School of Physical Sciences (SPS)

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School of Physical Sciences (SPS)

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Author: search.filters.author.Abubakar, SamuelEnd date: 2013

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    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.
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    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.
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    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.
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    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.
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    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.