Mathematics
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Mathematics
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Item Stability and Bifurcation Analysis of a Mathematical Modeling of Measles Incorporating Vitamin A Supplement(Sule Lamido University Journal of Science and Technology (SLUJST), 2021-01-20) Somma, Samul Abu; Akinwande, N. I.; Gana, P.; Ogwumu, O. D.; Ashezua, T. T.; Eguda, F. Y.Measles is transmissible disease that is common among children. The death caused by measles among children of five years and below is alarming in spite of the safe and effective vaccine. It has been discovered that Vitamin A Deficiency (VAD) in children increases their chances of measles infection. In this paper, the mathematical model of measles incorporating Vitamin A supplement as treatment was formulated and analyzed. The equilibrium points are obtained and analyzed for stability. Bifurcation and sensitivity analyses were carried out to gain further insight into the spread and control of measles. The stability analysis revealed that Disease Free Equilibrium (DFE) is stable if Reproduction Number, 0 R 0 1 . The bifurcation analysis revealed forward bifurcation while the sensitivity analysis shows the most sensitive parameters of the model that are responsible for the spread and control of the diseases. The effect of sensitive parameters on Basic R were presented graphically. Vaccination, recovery and Vitamin A supplement rates have been shown from the graphical presentation as the important parameter that will eradicate the measles from the population while contact and loss of immunity rates have shown that measles will persist in the population. People should be sensitized on the danger of living with infected persons. Government should do more in routine immunization and administration of Vitamin A Supplement.Item Homotopy Perturbation Method (HPM) for Solving Mathematical Modeling of MonkeyPox Virus(National Mathematical Centre (NMC) Journal of Mathematical Sciences, 2020-03-03) Somma, Samuel Abu; Ayegbusi, F. D.; Gana, P.; Adama, P. W.; Abdurrahman, N. O.; Eguda, F. Y.Mathematical modeling of real life problems such as transmission dynamics of infectious diseases resulted into non-linear differential equations which make it difficult to solve and have exact solution. Consequently, semi-analytical and numerical methods are used to solve these model equations. In this paper we used Homotopy Perturbation Method (HPM) to solve the mathematical modeling of Monkeypox virus. The solutions of HPM were validated numerically with the Runge-Kutta-Fehlberg 4-5th order built-in in Maple software. It was observed that the two solutions were in agreement with each other.Item Stability Analysis of the Mathematical Modelling of Transmission and Control of Rabies Incorporating Vaccination Class(Dutse Journal of Pure and Applied Sciences (DUJOPAS), 2022-03-02) Somma, Samuel Abu; Balogun, R. T.; Eguda, F. Y.; Abdurrahman, N. O.; Adama, P. W.; Yisa E. M.Rabies is a viral disease of nervous system that is often transmitted to human beings through the bite or scratch of rabid animals. The uprising of in-security globally has forced several people to get dogs in their houses. In this paper the mathematical model of rabies transmission and control was formulated by incorporating vaccination class. The Disease Free Equilibrium (DFE) state of the model was obtain and used to compute the basic reproduction number 0 R . Local stability analysis of the DFE was carried out using Jacobian Matrix techniques. The DFE is locally asymptotically stable ifItem A Mathematical Model for Water Quality Assessment: Evidence-Based from Selected Boreholes in Federal University Dutse, Nigeria(UMYU Scientifica, 2023-12-30) Eguda, F. Y.; Amoo, A. O.; Adamu, S. B.; Ogwumu, O. D.; Somma, Samuel Abu; Babura I. B.The present study assessed the quality of water sampled from different boreholes on the campus of Federal University Dutse, Nigeria, using a mathematical modelling approach. A model for estimating water quality was developed based on physicochemical parameters such as pH, electrical conductivity, temperature, turbidity, and total hardness measured from each borehole. The correlation analysis of physicochemical data indicates a strong correlation of about 99% between the real-life data collected from six (6) different boreholes and the model’s predictions. From the results, the sensitivity analysis revealed that electrical conductivity plays the highest role in determining water quality, followed by total hardness, temperature has the third highest impact, followed by turbidity, the fourth, and pH has the least impact in determining water quality in the listed boreholes. Therefore, in any case of intervention, the water quality regulatory body should be sent regularly to the tertiary institutions in the state for routine check-ups.