Mathematics - Scholarly Publications

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    Open Access
    On validation of an epidermiological model
    (Faculty of Science and Technology, University of El Oued, Algeria, 2019) Ayoade, A. A.; Peter; Ibrahim, M. O.; Amadiegwu, S.
    An epidemiological model is suitable to study disease dynamics in a population if it possesses the following properties: existence and uniqueness of solution, invariant region, and the positivity of solution. Based on that, we introduce an epidemiological model and the model is examined whether it possesses the aforementioned characteristics or not.
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    Open Access
    Mathematical Modeling of the Effect of Vaccination on the Dynamics of Infectious Diseases
    (School of Mathematical Sciences, Tribhuvan University, Nepal., 2023-02-28) Alimi, A. A.; Ayoade, A. A.
    The development of vaccines revolutionized the methods of controlling infectious diseases and has saved many lives. In this work, an SEIR epidemic model was designed to demonstrate the impact of vaccination on the control of epidemic diseases. The model was shown to possess positive solutions. The disease-free equilibrium and the endemic equilibrium of the model were derived and the stability properties of the two equilibriums were examined via stability theory of nonlinear differential equation. An important epidemic-controlled parameter, the reproduction number, was derived for the model and computed via simulation using parameter values from published data. The result of the simulation showed that vaccination was capable of inhibiting the outbreak of epidemic diseases whenever the numerical values for reproduction number are less than unity.
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    Open Access
    Mathematical Modeling and Threshold Analysis of Acceptable Failure Rate and Academic Standard
    (2023) Ayoade, A. A.; Manuel, M.; Adeosun, M.A.
    Certificate is an evidence of participating in a process and anyone who holds a certificate is believed to have a prerequisite to handle what the certificate qualifies him for. However, the impression might fail if the certificate had been obtained by cutting corners. [Objetive] In this paper, a compartmental model was developed to quantify factors that could put the authenticity of a certificate in doubt by examining the trade off between academic standard and failure rates in the context of tertiary institutions with reference to Nigeria. [Methodology] The model was proved valid using some ample mathematical theorems. The equilibria for the model and the threshold for acceptable academic performance were derived. Stability analysis was carried out by employing stability theory of differential equations based on the derived acceptable academic performance threshold. [Results] The theoretical results for the model were validated by means of numerical simulations and the results from the simulations linked acceptable failure rate to the academic performance that fell below the threshold of the institutions’ set standard. [Conclusions] The policy implication of the result is that increase in the supply of qualified graduates into the Nigeria labor markets as well as reduction in the rate of unemployment is a function of maintaining academic standards
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    Open Access
    Poly-Weighted Exponentiated Gamma Distribution with Application
    (Journal of Statistical Theory and Applications. Atlantis Press, 2020-09) Nkemnole, E.B; Ikegwu, E.M
    This paper proposes a weighting of the exponentiated gamma distribution with a polynomial function called the poly-weighted exponentiated gamma distribution (PWEGD). It shows that the modified distribution harnesses the multi-dimensional effects of the distribution. We provided an extensive mathematical treatment of this proposed distribution: obtained its parameters, estimated its statistical properties with applicable, tests and compared the estimates with existing distribution. The study estimated the cumulative distribution function, hazard function, survival function, skewness, kurtosis, mode, median and quartiles of the distribution and evaluated the distribution with Monte Carlo simulated data and the data of the wind direction (degrees) in Lagos, Nigeria. Empirical analysis showed that with increased polynomial function, the estimates and the statistical properties like the expectation, variance, standard error, median, mode, hazard and survival functions, cumulative distribution function (CDF), moments, skewness and kurtosis were significantly better than the existing root distributions. The MSE of the parameters decreased with increased power and the parameter is significant (p <0.05). It is concluded that the proposed distribution does not only provide better fitting but also establishes an efficient structure for lifetime data modelling.
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    Open Access
    Block method for numerical solution of differential-algebraic equations with hessenberg index-3
    (2014) OA Akinfenwa, SA Okunuga
    A Block Second Derivative Formula (BSDF) of order seven for the numerical solution of Hessenberg Differential Algebraic Equations (DAEs) of index 3 is presented. This is achieved by constructing a Continuous Second Derivative Formula (CSDF) used to obtain the main and additional methods which are combined to form a single block of methods that simultaneously provide the approximate solutions for the Hessenberg DAEs of index 3. The error constant and stability properties of the BSDF are discussed. The performance of the method is demonstrated on some numerical examples to show the accuracy and efficiency of the method.