Mathematics
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Mathematics
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Item An Appraisal on the Application of Reproduction Number for the Stability Analysis of Disease - Free Equilibrium State for S-I-R Type Models(Proceedings of International Conference on Mathematical Modelling Optimization and Analysis of Disease Dynamics (ICMMOADD) 2024, 2024-02-28) Abdurrahman, Nurat Olamide; Somma S. A.; Akinwande, N. I.; Ashezua, T. T.; Gweryina, R.One of the key ideas in mathematical biology is the basic reproduction number, which can be utilized to comprehend how a disease epidemic profile might evolve in the future. The basic reproduction number, represented by R0 , is the anticipated number of secondary cases that a typical infectious individual would cause in a population that is fully susceptible. This threshold parameter is highly valuable in characterizing mathematical problems related to infectious diseases. If R0 < 1, this suggests that, on average, during the infectious period, an infected individual produces less than one new infected individual, suggesting that the infection may eventually be eradicated from the population. On the other hand, if R0 < 1, every infected person develops an average of multiple new infections, it suggests that the disease may continue to spread throughout the population. We discuss the Reproduction number in this work and provide some examples, both for straightforward and complicated situations.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 Mathematical Modeling of Chemotherapy Effects on Brain Tumour Growth(International Conference and Advanced Workshop on Modelling and Simulation of Complex Systems, 2024-05-27) Abdurrahman, Nurat Olamide; Ibrahim, Mohammed Olanrewaju; Ibrahim, Jamiu OmotolaA brain tumor is an abnormal growth or mass of cells in or around the brain. It is also called a central nervous system tumor. Brain tumors can be malignant (cancerous) or benign (non-cancerous). In this work, we proposed a system of nonlinear differential equations that model brain tumor under treatment by chemotherapy, which considers interactions among the glial cells X(t), the cancer cells Y(t), the neurons Z(t), and the chemotherapeutic agent C(t). The chemotherapeutic agent serves as a predator acting on all the cells. We studied the stability analysis of the steady states for both cases of no treatment and continuous treatment using the Jacobian Matrix. We concluded the study with a numerical simulation of the model and discussed the results obtained.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 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 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 Population dynamics of a mathematical model for Campylobacteriosis(Proceedings of International Conference on Mathematical Modelling Optimization and Analysis of Disease Dynamics (ICMMOADD), 2024-02-22) Ashezua, T. T.; Salemkaan, M. T.; Somma, Samuel AbuThe bacterium campylobacter is the cause of campylobacteriosis, a major cause of foodborne illness that goes by the most common name for diarrheal illnesses. This paper develops and analyzes a new mathematical model for campylobacteriosis. It is demonstrated that in cases where the corresponding reproduction number is smaller than unity, the model's disease-free equilibrium is both locally and globally stable. The numerical simulation results indicate that increasing the treatment rate for both symptomatic and asymptomatic disease-infected individuals resulted in a decrease in the number of asymptomatic and symptomatic individuals, respectively, and a rise in the population's number of recovered individuals.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.Item The Algebraic Structure of an Implicit Runge- Kutta Type Method(International Journal for Research in Applied Science & Engineering Technology (IJRASET), 2024-11) Raihanatu Muhammad; Abdulmalik OyedejiIn this paper, the theory of linear transformation (Homomorphism) and monomorphism is applied to a first-order Runge-Kutta Type Method illustrated in a Butcher Table and the extended second order Runge- Runge-Kutta type Method to substantiate their uniform order and error constants obtained. A homomorphism is a mapping from one group to another group which preserves the group operations. It’s sometimes called the operation preserving function. The methods which initially are Linear Multistep were reformulated into Runge-Kutta (R-K) Type to establish the advantages the R-K has over Linear Multistep. The first-order Linear multistep was reformulated into first-order R-K type which was further extended to second order. This extension can be made to higher order. For this study, the extension was limited to the second order.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.