School of Physical Sciences (SPS)
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School of Physical Sciences (SPS)
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Item Approximate Solution of SIR Infectious Disease Model Using Homotopy Pertubation Method (HPM).(Pacific Journal of Science and Technology, 2013-11-20) 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 DERIVATION AND ANALYSIS OF BLOCK IMPLICIT HYBRID BACKWARD DIFFERENTIATION FORMULAE FOR STIFF PROBLEMS(Nigerian Journal of Mathematics and Applications, 2014) MUHAMMAD, R.; YAHAYA, Y. A.; IDRIS L.The Hybrid Backward Di erentiation Formula (HBDF) for the case k = 3 was reformulated into continuous form using the idea of multistep collocation. The continuous form was evaluated at some grid and o grid points which gave rise to discrete schemes employed as block methods for direct solution of rst order Ordinary Di erential Equation y0 = f(x; y). The requirement of a starting value and the overlap of solution model which are associated with conventional Linear Multistep Methods were eliminated by this approach. A convergence analysis of the derived hybrid schemes to establish their e ec- tiveness and reliability is presented. Numerical example carried out on sti problem further substantiates their performance.Item Formulation Of A Standard Runge- Kutta Type Method For The Solution First And Second Order Initial Value Problems(Researchjournali’s Journal of Mathematics, 2015-03) Muhammad R.; Y. A Yahaya; A.S AbdulkareemIn this paper, we present a standard Runge-Kutta Type Method (RKTM) for . The process produces Backward Differentiation Formula (BDF) scheme and its hybrid form which combined together to form a block method. The method is reformulated into a Runge-Kutta Type of the same step number for the solution of first and second order (special or general) initial value problem of Ordinary Differential Equation (ODE).Item Stability Analysis of Disease Free Equilibrium (DFE) State of a Mathematical Model of Yellow Fever Incorporating Secondary Host(Pacific Journal of Science and Technology, 2017-11-20) Somma, Samuel Abu; Akinwande, N. I.; Jiya, M.; Abdulrahaman, S.In this paper we formulate a mathematical model of yellow fever incorporating secondary host. We obtained the Disease Free Equilibrium (DFE) Points and compute the basic reproduction number. The local and global stability of the DFE was analyzed using Jacobian Matrix stability techniques and Lyapunov function respectively. The local and global stability was asymptotically stable if 1 0 R and 1 0 R , respectively. The basic reproduction number and control parameters of the model were presented graphically.Item Evaluation of the erosive potential of selected non-carbonated powdered sachet fruit drinks on the human enamel(Nigerian Journal of Technological Research, 2019-03-30) Bisiriyu, M. T; Koleola, A. A; Salau, R. B; James, D. U.This study was carried out to evaluate the erosive potentials of selected non-carbonated powdered sachet fruit drinks on the human dentition using physical examination and standard analytical procedures involving measurements of some physicochemical parameters such as pH, electrical conductivity and buffering capacity. The results of the physical examination revealed that all the fruit drinks complied with the NAFDAC specifications except that 50% of the drinks had no NAFDAC registration number, while the results of the physicochemical analyses showed that the pH of the fruit drinks ranged from 2.635±0.22 to 2.25±0.13, electrical conductivity ranged between 1631±0.05 and 493±0.0 µS/cm and buffering capacity ranged from 3.80±0.05 to 0.75±0.11cm3 of NaOH, respectively. The results showed that all fruit drinks analyzed were highly acidic as the pH values of the prepared solutions were less than the threshold pH (5.5) for enamel dissolution. Therefore, prolonged retention of such drinks in the mouth might result in enamel wearing and tooth decay as such food and drinks with high sugar content should only be taken in small quantities.Item Semi-Analytical Solution for the Mathematical Modeling of Yellow Fever Dynamics Incorporating Secondary Host(Communication in Mathematical Modeling and Applications, 2019-04-15) Somma, Samuel Abu; Akinwande, N. I.; Abah, R. T.,; Oguntolu, F. A.; Ayegbusi, F. D.In this paper we use Differential Transformation Method (DTM) to solve the mathematical modeling of yellow fever dynamics incorporating secondary host. The DTM numerical solution was compared with the MAPLE RungeKutta 4-th order. The variable and parameter values used for analytical solution were estimated from the data obtained from World Health Organization (WHO) and UNICEF. The results obtained are in good agreement with Runge-Kutta. The solution was also presented graphically and gives better understanding of the model. The graphical solution showed that vaccination rate and recovery rate play a vital role in eradicating the yellow fever in a community.Item THE ORDER AND ERROR CONSTANT OF A RUNGE-KUTTA TYPE METHOD FOR THE NUMERICAL SOLUTION OF INITIAL VALUE PROBLEM(Federal University Dutsin MA Journal of Sciences (FJS), 2020-06) Muhammad RIn this paper, we examine in details how to obtain the order, error constant, consistency and convergence of a Runge-Kutta Type method (RKTM) when the step number 𝑘 = 2. Analysis of the order, error constant, consistency and convergence will help in determining an effective Runge- Kutta Method (RKM) to use. 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.Item Application of Adomian Decomposition Method (ADM) for solving Mathematical Model of Measles(National Mathematical Center, 2021-03-22) Abdurrahman, Nurat Olamide; Somma S. A.; Ayegbusi F. D.; Gana P.; Adama P. W.; Yisa E. M.Item Synthesis And Physicochemical Studies Of Metal(II)Complexes Of 2-((4-Oxopentan-2-Ylidene)Amino)Benzoic Acid And Their 2,2′-Bipyridine And 1,10-Phenanthroline(2022) Anyanwu, S.K.; Adekoya, S.B.; Ibukun, D.T.; Omoregie, H.O.Item A 3-Person Non-Zero-Sum Game for Sachet Water Companies(Asian Research Journal of Mathematics, 2022-06-24) Nyor, N.; Muazu, M. I.; Somma Samuel AbuThe business of Sachet water (popularly called pure water) in Nigeria is often competitive due to the high demand for Sachet water by the populace. This is so because sachet water is the most affordable form of pure drinking water in Nigeria. As such, Sachet Water Firms that want to succeed in an ever increasing competitive market need to have the knowledge of Game Theory to identify which strategy will yield better profit independent of the strategy adopted by other competitors. This paper is aimed to investigate and determine the equilibrium point for three Sachet Water Firms using the Nash Equilibrium Method as it provides a systematic approach for deciding the best strategy in competitive situation. The result showed two Nash Equilibriums (promo, promo) and (stay-put, stay-put) with their respective payoffs of (82; 82; 82) and (147; 147; 147).Item Mathematical model of COVID-19 transmission dynamics incorporating booster vaccine program and environmental contamination(2022-12-10) Akinwande, N. I; Ashezua, T. T.; Gweryina, R. I.; Somma, Samuel Abu; Oguntolu, F. A.; A. UsmanCOVID-19 is one of the greatest human global health challenges that causes economic meltdown of many nations. In this study, we develop an SIR-type model which captures both human-to-human and environment-to-human-to-environment transmissions that allows the recruitment of corona viruses in the environment in the midst of booster vaccine program. Theoretically, we prove some basic properties of the full model as well as investigate the existence of SARS-CoV-2-free and endemic equilibria. The SARS-CoV-2-free equilibrium for the special case, where the constant inflow of corona virus into the environment by any other means, Ωis suspended (Ω =0)is globally asymptotically stable when the effective reproduction number 𝑅0𝑐<1and unstable if otherwise. Whereas in the presence of free-living Corona viruses in the environment (Ω >0), the endemic equilibrium using the centremanifold theory is shown to be stable globally whenever 𝑅0𝑐>1. The model is extended into optimal control system and analyzed analytically using Pontryagin’s Maximum Principle. Results from the optimal control simulations show that strategy E for implementing the public health advocacy, booster vaccine program, treatment of isolated people and disinfecting or fumigating of surfaces and dead bodies before burial is the most effective control intervention for mitigating the spread of Corona virus. Importantly, based on the available data used, the study also revealed that if at least 70%of the constituents followed the aforementioned public health policies, then herd immunity could be achieved for COVID-19 pandemic in the community.Item Physicochemical and bacteriological evaluation of sachet water sold in Minna metropolis, Niger State, Nigeria(International Journal of Advanced Chemistry Research, 2023-06-12) Mohammed, Ibrahim; Bisiriyu, Muhammad Taoheed; Salau, Rasaq Bolakale; Suleiman, Asmau Omowumi; Abdullahi, Hamidu; Ogbiko, Cyril; Rople, Gungshik John; Abdullah, Rabiat LawalPhysical assessment of the package labels (product name, manufacturing address, National Agency for Food and Drug Administration (NAFDAC) registration number, manufacturing and expiry date and batch number on the labeling) and quality evaluation of the physicochemical and bacteriological properties of the water samples collected was assess and analyzed in relation to level of compliance with package water recommended standards. Four (4) clusters were considered in which three samples were collected from vendors in each cluster making up a total of twelve (12) samples. Physical examinations revealed 100% compliance to standards in terms of the product name, manufacturing address and NAFDAC registration number but zero percent compliance for manufacturing and expiry dates but only about 17% of the samples had a batch number on the labeling. The physiochemical parameters show appreciable compliance to standards with an ambient temperature of 28 °C, pH range of 6.5 to 8.5 and conductivity values ranged between 104.67 - 225.67 µS/cm still lower compared to the maximum range of 1000 µS/cm by Nigerian Industrial Standard (NIS). Samples turbidity results recorded zero value for SWA1, SWB2, SWC3, SWE5, SWG5, SWH6, SWI7, SWJ8 and SWK9 except for sample SWD10, SWF11, and SWL12 with a turbidity of 2.00, 2.00 and 3.00 NTU, respectively and were still within NIS/WHO limit of 5 NTU. Total dissolved solids (TDS) values ranged from 70.20 - 171.67 mg/L but still within the threshold limit of 500 mg/L recommended by NIS. The bacteriological parameters gave total bacterial count (TBC) ranged between 1 - 16.50 cfu/cm3 accounting for SWB2=2.00, SWC3=1.50, SWD4=2.00, SWE5=1.00, SWF6=5.50, SWG7=4.00, SWH8=5.00, SWI9=13.00, SWJ10=8.50, SWK11=16.50,and SWL12=16.00 cfu/cm3 above the WHO limit of zero cfu/cm3 except SWA with 0.00 cfu/cm3 in conformity with the standard limit while TCC ranged from 1-1.50 cfu/cm3 for SWC3=1.50, SWD4=1.00, SWE5=1.00, SWG7=1.00, SWH8=1.50 and SWK11=1.50 cfu/cm3 which is all above the WHO limit of 0.00 cfu/cm3except six samples (SWA1, SWB2, SWF6, SWI9, SWJ10 and SWL12) having 0.00 cfu/cm3 accounting for 50% samples compliance with the tolerance limit. The concentration of Pb, Zn, Fe, and Cr in the samples was below the WHO/SON tolerant level of 0.01 mg/L for Pb, 5 mg/L for Zn, 0.3 mg/L for Fe and 0.05 mg/L for Cr except for samples SWF6, SWG7, and SWJ10 with Pb concentration of 0.04, 0.032, and 0.050 mg/L respectively, above permissible limits of WHO/SON. The corrosion of pipes used in the water processing may account for the Pb concentration hence, regular assessment of the sachet water products should be ensured by the regulating agencies to promote both water and health safety.Item Modelling the impacts of media campaign and double dose vaccination in controlling COVID-19 in Nigeria(Alexandria Engineering Journal, 2023-08-16) Akinwande, N. I.; Somma, Samuel Abu; Olayiwola, R. O.; Ashezua, T. T.; Gweryina, R. I.; Oguntolu, F. A.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 Ga(iBu)3 supported on meso H-ZSM-5: Effect of Si/Al ratio on the activity and selectivity in propane aromatization(Elsevier Catalysis Communications, 2024) Jessy, Abou Nakad; Firth, Daniel; Bisiriyu, Muhammad Taoheed; Szeto, Kai. C.; Merle, Nicolas; De Mallmann, Aimery; Gauvin, Regis M.; Delevoye, Laurent; Olsbye, Unni; Taoufik, MostafaThe grafting of Ga(iBu)3 on a series of meso-H-ZSM5, prepared by desilication-dealuminiation(Si/Al=25,50,100,200,∞) has been studied. The materials were characterized by IR, solid- state NMR, BET, ICP and EXAFS. Ga(iBu)3 reacts selectively with silanol groups, yielding a monopodal surface species in the mesopores. Importantly, the Bronsted acidic sites remain intact in the micropores, as IR and 1H MAS-NMR revealed. These materials can be regarded as bifunctional catalysts, containing isolated Ga sites and Bronsted sites in proximity, suitable for propane aromatization. Catalytic investigations show high activity and selectivity toward aromatics, toward aromatics, particularly for low Si/Al ratios.Item A 4-STAGE RUNGE-KUTTA TYPE METHOD FOR SOLUTION OF STIFF ORDINARY DIFFERENTIAL EQUATIONS(Pan-American Journal of Mathematics, 2024) RAIHANATU MUHAMMAD; ABDULMALIK OYEDEJIIn this paper, a 2 step implicit block hybrid linear multistep method was reformulated into a 4-stage block hybrid Runge-Kutta Type Method via the butcher analysis. The method can be used to solve first order stiff ordinary differential equations. A numerical example solved with the proposed method showed a better result in comparison with an existing methodItem Physiochemical Properties and Heavy Metals Analysis of Effluent Water from Selected Tannery Sites in Kano and Zaria(2024) Anyanwu, S.K.; Andrew, A.; Idika P.; Ndamitso. M.M.Item Production of biodiesel from Balanite aegyptiaca seed oilusing chemical-activated catalyst produced from coconutshell.(Nigerian Research Journal of Chemical Sciences, 2024) Alheri, A.; Ago, M. A.; Jamila, U. A.; Anyanwu, S.K.; Bisiriyu, M. T.; Aisha, K. U.