Browsing by Author "Somma, Samuel Abu"

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A 3-Person Non-Zero-Sum Game for Sachet Water Companies
(Asian Research Journal of Mathematics, 2022-08-12) Nyor, N.; Muazu, M. I.; Somma, Samuel Abu
The 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).
A Global Asymptotic Stability of COVID-19 Diabetes Complication Free Equilibrium
(Journal of Science, Technology, Mathematics and Education (JOSTMED), 2024-03-25) Yusuf, A,; Akinwande, N. I.; Olayiwola, R. O.; Kuta, F. A.; Somma, Samuel Abu
In this paper, a Mathematical modelling of COVID-19 incorporating the comorbidity of Diabetes was established base on the accompanying assumptions, a global asymptotic of the same model was developed by applying the theorem of Castillo-Chavez by fixing a point to be globally asymptotic stable equilibrium of the system, provided that and the two set conditions are satisfied. It is very clear that so the conditions are not met. Hence, may not be globally asymptotically stable when .
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.
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.
A MATHEMATICAL MODEL OF MONKEY POX VIRUS TRANSMISSION DYNAMICS
(Ife Journal of Science, 2019-06-10) Somma, Samuel Abu; Akinwande, N. I.; Chado, U. D.
In this paper a mathematical model of monkey pox virus transmission dynamics with two interacting host populations; humans and rodents is formulate. The quarantine class and public enlightenment campaign parameter are incorporated into human population as means of controlling the spread of the disease. The Disease Free Equilibrium (DFE) and Endemic Equilibrium (EE) are obtained. The basic reproduction number R 0 < h and R 0r 1 and R 1 < are computed and used for the analysis. The Disease Free Equilibrium (DFE) is analyzed for stability using Jacobian matrix techniques and Lyapunov function. Stability analysis shows that the DFE is stable if .
Application of Adomian Decomposition Method (ADM) for Solving Mathematical Model of Measles
(National Mathematical Centre (NMC) Journal of Mathematical Sciences,, 2021-03-03) Somma, Samuel Abu; Ayegbusi, F. D.; Gana, P.; Adama, P. W.; Abdurrahman, N. O.; Eguda F. Y.
Adomian Decomposition Method (ADM) is a semi-analytical method that give the approximate solution of the linear and non-linear differential equations. In this paper the Adomian Decomposition Method (ADM) was used to solve the mathematical model of measles. The ADM solution was validated with Runge-Kutta built-in in Maple software. The graphical solutions show the decrease and increase in the classes with time. It was revealed from the graphical solution that the ADM is in agreement with Runge-Kutta. Keywords: Mathematical modeling, Adomian Decomposition Method, numerical solution
APPROXIMATE SOLUTIONS FOR MATHEMATICAL MODELLING OF MONKEY POX VIRUS INCORPORATING QUARANTINE CLASS
(Transactions of the Nigerian Association of Mathematical Physics, 2021-03-30) Somma, Samuel Abu; Akinwande, N. I.,; Ashezua, T. T.; Nyor, N.; Jimoh, O. R.; Zhiri, A. B.
In this paper we used Homotopy Perturbation Method (HPM) and Adomian Decomposition Method (ADM) to solve the mathematical modeling of Monkeypox virus. The solutions of HPM and (ADM) obtained were validated numerically with the Runge-Kutta-Fehlberg 4-5th order built-in in Maple software. The solutions were also presented graphically to give more insight into the dynamics of the monkeypox virus. It was observed that the two solutions were in agreement with each other and also with Runge-Kutta.
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].
Differential Transformation Method (DTM) for Solving Mathematical Modelling of Monkey Pox Virus Incorporating Quarantine
(Proceedings of 2nd SPS Biennial International Conference Federal University of Technology, Minna, Nigeria, 2019-06-26) Somma, Samuel Abu; Akinwande, N. I.; Abdurrahman, N. O.; Zhiri, A. B.
In this paper the Mathematical Modelling of Monkey Pox Virus Incorporating Quarantine was solved semi-analytically using Differential Transformation Method (DTM). The solutions of difference cases were presented graphically. The graphical solutions gave better understanding of the dynamics of Monkey pox virus, it was shown that effective Public Enlightenment Campaign and Progression Rate of Quarantine are important parameters that will prevent and control the spread of Monkey Pox in the population.
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.
Homotopy Perturbation Analysis of the Spread and Control of Lassa Fever
(Proceedings of International Conference on Mathematical Modelling Optimization and Analysis of Disease Dynamics (ICMMOADD), 2024-02-22) Tsado, D.; Oguntolu, F. A.; Somma, Samuel Abu
Lassa fever, a viral infection transmitted by rodents, has emerged as a significant global health concern in recent times. It continues to garner significant attention daily basis owing to its rapid transmission and deadly nature. In this study, the Homotopy Perturbation Analysis was conducted to examine the spread and control of Lassa fever. The human population was categorized into susceptible, exposed, infected, and recovered compartments, while the rodent population was divided into susceptible and infected recovered compartments. By applying the Homotopy Perturbation Analysis to the nonlinear differential equations associated with these compartments, we were able to obtain the analytical solution for the spread and control of Lassa fever. The nonlinear differential equations were integrated into the Homotopy Perturbation framework and solved to form a power series solution. Finally, the final approximate solutions were obtained and simulation results were generated from the general solution graphically.
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.
Local and Global Stability Analysis of a Mathematical Model of Measles Incorporating Maternally-Derived-Immunity
(Proceedings of International Conference on Applied Mathematics & Computational Sciences (ICAMCS),, 2019-10-19) Somma, Samuel Abu; Akinwande, N. I.; Gana, P.
In this paper, the local stabilities of both the Disease Free Equilibrium (DFE) and Endemic Equilibrium (EE) were analyzed using the Jacobian matrix stability technique. The global stabilities were analyzed using Lyapunov function. The analysis shows that the DFE is locally and globally stable if the basic reproduction number R 0  1 R 0  1 and R 0  1 respectively. The EE is also locally and globally stable if . Vaccination and recovery rates have been shown from the graphical presentation as the important parameter that will eradicate measles from the population.
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
Local Stability Analysis of a River Blindness Disease Model with Control
(Pacific Journal of Science and Technology., 2018-05-12) Oguntolu, F. A.; Bolarin, G. A.; 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 .
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.
Local Stability Analysis of a Tuberculosis Model incorporating Extensive Drug Resistant Subgroup
(Pacific Journal of Science and Technology, 2017-05-25) 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 c R was obtained and conditions for local stability of the disease 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.
Mathematical analysis of a Chlamydia trachomatis with nonlinear incidence and recovery rates
(Proceedings of 2nd International Conference on Mathematical Modelling, Optimization and Analysis of Disease Dynamics (ICMMOADD) 2025. Federal University of Technology, Minna, Nigeria, 2025-02-20) Ashezua, T. T.; Abu, E. A.; Somma, Samuel Abu
Chlamydia, one of the commonest sexually transmitted infections (STIs), remain a public health concern in both underdeveloped and developed countries of the world. Chlamydia has caused worrying public health consequences hence much research work is needed to check the spread of the disease in the population. In this paper, a mathematical model for Chlamydia is developed and analyzed with nonlinear incidence and recovery rates. Qualitative analysis of the model shows that the disease-free equilibrium is locally asymptotically stable using the method of linearization. Further, using the comparison theorem method, the disease-free equilibrium is found to be globally asymptotically stable whenever the associated reproduction number is less than unity. Furthermore, mathematical analysis of the reproduction number shows that the intervention levels and the maximum per capita recovery rate due to effective treatment has a significant impact in reducing the burden of Chlamydia in the population. Numerical results show a relationship between the transmission rate, intervention levels, maximum per capita recovery rate and the reproduction number. Sensitivity analysis was conducted on the parameters connected to the reproduction number, Rc and results reveal that the top parameters that significantly drive the dynamics of Chlamydia in the population are the transmission rate, intervention levels and the maximum per capita recovery rate. These parameters need to be checked by healthcare policy makers if the disease must be controlled in the population.
Mathematical model of COVID-19 transmission dynamics incorporating booster vaccine program and environmental contamination
(2022-11-12) Akinwande, N. I.; Ashezua, T. T.; Gweryina, R. I.; Somma, Samuel Abu; Oguntolu, F. A.; Usman, A.
COVID-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.
Mathematical Modeling of Algae Population Dynamics on the Surface of Water
(2019-11-12) Abdurrahman, O. N.; Akinwande, N. I.; Somma, Samuel Abu
The paper presented an analytical solution of the exponential growth model of algae population dynamics on the water surface. The Computer Symbolic Algebraic Package, MAPLE is used to simulate the graphical profiles of the population with time while varying the parameters, such as diffusion and rate of change of algae density, governing the subsistence or extinction of the water organisms.