School of Physical Sciences (SPS)

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School of Physical Sciences (SPS)

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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 Abu
Abstract: 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].
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.
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 RAZAQ
In 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.
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.
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, Samuel
A 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.
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.
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, Samuel
This 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.
Arsenic level determination in selected well water from Sokoto state, Nigeria
(Elixir International Journal, 2014-10-23) Galadima, A; Bisiriyu, M.T
Twenty samples of domestic water sourced from different underground wells in the Gidan Dare and Gidan Igwai areas of Sokoto were collected and analyzed in the laboratory. The pH and the electrical conductivity (EC) of the water samples were also determined. The mean results obtained from the analyses were pH (7.68, 6.72) and electrical conductivities (1061µs/cm, 1057µs/cm) for Gidan Dare and Gidan Igwai, respectively. The results also showed mean arsenic concentrations of 0.110mg/L and 0.217mg/L for Gidan Dare and Gidan Igwai water samples, respectively, which are above the World Health Organization (WHO) drinking water guidelines. Wells in Gidan Dare and Gidan Igwai were found to be contaminated with an abnormal concentration of arsenic, high enough to cause serious adverse health effects to its consumers. The high arsenic concentrations could be attributed to both natural and anthropogenic activities such as erosion, underground weathering, toxic chemicals, improper waste and sewage disposal waste from industries, agricultural activities and vehicular emissions.
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, Samuel
The 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.
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 Abdulkareem
Implicit 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.
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 Abu
Ebola 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.
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.
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.
Receptor Modeling Application on Surface Water Quality and Source Apportionment
(2016-02-05) Animashaun, Iyanda Murtala; Ahaneku, Isiguzo Edwin; Busari, Musa Bola; Bisiriyu, Muhammad Taoheed
There is a need for regular monitoring of river water quality to determine specific pollutants in order to aid amelioration schemes. In this study, Principal Component Analysis (PCA) was applied to eighteen water quality parameters; pH, conductivity, dissolved oxygen(DO), turbidity, temperature, total dissolved solids (TDS), total solids (TS), total hardness (TH), biochemical oxygen demand (BOD), carbon dioxide (CO2), ammonia (NH3), nitrate (NO3-), chloride (Cl-), lead (Pb), iron (Fe), chromium (Cr), copper (Cu) and manganese (Mn) to identify major sources of water pollution of river Asa. The generated Principal Components (PCs) were used as independent variables and the water quality index (WQI) as the dependent variable to predict the contribution of each of the sources using the multiple linear regression model (MLR). The PCs results showed that the sources of pollution are storm water runoff, industrial effluent, erosion and municipal waste, while MLR identified storm water runoff (0.786) and industrial effluent (0.241) as the respective major contributors of pollution. The study showed that the PC-MLR model gives a good prediction (R2=0.8) for the water quality index.
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 Abu
This 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.
Existence of Equilibrium points for the Mathematical Modeling of Yellow Fever Transmission Incorporating Secondary Host
(Journal of the Nigerian Association of Mathematical Physics, 2017-07-15) Somma, Samuel Abu; Akinwande, N. I.; Jiya, M.; Abdulrahman, S.
In this paper we, formulated a mathematical model of yellow fever transmission incorporating secondary host using first order ordinary differential equation. We verified the feasible region and the positivity of solution of the model. There exist two equilibria; disease free equilibrium (DFE) and endemic Equilibrium (EE). The disease free equilibrium (DFE) points were obtained.
STABILITY AND BIFURCATION ANALYSIS OF ENDEMIC EQUILIBRIUM OF A MATHEMATICAL MODEL OF YELLOW FEVER INCORPORATING SECONDARY HOST
(Transactions of the Nigerian Association of Mathematical Physics, 2018-03-10) Somma, Samuel Abu; Akinwande, N. I.; Jiya, M.; Abdulrahman, S.; Ogwumu, O. D.
In this paper we used the Centre Manifold theorem to analyzed the local stability of Endemic Equilibrium (EE). We obtained the endemic equilibrium point in terms of forces of infection and use it to analyze for the bifurcation of the model. We carried out the bifurcation analysis of the model with four forces of infection which resulted into bifurcation diagram. The forces of infection of vector-primary host and vector secondary host transmissions were plotted against basic reproduction number. The bifurcation diagram revealed that the model exhibit forward bifurcation.
Mathematical Modelling for the Effect of Malaria on the Heterozygous and Homozygous Genes
(ICAPTA, 2018-03-25) Abdurrahman, Nurat Olamide; Akinwande, Ninuola Ifeoluwa; Somma, S. A.
This paper models the effect of malaria on the homozygous for the normal gene (AA), heterozygous for the sickle cell gene (AS), and homozygous for the 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.
Local Stability Analysis of a River Blindness Disease Model with Control
(Pacific Journal of Science and Technology, 2018-05-22) Oguntolu, F. A.; Bolarin, G.; 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 . R 0  1 and
STABILITY ANALYSIS OF LOGISTIC GROWTH MODELOF ALGAE POPULATION DYNAMICS ON A WATER BODY
(Journal of Science, Technology, Mathematics and Education (JOSTMED), 2019-03-12) Abdurrahman, Nurat Olamide
This work analyses the stability of the equilibrium state of a logistic growth model of the Algae population dynamics on a water body, thereby obtaining the critical patch length, which will determine the subsistence or extinction of the water organisms.