Mathematics

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Mathematics

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Author: search.filters.author.Somma, Samuel AbuEnd date: 2024

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    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
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    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.
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    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.
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    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.
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    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.
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    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 .
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    SENSITIVITY ANALYSIS FOR THE MATHEMATICAL MODELLING OF MONKEY POX VIRUS INCORPORATING QUARANTINE AND PUBLIC ENLIGHTENMENT CAMPAIGN
    (FULafia Journal of Science & Technology, 2020-03-15) Somma, Samuel Abu
    In this paper sensitivity analysis was carried out for the mathematical modeling of Monkey pox virus incorporating quarantine and public enlightenment campaign into the human population. The model was formulated using first order ordinary differential equations. The model equation was divided into two populations of human and rodents. There are two equilibrium points that exist in the model; Disease Free Equilibrium (DFE) and Endemic Equilibrium (EE). The Local and Global stabilities of Disease Free Equilibrium (DFE) were R and rodent to rodent analyzed. The basic reproduction numbers of human to human 0h r R0 transmission was computed. The sensitivity analysis of the Basic reproduction number with the parameters was carried out. The Disease Free Equilibrium (DFE) is Locally and Globally Asymptotically Stable if R 0 h < 1 and R 0 r < 1 . The graphical presentation of the Basic reproduction number and the sensitive parameters shows that effective progression rate from infected class to Quarantine and effective public enlightenment campaign are the most sensitive parameters that will eradicate the disease from the population.
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    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.
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    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
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    MODELLING FIRE SPREAD REACTION RATE IN ATMOSPHERIC WEATHER CONDITION
    (Science World Journal, 2021-05-12) Zhiri, A. B.,; Olayiwola, R.O.; Somma, Samuel Abu; Oguntolu, F. A.
    Fire spread in any fire environment is a thing of great concern as wind is arguably the most important weather factor that influences the spread of fire. In this paper, we present equations governing the phenomenon and assume the fire depends on the space variablex. Analytical solution is obtained via perturbation method, direct integration and eigenfunction expansion technique, which depicts the influence of parameters involved in the system. The effect of change in parameters such as Peclet mass number and Equilibrium wind velocity are presented graphically and discussed. The results obtained revealed that both Peclet mass number and Equilibrium wind velocity enhanced oxygen concentration during fire spread.