The fluid motion deflates for growing Casson parameter and magnetic field intensity. The rising chemical reaction parameter suppresses the concentration and velocity distributions. Very importantly it is distinguished that fluid momentum, temperature, and concentration are quicker in the instance of isothermal plate temperature than ramp wall temperature. This kind of research may find specific industrial and medical utilizations such as glass manufacturing, crude oil purification, lubrication, paper production, blood transport study in cardiovascular design, etc.Item A review of the mathematical models for the impact of seasonal weather variation and infections on prey predator interactions in Serengeti ecosystem(Scientific Research Publishing, 2022) Charles, Raymond; Makinde, Oluwole Daniel; Kung’aro, MonicaInteraction between prey and predator species is a complex and non-linear process. Understanding various phenomena in the dynamics of prey-predator systems is vital to both mathematical ecology and conservation biology. Mathematical models on prey-predator systems have been the hot sport providing important information regarding the interactions of prey and predator species in various ecosystems. In this paper, a review of the available mathematical models on prey-predator systems was done. Our aim was to assess their structure, behaviour, available control strategies, population involved and their ability in predicting the future behaviour of the ecosystems. We observed diversities in the reviewed mathematical models, some model incorporated factors such as drought, harvesting and prey refuge as the factors that affect ecosystems, some ignored the contribution of environmental variations while others considered the variable carrying capacity. Most of the models reviewed have not considered the contribution of diseases and seasonal weather variation in the dynamics of prey predator systems. Some of the reviewed models do not match the real situation in most modelled ecosystems. Thus, to avoid unreliable results, this review reveals the need to incorporate seasonal weather variations and diseases in the dynamics of prey predator systems of Serengeti ecosystem.Item The odd log-logistic generalized exponential distribution: Application on survival times of chemotherapy patients data(F1000Research, 2022) Fulment, Arnold K.; Gadde, Srinivasa Rao; Peter, Josephat KThe creation of developing new generalized classes of distributions has attracted applied and theoretical statisticians owing to their properties of flexibility. The development of generalized distribution aims to find distribution flexibility and suitability for available data. In this decade, most authors have developed classes of distributions that are new, to become valuable for applied researchers. This study aims to develop the odd log-logistic generalized exponential distribution (OLLGED), one of the lifetime newly generated distributions in the field of statistics. The advantage of the newly generated distribution is the heavily tailed distributed lifetime data set. Most of the probabilistic properties are derived including generating functions, moments, and quantile and order statistics. Estimation of the model parameter is done by the maximum likelihood method. The performance of parametric estimation is studied through simulation. Application of OLLGED and its flexibilities is done using two data sets and while its performance is done on the randomly simulated data set. The application and flexibility of the OLLGED are ensured through empirical observation using two sets of lifetime data, establishing that the proposed OLLGED can provide a better fit in comparison to existing rival models, such as odd generalized log- logistic, type-II generalized log-logistic, exponential distributions, odd exponential log-logistic, generalized exponential, and log-logistic.Item Mathematical model for the effects of intervention measures on the transmission dynamics of Tungiasis(Islamic Azad University, 2021) Shinzeh, Jairos Kahuru; Luboobi, Livingstone S.Tungiasis is a zoonosis affecting human beings and a broad range of domestic and syvatic animals caused by the penetration of an ectoparasite known as “Tunga penetrans” into the skin of its host. In this paper we derive and analyze a mathematical model of control measures and then examine the effect of the control strategies on the transmission dynamics of Tungiasis. The model effective reproduction number is determined using the next generation operator method and the analysis is performed using the stability theory of the differential equations. The analytical results show that the disease free equilibrium is locally asymptotically stable when and unstable when . Using Meltzer matrix stability theorem we found that the disease free equilibrium is globally asymptotically stable and by Lyapunov method, the endemic equilibrium is globally asymptotically stable when . From the numerical simulation it was observed that the control strategies have positive impact on the reduction of transmission of Tungiasis disease and that they work better in combination than when applied as singly. The results from simulations will help the decision makers from national health care to advise people at risk with Tungiasis to apply the control strategies based on: educational campaign, personal protection, personal treatment, environmental hygiene and insecticides application to control the flea.Item Charged anisotropic models via embedding(Springer, 2021) Mathias, Alberto K.; Maharaj, Sunil D.; Sunzu, Jefta M.; Mkenyeleye, Jason M.We generate exact solutions to the Einstein–Maxwell field equations by analysing the embedding condition. We obtain a relationship between gravitational potentials that helps to solve the embedding condition and integrate the field equations. Our choice of the measure of anisotropy and electric field are physically realistic. Our model contains several previously known solutions as special cases. These include the investigations of interior Schwarzchild metric, Finch and Skea, Hansraj and Maharaj, Feroze and Siddiqui, and Manjonjo, Maharaj and Moopanar. We also describe the structure and properties of the relativistic star by including graphical representations. Our analysis shows that the body is stable, all energy conditions are satisfied, the regularity condition is not violated, forces under equilibrium condition are balanced, all matter variables are well behaved and the matching conditions are satisfied at the boundary of the relativistic star.Item Modelling african trypanosomiasis in human with optimal control and cost-effectiveness analysis(The Korean Society for Computational and Applied Mathematics, 2021) Gervas, Hamenyimana Emanuel; Hugo, Alfred K.Human African Trypanosomiasis (HAT) also known as sleeping sickness, is a neglected tropical vector borne disease caused by trypanosome protozoa transmitted by bites of infected tsetse fly. The basic reproduction number, R0 derived using the next generation matrix method which shows that the disease persists in the population if the value of R0 > 1. The numerical simulations of optimal control model carried out to determine the control strategy that can combat HAT under the minimum cost. The results indicate that, the use of both education campaign, treatment and insecticides are more efficient and effective to eliminate HAT in African community but too costly. Furthermore, the cost-effectiveness of the control measures (education campaign, treatment and insecticides) were determined using incremental cost-effectiveness ratio (ICER) approach and the results show that, the use of education and treatment of infected people as the best cost effective strategy compared to other strategies.Item Mathematical modeling of the transmission dynamics of amoebiasis with some interventions(Europe PMC, 2022) Mwaijande, Stephen Edward; Mpogolo, Godfrey EdwardA mathematical model for amoebiasis is developed and presented. The model captures some control interventions such as screening, treatment, and sanitation. The effective reproductive number is computed and is used to analyze the stability of the model system. Sensitivity analysis is used to investigate the parameters that impact the transmission of the disease; as such, it could need more attention to bring the disease to an end. Numerical results show a reduction in infections when at least each of the control measures considered is applied efficiently. Moreover, the findings show that carriers play a potential role in the prevalence of amoebiasis, ignoring them undermines the efforts of containing this epidemic. On the other hand, sensitivity analysis shows that indirect transmission contributes to more infections than direct transmission.Item Competency and performance gap between executive and non-executive employees of banks in Kerala, India(WJRR Journal, 2021) Balan, Ramkumar T.This paper assesses the Competency and Performance of bank employees of Four banks in Kerala, India. The gap in the performance and competency of executive and non- executive employees of the banks were determined. The linear regression model is estimated on dimensions of this efficiency measures. Also logistic regression models on competency and performance for executive and non-executive employees were identified. The dimensions of effectiveness of employees in a banking work place on both groups were compared. The gap in the characteristics of two sets of employees is illustrated for various demographic groups.Item Probability distribution analysis of patients arriving at Regional Referral hospital Dodoma, Tanzania (2017-2018).(World Wide Journals PVT LTD, 2021) Balan, Ramkumar T.; Loibor, Julius MoingetHealth care is essential to the general welfare of society. Studying the hospital patients' data distribution through the probability distribution analysis model is very important in the health care system. This study has examined the hospital inpatients and outpatients' daily data for two years taken from DRRH through the hospital electronic health management information system. This study seeks to identify comprehensively the appropriate statistical distributions on inpatient and outpatient data of the DRR hospital. The primary fitting of the distributions to inpatient and outpatient data was performed by the Easyfit 5.5 Profession statistical software. The software deals with 61 continuous distributions, including three goodness of fit test for raw data and two for frequency data. Kolmogorov- Smirnov test, Anderson- Darling test and Chi-Square test only for raw data. The parameters of the selected distributions were estimated by the maximum likelihood method. The final selection of fittest distribution was done with respect to the minimum calculated value of log-likelihood and hence AIC and BIC values. The research work revealed that Generalized Extreme Value distribution is the best-fit distribution model for the hospital inpatient daily data. Also, the Dagum distribution followed by Log logistic (3P) distribution was selected to be the best-fit distribution model representing the hospital outpatients' daily data.Item Numerical study on heat absorbing MHD radiating and reacting flow past an impulsively moving vertical plate with ramped temperature and concentration with Hall current(Taylor & Francis, 2021) Reddy, B. Prabhakar; Makinde, O. D.In this paper, we made elaborate investigation of the Hall current and radiation effects on MHD heat absorbing unsteady natural convection flow of a viscous incompressible electrically conducting fluid past an impulsively moving infinite vertical plate with ramped temperature and concentration in the presence of first order chemical reaction. The constructing coupled PDEs of the model along with initial and boundary conditions are solved numerically by utilizing the robust FEM. The effects of significant parameters on the primary and secondary velocities, temperature and concentration within the boundary layer are examined. The computational assessment of the primary and secondary shear stresses, rate of heat and mass transfer at the plate surface are put in tabular form. The thermal and mass buoyancy effects elevate both primary and secondary velocity components whilst reverse trend takes place when radiation and chemical reaction parameters are increased. Both primary and secondary velocity components decrease with increasing magnetic parameter whilst opposite trend are noticed with increasing Hall parameter. An increase in Prandtl number and radiation parameter results to reduce temperature distribution. The concentration distribution decreases with increase in Schmidt number and chemical reaction parameter. The significant difference between the fluid velocities is noticed due to the ramped and isothermal boundary conditions.Item Modelling transmission dynamics of coronavirus with infected immigrants in Tanzania(Kenyatta University, 2021) Alfred, H.; Laurencia, N.; Raymond, K.This paper proposes and analyses a compartmental deterministic nonlinear model for coronavirus transmission dynamics in Tanzania. The differential equation of stability theory is used to qualitatively evaluate the mathematical model. The basic reproductive number obtained, which represents the epidemic threshold for coronavirus elimination or persistence. Local stability analysis was performed with parameter values calculated based on data availability and accessibility in Tanzania. The findings revealed that infected immigrants have a greater influence on COVID-19 transmission in a population. Furthermore, it demonstrates that an increase in the number of infected immigrants may result in a high infection rate in the community. Besides that, social interactions among members of the community increase the rate of transmission.Item On some fixed point theorems for multivalued F-contractions in partial metric space(De Gruyter Open Access, 2021) Kumar, Santosh; Luambano, SholasticaAltun et al. explored the existence of fixed points for multivalued F-contractions and proved some fixed point theorems in complete metric spaces. This paper extended the results of Altun et al. in partial metric spaces and proved fixed point theorems for multivalued F-contraction mappings. Some illustrative examples are provided to support our results. Moreover, an application for the existence of a solution of an integral equation is also enunciated, showing the materiality of the obtained results.Item Designing of multiple dependent state repetitive sampling plan for type-II generalized half logistic distribution(Springer Nature, 2021) Rao, Gadde Srinivasa; Jilani, S. D.; Rao, A. VasudevaIn this article, we present a new multiple dependent state repetitive (MDSR) sampling plan for attributes based on consider Type-II generalized half logistic distribution (TGHLD) with known shape parameter is consider here. The optimal parameter of the proposed plan is used to determine the operating characteristic (OC) curve approach using two point’s method. The results are explained with tables. We have made the comparison of proposed design with the usual multiple dependent state (MDS) sampling plans, repetitive acceptance sampling plan (RASP) and single sampling plan (SSP) in Average Sample Number (ASN). The proposed plan is demonstrated with the help of real- life data.Item Objective Bayesian inference for the capability index of the Gamma distribution(John Wiley & Sons, Inc., 2021) de Almeida, Marcello Henrique; Ramos, Pedro Luiz; Rao, Gadde Srinivasa; Moala, Fernando AntonioThe Gamma distribution has been applied in research in several areas of knowledge, due to its good flexibility and adaptability nature. Process capacity indices like 𝐶𝑝𝑘 are widely used when the measurements related to the data follow a normal distribution. This article aims to estimate the 𝐶𝑝𝑘 index for nonnormal data using the Gamma distribution. We discuss maximum likelihood estimation and a Bayesian analysis through the Gamma distribution using an objective prior, known as a matching prior that can return Bayesian estimates with good properties for the 𝐶𝑝𝑘. A comparative study is made between classical and Bayesian estimation. The proposed Bayesian approach is considered with the Markov chain Monte Carlo method to generate samples of the posterior distribution. A simulation study is carried out to verify whether the posterior distribution presents good results when compared with the classical approach in terms of the mean relative errors and the mean square errors, which are the two commonly used metrics to evaluate the parameter estimators. Based on the real dataset, Bayesian estimates and credibility intervals for unknown parameters and the prior distribution are achieved to verify if the process is under control.