Mathematics
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Mathematics
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Item COA-SOWUNMI'S LEMMA AND ITS APPLICATION TO THE STABILITY ANALYSIS OF EQUILIBRIUM STATES OF THE NON-LINEAR AGE-STRUCTURED POPULATION MODEL(International Journal of Mathematics and Physical Sciences Research, 0205-04-10) Akinwande, N. I.; Somma, Samuel AbuAbstract: In this work, we present a result in the form of a lemma which we name COA-Sowunmi’s Lemma, its proof and application to the stability analysis of the transcendental characteristics equation arising from the perturbation of the steady state of the non-linear age-structured population model of Gurtin and MacCamy [11]. Necessary condition for the asymptotic stability of the equilibrium state of the model is obtained in the form of constrained inequality on the vital parameters of the model. The result obtained is then compared with that of an earlier work by the [4].Item A MATHEMATICAL MODEL OF MEASLES DISEASE DYNAMICS(Journal of Science, Technology, Mathematics and Education (JOSTMED), 2012-08-25) Abubakar, Samuel; Akinwande, N. I.; Abdulrahman, S.In this paper a Mathematical model was proposed for measles disease dynamics. The model is a system of first order ordinary differential equations with three compartments: Susceptible S(t); Infected I(t) and Recovered R(t). The equilibrium state for both Disease Free and Endemic equilibrium are obtained. Conditions for stability of the Disease Free and Endemic equilibrium are obtained from characteristics equation and Bellman and Cooke theorem respectively. The hypothetical values were used to analyze the Endemic Equilibrium and the result was presented in tabular form. The results from the Disease Free and Endemic Equilibrium state showed that once the epidemic breaks out, the population cannot sustain it.Item Computational Analysis of a one-dimensional nonlinear reactive contaminant flow with an initial continuous point source by homotopy-perturbation method.(Journal of the Nigerian Association of Mathematical Physics, 2012-11-05) Aiyesimi, Y. M.; JIMOH, OMANANYI RAZAQIn this paper, a Homotopy-perturbation analysis of a non–linear reactive contaminant flow equation with initial continuous point source is provided. The equation is described by advection, diffusion and adsorption. We assume that the adsorption term is modeled by Freudlich Isotherm. We provide an approximation of this equation using homotopy-perturbation transformation and solve the resulting linear equations analytically. The graphs of the concentration against the distance, reaction parameter and time are presented and analyzed to determine the effects of increase in the reaction coefficient, time and distance on the concentration. Findings from this research show that the concentration of the contaminant decreases with time and decreases faster when the value of the reaction parameter α is high.Item A Homotopy-Perturbation analysis of the non-linear contaminant transport problem in one dimension with an initial continuous point source.(NIGERIAN JOURNAL OF TECHNOLOGICAL RESEARCH (NJTR), 2013-02-28) Aiyesimi, Y. M.; JIMOH, OMANANYI RAZAQIn this research work, a Homotopy-perturbation analysis of a non –linear contaminant flow equation with an initial continuous point source is provided. The equation is characterized by advection, diffusion and adsorption. We assume that the adsorption term is modeled by Freudlich Isotherm. We provide an approximation of this equation using homotopy-perturbation transformation and solve the resulting linear equations analytically by homotopy-perturbation method. Graphs are plotted using the solution obtained from the method and the results are presented, discussed and interpreted. The research findings show that the concentration increases with time and decreases as distance increases.Item Comparative Analysis of a Non-Reactive Contaminant Flow Problem for Constant Initial Concentration in Two Dimensions by Homotopy-Perturbation and Variational Iteration Methods.(Pacific Journal of Science and Technology, 2013-05-10) JIMOH, OMANANYI RAZAQIn this paper, we present a comparative analysis of non-reactive contaminant flow problem for constant initial concentration in two dimensions by homotopy-perturbation and Variational Iteration method. We provide an approximation of this equation using homotopy-perturbation transformation and solve the resulting linear equations analytically by homotopy-perturbation method (HPM) and Variational Iteration Method (VIM). Graphs are plotted using the solution obtained from the method and the results are presented and discussed.Item Stability Analysis of the Disease-Free Equilibrium State for Yellow Fever Disease(Development Journal of Science and Technology Research, 2013-08-22) Bawa, M.,; Abdulrahman, S.; Abubakar, Samuel; Aliyu, Y. B.In this paper, we developed and anaysed the disease-free equilibrium state of a new mathematical model for the dynamics of yellow fever infection in a population with vital dynamics, incorporating vaccination as control measure. We obtained the effective basic reproduction number which can be used to control the transmission of the disease and hence, established the conditions for local and global stability of the disease free equilibrium.Item A Mathematical Study of Contaminant Transport with First-order Decay and Time-dependent Source Concentration in an Aquifer(Universal Journal of Applied Mathematics, 2013-11-05) Olayiwola, R. O.; Jimoh, O. R.; Yusuf, A.; Abubakar, SamuelA mathematical model describing the transport of a conservative contaminant through a homogeneous finite aquifer under transient flow is presented. We assume the aquifer is subjected to contamination due to the time-dependent source concentration. Both the sinusoidally varying and exponentially decreasing forms of seepage velocity are considered for the purposes of studying seasonal variation problems. We use the parameter-expanding method and seek direct eigenfunctions expansion technique to obtain analytical solution of the model. The results are presented graphically and discussed. It is discovered that the contaminant concentration decreases along temporal and spatial directions as initial dispersion coefficient increases and initial groundwater velocity decreases. This concentration decreases as time increases and differs at each point in the domain.Item Approximate Solution of SIR Infectious Disease Model Using Homotopy Perturbation Method (HPM).(The Pacific Journal of Science and Technology, 2013-11-13) S. Abubakar; N.I. Akinwande; JIMOH, OMANANYI RAZAQ; F.A. Oguntolu; O.D. OgwumuIn this paper we proposed a SIR model for general infectious disease dynamics. The analytical solution is obtained using the Homotopy Perturbation Method (HPM). We used the MATLAB computer software package to obtain the graphical profiles of the three compartments while varying some salient parameters. The analysis revealed that the efforts at eradication or reduction of disease prevalence must always match or even supersede the infection rate.Item A Mathematical Study of Contaminant Transport with First-order Decay and Time-dependent Source Concentration in an Aquifer(Universal Journal of Applied Mathematics, 2013-12-10) Rasaq O. Olayiwola; JIMOH, OMANANYI RAZAQ; Abdulhakeem Yusuf; Samuel AbubakarA mathematical model describing the transport of a conservative contaminant through a homogeneous finite aquifer under transient flow is presented. We assume the aquifer is subjected to contamination due to the time-dependent source concentration. Both the sinusoidally varying and exponentially decreasing forms of seepage velocity are considered for the purposes of studying seasonal variation problems. We use the parameter-expanding method and seek direct eigenfunctions expansion technique to obtain analytical solution of the model. The results are presented graphically and discussed. It is discovered that the contaminant concentration decreases along temporal and spatial directions as initial dispersion coefficient increases and initial groundwater velocity decreases. This concentration decreases as time increases and differs at each point in the domain.Item Bifurcation Analysis on the Mathematical Model of Measles Disease Dynamics(Universal Journal of Applied Mathematics, 2013-12-12) Abubakar, Samuel; Akinwande, N. I.; Abdulrahman, S.; Oguntolu, F. A.In this paper we proposed a Mathematical model of Measles disease dynamics. The Disease Free Equilibrium (DFE) state, Endemic Equilibrium (EE) states and the characteristic equation of the model were obtained. The condition for the stability of the Disease Free equilibrium state was obtained. We analyze the bifurcation of the Disease Free Equilibrium (DFE) and the result of the analysis was presented in a tabular form.Item Approximate Solution of SIR Infectious Disease Model Using Homotopy Pertubation Method (HPM)(Pacific Journal of Science and Technology (PJST), 2013-12-25) Abubakar, Samuel; Akinwande, N. I.; Jimoh, O. R.; Oguntolu, F. A.; Ogwumu, O. D.In this paper we proposed a SIR model for general infectious disease dynamics. The analytical solution is obtained using the Homotopy Perturbation Method (HPM). We used the MATLAB computer software package to obtain the graphical profiles of the three compartments while varying some salient parameters. The analysis revealed that the efforts at eradication or reduction of disease prevalence must always match or even supersede the infection rate.Item Application of Computerized Monte Carlo Simulation in Evaluating Definite Integrals and Testing of the Properties of Probability Density Functions(International Journal of Modern Mathematical Sciences,, 2014-05) Ogwumu, David. O,; James, Friday. E; Abubakar, SamuelThis work explores a certain application of the Monte Carlo simulation technique in evaluating definite Integrals and x-rays the complexity of solving realistic models by mathematical methods to arrive at an analytic solution. The study has shown that certain complex problems that cannot be solved analytically could be subject to simulations to provide approximate solutions. The work equally studies numerous definite Integrals but provides a result for few through which it is possible to make a generalization in the end of the study. Five probability distributions were highlighted in this work (among others that were investigated) and their properties by Monte Carlo simulation using a PASCAL program where random numbers were generated after numerous trials. Some areas of applications of simulation and the probability distributions studied have been discussed in this study alike.Item Mathematical Analysis of a Contaminant Flow in a Finite Medium using the Weighted Residual Method(Ilorin Journal of Science, 2015-02-01) JIMOH, OMANANYI RAZAQ; Aiyesimi, Y. M.; Jiya, M.; Bolarin, G. A.In this paper, a Galerkin weighted Residual method is used in providing an analytical solution of two-dimensional contaminant flow problem with non-zero initial concentration. The equation is described by advection, dispersion, adsorption, first order decay and zero-order source. It is assumed that the adsorption term is modeled by Freudlich isotherm. Using Bubnov-Galerkin method, the governing equation was converted to a discrete problem. Thereafter, the approximate solution of the resulting system of initial value problem was obtained. The results obtained are expressed in graphical form to show the effect of change in the parameters on the concentration of the contaminants. From the analysis of the results, it was discovered that the contaminant concentration decreases with increase in the distance from the origin while it increases with increase in the zero-order source coefficient.Item A Mathematical Model for Estimating the Weight of Human Beings Using Some Anthropometric Parameters (A Case Study of Taraba State of Nigeria’s Community)(British Journal of Mathematics & Computer Science, 2015-03-27) Ogwumu, O. D.; Amoo, S. A.; Eguda, F. Y.; Adeyefa, E. O.; Abubakar, SamuelThe research is concerned with the development of a mathematical model for estimating the body weight of human beings in relation to some of their anthropometric parameters (height and waist sizes). The model was optimized to know whether it is possible for humans to have a maximum or minimum body weight. However, the optimization result showed that there is no specific body weight that could be called a maximum or minimum. Emphasis was laid mainly on a particular proportion of Nigerians from the north- west geopolitical zone (as a case study ) in order to be able to make generalizations about the entire country and beyond. Hence, the population sample for the research was the Taraba State of Nigeria’s Community. Moreover, several recommendations were made at the end of the model analysis which when adhered to, would bring about some medical breakthroughs to the entire human populace.Item Error and Convergence Analysis of a Hybrid Runge- Kutta Type Method(International Journal of Science and Technology Publications UK, 2015-04) Muhammad R; Y. A Yahaya,; A.S AbdulkareemImplicit Runge- Kutta methods are used for solving stiff problems which mostly arise in real life problems. Convergence analysis helps us to determine an effective Runge- Kutta Method (RKM) to use, but due to the loss of linearity in Runge –Kutta Methods and the fact that the general Runge –Kutta Method makes no mention of the differential equation makes it impossible to define the order of the method independently of the differential equation. In this paper, we derived a hybrid Runge -Kutta Type method (RKTM) for 𝑘=1, obtained the order and error constant and convergence analysis of the method.Item Stability Analysis of the Disease Free Equilibrium State of a Mathematical Model of Ebola Fever Disease Epidemic(. International Journal of Innovation in Science and Mathematics (IJISM), 2015-06-01) Abah, R. T.,; Akinwande, N. I.; Enagi, I. A.; Kuta, F. A.,; Abdulrahaman, S.; Somma, Samuel AbuEbola fever has been a major cause of death in recent times. It has claimed thousands of lives in West Africa since 2014 till date. Very few mathematical models have been developed to study its transmission dynamics. In this paper the stability analysis of the disease free equilibrium state of a mathematical model of Ebola Fever disease epidemic were carried out.Item Modified Maternally-Derived-Immunity Susceptible Infectious Recovered (MSIR) Model of Infectious Disease: Existence of Equilibrium and Basic Reproduction Number(Nigerian Journal of Technological Research, 2015-06-03) Somma, Samuel Abu; Akinwande, N. I.; Gana, P.; Abdulrahaman, S.; Ashezua, T. T.In this paper we modified the MSIR Model by adding the vaccination rate and death rate due to the disease to the existing MSIR model. We verified the positivity of the solution and obtained the Disease Free Equilibrium (DFE) of the model. We also determined the basic reproduction number using next generation Matrix and Jacobian matrix method.Item A Mathematical Model of a Yellow Fever Dynamics with Vaccination(Journal of the Nigerian Association of Mathematical Physics, 2015-11) Oguntolu, F. A.; Akinwande, N. I.; Somma, Samuel Abu; Eguda, F. Y.; Ashezua. T. T.In this paper, a mathematical model describing the dynamics of yellow fever epidemics, which involves the interactions of two principal communities of Hosts (Humans) and vectors (mosquitoes) is considered .The existence and uniqueness of solutions of the model were examined by actual solution. We conduct local stability analysis for the model. The results show that it is stable under certain conditions. The system of equations describing the phenomenon was solved analytically using parameter-expanding method coupled with direct integration. The results are presented graphically and discussed. It is discovered that improvement in Vaccination strategies will eradicate the epidemics.Item Local Stability Analysis of a Tuberculosis Model incorporating Extensive Drug Resistant Subgroup(Pacific Journal of Science and Technology (PJST), 2017-05-20) Eguda, F. Y.; Akinwande, N. I.; Abdulrahman, S.; Kuta, F. A.; Somma, Samuel AbuThis paper proposes a mathematical model for the transmission dynamics of Tuberculosis incorporating extensive drug resistant subgroup. The effective reproduction number was obtained and conditions for local stability of the disease R c free equilibrium and endemic equilibrium states were established. Numerical simulations confirmed the stability analysis and further revealed that unless proper measures are taken against typical TB, progression to XDR-TB, mortality and morbidity of infected individuals shall continue to rise.Item Semi-analytical Study of a One-dimensional Contaminant Flow in a Finite Medium(Journal of Applied Science Environmental Management (JASEM), 2017-05-21) JIMOH, OMANANYI RAZAQ; AIYESIMI, YM; JIYA, M.; BOLARIN, GAThe Bubnov-Galerkin weighted residual method was used to solve a onedimensional contaminant flow problem in this paper. The governing equation of the contaminant flow, which is characterized by advection, dispersion and adsorption was discretized and solved to obtain the semi-analytical solution. The adsorption isotherm was assumed to be of Freudlich type. The results obtained were expressed in graphical form to show the effect of change in the parameters on the concentration of the contaminants. From the analysis of the results, it was discovered that the contaminant concentration decreases with increase in the distance from the origin as the dispersion and velocity coefficient decrease.