Mathematics
Permanent URI for this collectionhttp://197.211.34.35:4000/handle/123456789/100
Mathematics
Browse
Item A TWO POINT BLOCK HYBRID METHOD FOR SOLVING STIFF INITIAL VALUE PROBLEMS(JOURNAL OF MATHEMATICAL SCIENCES, 2011) Muhammad RIn this paper, a self starting hybrid method of order (3, 3,3) is proposed for the solution of stiff initial value problem of the form y' = f(x.y). The continous formation of the integrator enables us to differentiate and evaluate at grid and off grid points. The schemes compared favourably with exact results and results from Okunuga (2008)Item Reformulation of Block Implicit Linear Multistep Method into Runge Kutta Type Method for Initial Value Problem(International Journal of Science and Technology Publications UK, 2015-04) Muhammad R; Y.A Yahaya; A.S. AbdulkareemIn this research work, we reformulated the block hybrid Backward Differentiation Formula (BDF) for 𝑘=4 into Runge Kutta Type Method (RKTM) of the same step number for the solution of Initial value problem in Ordinary Differential Equation (ODE). The method can be use to solve both first and second order (special or general form). It can also be extended to solve higher order ODE. This method differs from conventional BDF as derivation is done only onceItem A MATHEMATICAL MODEL OF YELLOW FEVER DISEASE DYNAMICS INCORPORATING SPECIAL SATURATION INTERACTIONS FUNCTIONS(1st SPS Biennial International Conference Federal University of Technology, Minna, Nigeria, 2017-05-05) Akinwande, N. I.; Abdulrahman, S.; Ashezua, T. T.; Somma, Samuel AbuWe proposed an Mathematical Model of Yellow Fever Disease Dynamics Incorporating Special Saturation Process functions, obtained the equilibrium states of the model equations and analyzed same for stability. Conditions for the elimination of the disease in the population are obtained as constraint inequalities on the parameters using the basic reproduction number 0 R demographic and epidemiological data. . Graphical simulations are presented using someItem SENSITIVITY ANALYSIS FOR THE MATHEMATICAL MODELING OF MEASLES DISEASE INCORPORATING TEMPORARY PASSIVE IMMUNITY(1st SPS Biennial International Conference Federal University of Technology, Minna, Nigeria, 2017-05-05) Somma, Samuel Abu; Akinwande, N. I.Measles is an airborne disease which spreads easily through the coughs and sneezes of those infected. Measles antibodies are transferred from mothers who have been vaccinated against measles or have been previously infected with measles to their newborn children. These antibodies are transferred in low amounts and usually last six months or less. In this paper a mathematical model of measles disease was formulated incorporating temporary passive immunity. There exist two equilibria in the model; Disease Free Equilibrium (DFE) and Endemic Equilibrium (EE). The Disease Free Equilibrium (DFE) state was analyzed for local and global stability. The Basic Reproduction Number 0 R was computed and used to carried out the sensitivity analysis with some parameters of the mode. The analysis shows that as contact rate increases the 0 as the vaccination rate v increases the 0 R decreases. Sensitive parameters with the R R 0 increases and were presented graphically. The disease will die out of the population if the attention is given to high level immunization.Item Local Stability Analysis of a Tuberculosis Model incorporating Extensive Drug Resistant Subgroup(Pacific Journal of Science and Technology, 2017-05-25) 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 c R was obtained and conditions for local stability of the disease 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 Local Stability Analysis of a River Blindness Disease Model with Control(Pacific Journal of Science and Technology., 2018-05-12) Oguntolu, F. A.; Bolarin, G. A.; Somma, Samuel Abu; Bello, A. O.In this paper, a mathematical model to study the dynamics of River Blindness is presented. The existence and uniqueness of solutions of the model were examined by actual solution. The effective reproduction number was obtained using the next generation matrix. The Disease Free Equilibrium (DFE) State was obtained and analysed for stability. It was found that, the DFE State is Locally Asymptotically Stable (LAS) if the effective unstable if reproduction number R 0 1 .Item Mathematical Modelling for the Effect of Malaria on the Heterozygous and Homozygous Genes(6th International Conference on Mathematical Analysis and Optimization: Theory and Applications (ICAPTA 2019), 2019-03-29) Abdurrahman, N. O.; Akinwande, N. I.; Somma, Samuel AbuThis paper models the effect of malaria on the homozygous for the normal gene (AA), heterozygous for sickle cell gene (AS) and homozygous for sickle cell gene (SS) using the first order ordinary differential equation. The Diseases Free Equilibrium (DFE) was obtained and used to compute the basic reproduction Number Ro. The local stability of the (DFE) was analyzed.Item Differential Transformation Method (DTM) for Solving Mathematical Modelling of Monkey Pox Virus Incorporating Quarantine(Proceedings of 2nd SPS Biennial International Conference Federal University of Technology, Minna, Nigeria, 2019-06-26) Somma, Samuel Abu; Akinwande, N. I.; Abdurrahman, N. O.; Zhiri, A. B.In this paper the Mathematical Modelling of Monkey Pox Virus Incorporating Quarantine was solved semi-analytically using Differential Transformation Method (DTM). The solutions of difference cases were presented graphically. The graphical solutions gave better understanding of the dynamics of Monkey pox virus, it was shown that effective Public Enlightenment Campaign and Progression Rate of Quarantine are important parameters that will prevent and control the spread of Monkey Pox in the population.Item Local and Global Stability Analysis of a Mathematical Model of Measles Incorporating Maternally-Derived-Immunity(Proceedings of International Conference on Applied Mathematics & Computational Sciences (ICAMCS),, 2019-10-19) Somma, Samuel Abu; Akinwande, N. I.; Gana, P.In this paper, the local stabilities of both the Disease Free Equilibrium (DFE) and Endemic Equilibrium (EE) were analyzed using the Jacobian matrix stability technique. The global stabilities were analyzed using Lyapunov function. The analysis shows that the DFE is locally and globally stable if the basic reproduction number R 0 1 R 0 1 and R 0 1 respectively. The EE is also locally and globally stable if . Vaccination and recovery rates have been shown from the graphical presentation as the important parameter that will eradicate measles from the population.Item Mathematical Modeling of Algae Population Dynamics on the Surface of Water(2019-11-12) Abdurrahman, O. N.; Akinwande, N. I.; Somma, Samuel AbuThe paper presented an analytical solution of the exponential growth model of algae population dynamics on the water surface. The Computer Symbolic Algebraic Package, MAPLE is used to simulate the graphical profiles of the population with time while varying the parameters, such as diffusion and rate of change of algae density, governing the subsistence or extinction of the water organisms.Item Improving Accuracy Through the Three Steps Block Methods For Direct Solution of Second Order Initial Value Problem Using Interpolation and Collocation Approach(KASU JOURNAL OF MATHEMATICAL SCIENCES (KJMS), 2020-06) R. Muhammad; I. D. ZakariyauThis paper presents three-step block method for direct solution of second order initial value problems of ordinary differential equations. The collocation and interpolation approach was adopted to generate a continuous block method using power series as basis function. The properties of the proposed approach such as order, error constant, zero-stability, consistency and convergence were also investigated. The proposed method competes favorably with exact solution and the existing methods.Item An Implicit Runge-Kutta Type Method for the Solution of Initial Value Problems(KASU JOURNAL OF MATHEMATICAL SCIENCES, 2020-06) R. Muhammad; Y. A. Yahaya; A. S. AbdulkareemIn this research paper, an implicit block hybrid Backward Differentiation Formula (BDF) for 𝑘=2 is reformulated into a Runge-Kutta Type Method (RKTM) of the same step number. The method can be used to solve both first and second order (special or general form) initial value problem in Ordinary Differential Equation (ODE). This method differs from conventional BDF as derivation is done only once. It can also be extended to solve higher order ODE.Item Stability Analysis for Mathematical Modeling of Dengue Fever Transmission and Control(Proceedings of International Conference on Contemporary Developments in Mathematical Sciences (ICCDMS), 2021-04-13) Aliyu, A. H.; Akinwande, N. I.; Somma Samuel AbuDengue fever is one of the greatest health challenges in the present world. In this work, mathematical modeling of dengue fever transmission and control was formulated. The model considered the human population h N and the vector population m N which are further subdivided into six classes, susceptible human 𝑆, infected human 𝐼, temporary recovered human class 1 R, permanently recovered human class 2 R , susceptible mosquito 1 M, and infected mosquito class 2 M . The Disease Free Equilibrium (DFE) point was obtained and the basic Reproduction number 0 R was computed. The Disease Free Equilibrium (DFE) is locally and globally asymptotically stable when 1 0 R .Item A MATHEMATICAL MODEL OF SCABBY MOUTH DISEASE INCORPORATING THE QUARANTINE CLASS.(39th Annual Conference of the Nigerian Mathematical Society, (NMS), 2021-04-23) Abdurrahman, Nurat Olamide; Somma S. A.; Aboyeji Folawe Ibironke; Akinwande Ninuola IfeoluwaWe propose a mathematical model to study the transmission and control of scabby mouth disease in sheep, incorporating the vaccinated and quarantine classes. The Disease-free equilibrium was obtained, and the reproduction number was also computed. The local stability of DFE was analyzed for stability. Sensitivity analysis of the basic reproduction number with respect to some parameters of the model was carried out, and the sensitive parameters withR_0 are presented graphically. The local stability of DFE is stable if R_0<1. The sensitivity analysis shows that the contact rateα is the most sensitive parameter to increase the spread of the disease, and vaccination rate ω is the highest sensitive parameter to control the transmission of scabby.Item Sensitivity Analysis for the Mathematical Modeling Transmission and Control of Rabies Incorporating Vaccination Class(40th Annual Conference of the Nigerian Mathematical Society (NMS), 2021-05) Abdurrahman, Nurat Olamide; Somma S. A.; Balogun R. T.In this paper, the Disease Free Equilibrium (DFE) of the model was obtained. The Basic Reproduction Number R0 was also computed and used to carry out the sensitivity analysis. The analysis revealed the sensitive parameters for the spread and control of Rabies. It was also shown that the contact rate of dogs and the vaccination rate of dogs are the most sensitive parameters to increase and decrease the transmission of rabies. The reproduction number was presented graphically against the sensitive parameters.Item A NOTE ON COMBUSTIBLE FOREST MATERIAL (CFM) OF WILDLAND FIRE SPREAD(Proceedings of 3rd SPS Biennial International Conference Federal University of Technology, Minna, Nigeria, 2021-10-28) Zhiri, A. B.; Olayiwola, R. O.; Somma Samuel Abufire is presented. The equations describing the fractional components of forest fire were carefully studied. The reaction before a forest can burn or before fire can spread must involves fuel, heat and oxygen. The coupled dimensionless equations describing the phenomenon have been decoupled using perturbation method and solved analytically using eigen function expansion technique. The results obtained were graphically discussed and analysed. The study revealed that varying Radiation number and Peclet energy number enhances volume fractions of dry organic substance and moisture while they reduced volume fraction of coke.Item A MULTIGRID METHOD FOR NUMERICAL SOLUTION OF ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS(IJSAR Journal of Mathematics and Applied Statistics (IJSAR-JMAS), 2022-12) I. O. Isah; A. Ndanusa; R. Muhammad; K. A. Al-MustaphaTechniques and analyses of multigrid method for solving elliptic partial differential equations (PDEs) in two dimensions are presented. The focal point of this paper is the applicability of the parametric reaccelerated overrelaxation (PROR) iterative method as a smoother in multigrid solution of elliptic PDEs. The two-dimensional Poisson equation on a unit square domain with Dirichlet boundary conditions is adopted as the model PDE. We present some practical formulae and techniques for building the various multigrid components using Kronecker tensor product of matrices. In addition, we carryout smoothing analysis of the PROR method using Local Fourier Analysis (LFA) and show how optimal relaxation parameters and smoothing factors can be obtained from analytic formulae derived to ensure better convergence. This analysis combines full standard coarsening strategy (doubling) and second order finite difference scheme. The result of PROR smoothing factors in comparison with those of other widely used smoothers is also presented. Results obtained from numerical experiment are displayed and compared with theoretical results.Item Modelling the Impacts of Media Campaign and Double Dose Vaccination in Controlling COVID-19 in Nigeria.(Alexandria Engineering Journal, 2023-02-21) Akinwande, N. I.; Somma, Samuel Abu; Olayiwola, R. O.; Ashezua, T. T.; Gweryina, R. I.; Oguntolu, F. A.; Abdurahman, O. N.Corona virus disease (COVID-19) is a lethal disease that poses public health challenge in both developed and developing countries of the world. Owing to the recent ongoing clinical use of COVID-19 vaccines and noncompliance to COVID-19 health protocols, this study presents a deterministic model with an optimal control problem for assessing the community-level impact of media campaign and double-dose vaccination on the transmission and control of COVID-19. Detailed analysis of the model shows that, using the Lyapunov function theory and the theory of centre manifold, the dynamics of the model is determined essentially by the control reproduction number (𝑅𝑚𝑣). Consequently, the model undergoes the phenomenon of forward bifurcation in the absence of the double dose vaccination effects, where the global disease-free equilibrium is obtained whenever 𝑅𝑚𝑣 ≤ 1. Numerical simulations of the model using data relevant to the transmission dynamics of the disease in Nigeria, show that, certain values of the basic reproduction number ((𝑅0 ≥ 7)) may not prevent the spread of the pandemic even if 100% media compliance is achieved. Nevertheless, with assumed 75% (at 𝑅0 = 4)) media efficacy of double dose vaccination, the community herd immunity to the disease can be attained. Furthermore, Pontryagin’s maximum principle was used for the analysis of the optimized model by which necessary conditions for optimal controls were obtained. In addition, the optimal simulation results reveal that, for situations where the cost of implementing the controls (media campaign and double dose vaccination) considered in this study is low, allocating resources to media campaign-only strategy is more effective than allocating them to a firstdose vaccination strategy. More so, as expected, the combined media campaign-double dose vaccination strategy yields a higher population-level impact than the media campaign-only strategy, double-dose vaccination strategy or media campaign-first dose vaccination strategy.Item A 4-Step Order (K + 1) Block Hybrid Backward Differentiation Formulae (BHBDF) for the Solution of General Second Order Ordinary Differential Equations(2023-12) Muhammad R; Hussaini AIn this paper, the block hybrid backward differentiation formulae (BHBDF) for the step number 𝑘 = 4 was developed using power series as basis function for the solution of general second order ordinary differential equation. The idea of interpolation and collocation of the power series at some selected grid and off- grid points gave rise to continuous schemes which were further evaluated at those points to produce discrete schemes combined together to form block methods. Numerical problems were solved with the proposed methods and were found to perform effectively.Item Homotopy Perturbation Analysis of the Spread and Control of Lassa Fever(Proceedings of International Conference on Mathematical Modelling Optimization and Analysis of Disease Dynamics (ICMMOADD), 2024-02-22) Tsado, D.; Oguntolu, F. A.; Somma, Samuel AbuLassa fever, a viral infection transmitted by rodents, has emerged as a significant global health concern in recent times. It continues to garner significant attention daily basis owing to its rapid transmission and deadly nature. In this study, the Homotopy Perturbation Analysis was conducted to examine the spread and control of Lassa fever. The human population was categorized into susceptible, exposed, infected, and recovered compartments, while the rodent population was divided into susceptible and infected recovered compartments. By applying the Homotopy Perturbation Analysis to the nonlinear differential equations associated with these compartments, we were able to obtain the analytical solution for the spread and control of Lassa fever. The nonlinear differential equations were integrated into the Homotopy Perturbation framework and solved to form a power series solution. Finally, the final approximate solutions were obtained and simulation results were generated from the general solution graphically.