Browsing by Author "Akinwande, N. I."

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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.
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.
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 .
An Appraisal on the Application of Reproduction Number for the Stability Analysis of Disease - Free Equilibrium State for S-I-R Type Models
(Proceedings of International Conference on Mathematical Modelling Optimization and Analysis of Disease Dynamics (ICMMOADD) 2024, 2024-02-28) Abdurrahman, Nurat Olamide; Somma S. A.; Akinwande, N. I.; Ashezua, T. T.; Gweryina, R.
One of the key ideas in mathematical biology is the basic reproduction number, which can be utilized to comprehend how a disease epidemic profile might evolve in the future. The basic reproduction number, represented by R0 , is the anticipated number of secondary cases that a typical infectious individual would cause in a population that is fully susceptible. This threshold parameter is highly valuable in characterizing mathematical problems related to infectious diseases. If R0 < 1, this suggests that, on average, during the infectious period, an infected individual produces less than one new infected individual, suggesting that the infection may eventually be eradicated from the population. On the other hand, if R0 < 1, every infected person develops an average of multiple new infections, it suggests that the disease may continue to spread throughout the population. We discuss the Reproduction number in this work and provide some examples, both for straightforward and complicated situations.
Approximate Solution of SIR Infectious Disease Model Using Homotopy Pertubation Method (HPM).
(Pacific Journal of Science and Technology, 2013-11-20) 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.
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.
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.
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 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 Modeling of Algae Population Dynamics on the Surface of Water
(The Pacific Journal of Science and Technology, 2019-11-22) Abdurrahman, Nurat Olamide; Somma, S. A.; Akinwande, N. I.
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.
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.
Mathematical Modelling for the Effect of Malaria on the Heterozygous and Homozygous Genes
(6th International Conference on Mathematical Analysis and Optimization: Theory and Applications (ICAPTA 2019), 2019-03-29) Abdurrahman, N. O.; Akinwande, N. I.; Somma, Samuel Abu
This paper models the effect of malaria on the homozygous for the normal gene (AA), heterozygous for sickle cell gene (AS) and homozygous for sickle cell gene (SS) using the first order ordinary differential equation. The Diseases Free Equilibrium (DFE) was obtained and used to compute the basic reproduction Number Ro. The local stability of the (DFE) was analyzed.
Modelling the impacts of media campaign and double dose vaccination in controlling COVID-19 in Nigeria
(Alexandria Engineering Journal, 2023-08-16) Akinwande, N. I.; Somma, Samuel Abu; Olayiwola, R. O.; Ashezua, T. T.; Gweryina, R. I.; Oguntolu, F. A.
Corona virus disease (COVID-19) is a lethal disease that poses public health challenge in both developed and developing countries of the world. Owing to the recent ongoing clinical use of COVID-19 vaccines and noncompliance to COVID-19 health protocols, this study presents a deterministic model with an optimal control problem for assessing the community-level impact of media campaign and double-dose vaccination on the transmission and control of COVID-19. Detailed analysis of the model shows that, using the Lyapunov function theory and the theory of centre manifold, the dynamics of the model is determined essentially by the control reproduction number (𝑅𝑚𝑣). Consequently, the model undergoes the phenomenon of forward bifurcation in the absence of the double dose vaccination effects, where the global disease-free equilibrium is obtained whenever 𝑅𝑚𝑣 ≤ 1. Numerical simulations of the model using data relevant to the transmission dynamics of the disease in Nigeria, show that, certain values of the basic reproduction number ((𝑅0 ≥ 7)) may not prevent the spread of the pandemic even if 100% media compliance is achieved. Nevertheless, with assumed 75% (at 𝑅0 = 4)) media efficacy of double dose vaccination, the community herd immunity to the disease can be attained. Furthermore, Pontryagin’s maximum principle was used for the analysis of the optimized model by which necessary conditions for optimal controls were obtained. In addition, the optimal simulation results reveal that, for situations where the cost of implementing the controls (media campaign and double dose vaccination) considered in this study is low, allocating resources to media campaign-only strategy is more effective than allocating them to a firstdose vaccination strategy. More so, as expected, the combined media campaign-double dose vaccination strategy yields a higher population-level impact than the media campaign-only strategy, double-dose vaccination strategy or media campaign-first dose vaccination strategy.
Modified Maternally-Derived-Immunity Susceptible Infectious Recovered (MSIR) Model of Infectious Disease: Existence of Equilibrium and Basic Reproduction Number
(Nigerian Journal of Technological Research, 2015-06-03) Somma, Samuel Abu; Akinwande, N. I.; Gana, P.; Abdulrahaman, S.; Ashezua, T. T.
In this paper we modified the MSIR Model by adding the vaccination rate and death rate due to the disease to the existing MSIR model. We verified the positivity of the solution and obtained the Disease Free Equilibrium (DFE) of the model. We also determined the basic reproduction number using next generation Matrix and Jacobian matrix method.
SENSITIVITY ANALYSIS FOR THE MATHEMATICAL MODELING OF MEASLES DISEASE INCORPORATING TEMPORARY PASSIVE IMMUNITY
(1st SPS Biennial International Conference Federal University of Technology, Minna, Nigeria, 2017-05-05) Somma, Samuel Abu; Akinwande, N. I.
Measles is an airborne disease which spreads easily through the coughs and sneezes of those infected. Measles antibodies are transferred from mothers who have been vaccinated against measles or have been previously infected with measles to their newborn children. These antibodies are transferred in low amounts and usually last six months or less. In this paper a mathematical model of measles disease was formulated incorporating temporary passive immunity. There exist two equilibria in the model; Disease Free Equilibrium (DFE) and Endemic Equilibrium (EE). The Disease Free Equilibrium (DFE) state was analyzed for local and global stability. The Basic Reproduction Number 0 R was computed and used to carried out the sensitivity analysis with some parameters of the mode. The analysis shows that as contact rate  increases the 0 as the vaccination rate v increases the 0 R decreases. Sensitive parameters with the R R 0 increases and were presented graphically. The disease will die out of the population if the attention is given to high level immunization.
Stability Analysis for Mathematical Modeling of Dengue Fever Transmission and Control
(Proceedings of International Conference on Contemporary Developments in Mathematical Sciences (ICCDMS), 2021-04-13) Aliyu, A. H.; Akinwande, N. I.; Somma Samuel Abu
Dengue fever is one of the greatest health challenges in the present world. In this work, mathematical modeling of dengue fever transmission and control was formulated. The model considered the human population h N and the vector population m N which are further subdivided into six classes, susceptible human 𝑆, infected human 𝐼, temporary recovered human class 1 R, permanently recovered human class 2 R , susceptible mosquito 1 M, and infected mosquito class 2 M . The Disease Free Equilibrium (DFE) point was obtained and the basic Reproduction number 0 R was computed. The Disease Free Equilibrium (DFE) is locally and globally asymptotically stable when 1 0  R .
Stability Analysis of Disease Free Equilibrium (DFE) State of a Mathematical Model of Yellow Fever Incorporating Secondary Host
(Pacific Journal of Science and Technology, 2017-11-20) Somma, Samuel Abu; Akinwande, N. I.; Jiya, M.; Abdulrahaman, S.
In this paper we formulate a mathematical model of yellow fever incorporating secondary host. We obtained the Disease Free Equilibrium (DFE) Points and compute the basic reproduction number. The local and global stability of the DFE was analyzed using Jacobian Matrix stability techniques and Lyapunov function respectively. The local and global stability was asymptotically stable if 1 0 R  and 1 0 R  , respectively. The basic reproduction number and control parameters of the model were presented graphically.