Papers by ADEJIMI A ADENIJI
Scientific Reports
In this study, a deterministic model for the dynamics of Marburg virus transmission that incorpor... more In this study, a deterministic model for the dynamics of Marburg virus transmission that incorporates the impact of public health education is being formulated and analyzed. The Caputo fractional-order derivative is used to extend the traditional integer model to a fractional-based model. The model’s positivity and boundedness are also under investigation. We obtain the basic reproduction number $$\mathfrak {R_0}$$ R 0 and establish the conditions for the local and global asymptotic stability for the disease-free equilibrium of the model. Under the Caputo fractional-order derivative, we establish the existence-uniqueness theory using the Banach contraction mapping principle for the solution of the proposed model. We use functional techniques to demonstrate the proposed model’s stability under the Ulam-Hyers condition. The numerical solutions are being determined through the Predictor-Corrector scheme. Awareness, as a form of education that lowers the risk of danger, is reducing susc...
Russian journal of nonlinear dynamics, 2022
The oscillatory motion in nonlinear nanolattices having different interatomic potential energy fu... more The oscillatory motion in nonlinear nanolattices having different interatomic potential energy functions is investigated. Potential energies such as the classical Morse, Biswas-Hamann and modified Lennard-Jones potentials are considered as interaction potentials between atoms in one-dimensional nanolattices. Noteworthy phenomena are obtained with a nonlinear chain, for each of the potential functions considered. The generalized governing system of equations for the interaction potentials are formulated using the well-known Euler-Lagrange equation with Rayleigh's modification. Linearized damping terms are introduced into the nonlinear chain. The nanochain has statistical attachments of 40 atoms, which are perturbed to analyze the resulting nonlinearities in the nanolattices. The range of initial points for the initial value problem (presented as second-order ordinary differential equations) largely varies, depending on the interaction potential. The nanolattices are broken at some initial point(s), with one atom falling off the slender chain or more than one atom falling off. The broken nanochain is characterized by an amplitude of vibration growing to infinity. In general, it is observed that the nonlinear effects in the interaction potentials cause growing amplitudes of vibration, accompanied by disruptions of the nanolattice or by the translation of chaotic motion into regular motion (after the introduction of linear damping). This study provides a computationally efficient approach for understanding atomic interactions in long nanostructural components from a theoretical perspective.
Frontiers in Public Health, Feb 17, 2023
Fractal and Fractional
The rising tide of smoking-related diseases has irreparably damaged the health of both young and ... more The rising tide of smoking-related diseases has irreparably damaged the health of both young and old people, according to the World Health Organization. This study explores the dynamics of the age-structure smoking model under fractal-fractional (F-F) derivatives with government intervention coverage. We present a new fractal-fractional model for two-age structure smokers in the Caputo–Fabrizio framework to emphasize the potential of this operator. For the existence-uniqueness criterion of the given model, successive iterative sequences are defined with limit points that are the solutions of our proposed age-structure smoking model. We also use the functional technique to demonstrate the proposed model stability under the Ulam–Hyers condition. The two age-structure smoking models are numerically characterized using the Newton polynomial. We observe that in Groups 1 and 2, a change in the fractal-fractional orders has a direct effect on the dynamics of the smoking epidemic. Moreover,...
IOSR Journal of Mathematics, 2014
In this paper, we obtain a new version of the proof of 1 nn and the Legendre duplic... more In this paper, we obtain a new version of the proof of 1 nn and the Legendre duplicating formulas for positive integer n, by using a simple analytical technique
Mathematics and Statistics, 2021
Predator-prey models are the building blocks of the ecosystems as biomasses are grown out of thei... more Predator-prey models are the building blocks of the ecosystems as biomasses are grown out of their resource masses. Different relationships exist between these models as different interacting species compete, metamorphosis occurs and migrate strategically aiming for resources to sustain their struggle to exist. To numerically investigate these assumptions, ordinary differential equations are formulated, and a variety of methods are used to obtain and compare approximate solutions against exact solutions, although most numerical methods often require heavy computations that are time-consuming. In this paper, the traditional differential transform (DTM) method is implemented to obtain a numerical approximate solution to prey-predator models. The solution obtained with DTM is convergent locally within a small domain. The multi-step differential transform method (MSDTM) is a technique that improves DTM in the sense that it increases its interval of convergence of the series expansion. One predator-one prey and two-predator-one prey models are considered with a quadratic term which signifies other food sources for its feeding. The result obtained numerically and graphically showspoint DTM diverges. The advantage of the new algorithm is that the obtained series solution converges for wide time regions and the solutions obtained from DTM and MSDTM are compared with solutions obtained using the classical Runge-Kutta method of order four. The results demonstrated is that MSDTM computes fast, is reliable and gives good results compared to the solutions obtained using the classical Runge-Kutta method.
Computation
In this paper, we develop a deterministic mathematical epidemic model for tuberculosis outbreaks ... more In this paper, we develop a deterministic mathematical epidemic model for tuberculosis outbreaks in order to study the disease’s impact in a given population. We develop a qualitative analysis of the model by showing that the solution of the model is positive and bounded. The global stability analysis of the model uses Lyapunov functions and the threshold quantity of the model, which is the basic reproduction number is estimated. The existence and uniqueness analysis for Caputo fractional tuberculosis outbreak model is presented by transforming the deterministic model to a Caputo sense model. The deterministic model is used to predict real data from Uganda and Rwanda to see how well our model captured the dynamics of the disease in the countries considered. Furthermore, the sensitivity analysis of the parameters according to R0 was considered in this study. The normalised forward sensitivity index is used to determine the most sensitive variables that are important for infection con...
Journal of Mathematics and Computer Science
Unemployment poses to be a threat in many countries which has been a long age battle with the hum... more Unemployment poses to be a threat in many countries which has been a long age battle with the human race. Our study considers Africa (South Africa to be precise) and focuses on the academic and industry sectors, with PhD graduates and postdoctoral research fellows as key participants. The movement of PhD graduates and postdocs between academia and industry, and its impact (increase or decrease) in unemployment within the sectors was investigated. For the population of University, PhDs, Postdocs, and industry compartments, a model was developed. The primary objectives investigates the model by analyzing the stability at the University-PhD-Postdoc-Industry free equilibrium, University-PhD-Postdoc-Industry equilibrium, determine the recruitment number R UE and understand how to mitigate migrations within the University and Industry compartments. Our findings help to understand the cause and effects of migration, and aims to manage the migration of PhD graduates and Postdocs moving into the Industry while the university suffers research capacities.
Journal of Mathematics and Computer Science, 2023
Unemployment poses to be a threat in many countries which has been a long age battle with the hum... more Unemployment poses to be a threat in many countries which has been a long age battle with the human race. Our study considers Africa (South Africa to be precise) and focuses on the academic and industry sectors, with PhD graduates and postdoctoral research fellows as key participants. The movement of PhD graduates and postdocs between academia and industry, and its impact (increase or decrease) in unemployment within the sectors was investigated. For the population of University, PhDs, Postdocs, and industry compartments, a model was developed. The primary objectives investigates the model by analyzing the stability at the University-PhD-Postdoc-Industry free equilibrium, University-PhD-Postdoc-Industry equilibrium, determine the recruitment number R UE and understand how to mitigate migrations within the University and Industry compartments. Our findings help to understand the cause and effects of migration, and aims to manage the migration of PhD graduates and Postdocs moving into the Industry while the university suffers research capacities.
Journal of the Nigerian Society of Physical Sciences
The analysis of the derivation of the Riemann Analytic Continuation Formula from Euler’s Quadrati... more The analysis of the derivation of the Riemann Analytic Continuation Formula from Euler’s Quadratic Equation is presented in this paper. The connections between the roots of Euler’s quadratic equation and the Analytic Continuation Formula of the Riemann Zeta equation are also considered. The method of partial summation is applied twice on the resulting series, thus leading to the Riemann Analytic Continuation Formula. A polynomial approach is anticipated to prove the Riemann hypothesis; thus, a general equation for the zeros of the Analytic Continuation Formula of the Riemann Zeta equation based on a polynomial function is also obtained. An expression in Terms of Prime numbers and their products is considered and obtained. A quadratic function, G(tn), that is required for Euler’s quadratic equation (EQE) to give the Analytic Continuation Formula of the Riemann Zeta equation (ACF) is presented. This function thus allows a new way of defining the Analytic Continuation Formula of the Ri...
International Journal of Advanced Computer Science and Applications, 2021
The purpose of this research is to perform a comparative numerical analysis of an efficient numer... more The purpose of this research is to perform a comparative numerical analysis of an efficient numerical methods for second-order ordinary differential equations, by reducing the second-order ODE to a system of first-order differential equations. Then we obtain approximate solutions to the system of ODE. To validate the accuracy of the algorithm, a comparison between Euler's method and the Runge-Kutta method or order four was carried out and an exact solution was found to verify the efficiency, accuracy of the methods. Graphical representations of the parametric plots were also presented. Time inference analysis is taken to check the time taken to executes the algorithm in Mathematica®12.2.0. The obtained approximate solution using the algorithm shows that the Runge-Kutta method of order four is more efficient for solving system of linear ordinary differential equations.
Numerical investigation of the index of the vector field of Holling-Tanner model by the fast Fourier transform
Journal of Mathematical and Computational Science, 2021
The following Van der Pol and Holling-Tanner equations is analyzed from the qualitative viewpoint... more The following Van der Pol and Holling-Tanner equations is analyzed from the qualitative viewpoint by investigating their vector fields and analyzing the nature of the stationary points of these equations. The winding numbers (indices) of the stationary points are investigated by calculating the Poincare integrals. This calculation is performed by a novel method which is based on application of the fast Fourier transform (FFT) formation to the Poincare integrand.
The integral-differential and integral approach for the estimation of the classical Lennard-Jones and Biswas-Hamann potentials
International Journal of Mathematical Modelling and Numerical Optimisation, 2020
Many well-known semiempirical potential energy functions have been used to construct potential en... more Many well-known semiempirical potential energy functions have been used to construct potential energy curves from the physical or chemical properties of atoms. In this study, we identify the Lennard-Jones and Biswas-Hamann potential parameters and use these to calculate and reconstruct potential energy curves using experimental datasets of gold atom. Two different approaches are studied in detail. The Lennard-Jones potential yielded complex conjugate eigenvalues for both approaches. Numerical estimates proved the considered approaches gives better approximations as constructed and reconstructed potential energy curves were almost graphically indistinguishable.
Numerical Investigation of Diffusive Predator-Prey Model with Application to Annular Habitat
Far East Journal of Mathematical Sciences (FJMS), 2018
A simplified diffusive predator-prey model of the Lotka-Volterra type is considered for annular ... more A simplified diffusive predator-prey model of the Lotka-Volterra type is considered for annular habitat which is used for description of predator and prey coexistence at habitats surrounding lakes, mountains at particular heights,etc. The model is formulated as a system of two partial differential equations in which unknown populations of the predator and prey are described by functions depending on time and polar angle. A mixed problem is formulated so that the boundary conditions are $2\\pi$-periodic and in the initial conditions is assumed that populations of the predator and prey are completely separated on the annular habitat. The problem is solved by the method of lines by means of which the original system of partial differential equation is converted to the system of several hundred nonlinear ordinary differential equations. It's shown that predator and prey start slowly propagating through the annular habitat and their interaction commences after a time interval in the course of which the population of the predator is decreasing and the population of the prey is increasing. An intensive interaction of the predator and prey occurs after their meeting. The dynamics of the transient populations of predator and prey and the tendency of their steady state is analyzed.
BIOMATH, 2018
In this paper we undertake to consider the inverse problem of parameter identification of nonline... more In this paper we undertake to consider the inverse problem of parameter identification of nonlinear system of ordinary differential equations for a specific case of complete information about solution of the Holling-Tanner model for finite number of points for the finite time interval. In this model the equations are nonlinearly dependent on the unknown parameters. By means of the proposed transformation the obtained equations become linearly dependent on new parameters functionally dependent on the original ones. This simplification is achieved by the fact that the new set of parameters becomes dependent and the corresponding constraint between the parameters is nonlinear. If the conventional approach based on introduction of the Lagrange multiplier is used this circumstance will result in a nonlinear system of equations. A novel algorithm of the problem solution is proposed in which only one nonlinear equation instead of the system of six nonlinear equations has to be solved. Diff...
IOSR Journal of Mathematics, 2013
Intrigues most researchers about the Riemann zeta hypothesis is the ability to employ cum differe... more Intrigues most researchers about the Riemann zeta hypothesis is the ability to employ cum different approaches with instinctive mindset to obtain some very interesting results. Motivated by their style of reasoning, the result obtained in this work of redefining or re-representation of Riemann zeta function in different forms by employing different techniques on two functional equations made the results better, simpler and concise new representations of Riemann zeta function.
A Comparative Investigation of Complex Conjugate Eigenvalues of Generalized Morse and Classical Lennard-Jones Potential for Metal Atoms
Nanoscience & Nanotechnology-Asia,, 2019
The knowledge of parameter estimation for interatomic potentials is useful in the computation of ... more The knowledge of parameter estimation for interatomic potentials is useful in the computation of the vibrational structure of van der Waals molecules. On the estimation of the Generalized Morse and Classical Lennard-Jones potential energy functions, complex conjugates eigenvalues may be obtained. Different approaches can be used to solve this resulting problem. A method that uses the objective least squares function method to estimate parameters of the interatomic potentials is employed. Numerical simulation of the systems using metal atoms yields complex conjugates eigenvalues at some initial point. Other approaches of solving the complex conjugates eigenvalues problem are discussed comprehensively.
Inverse problems of the Holling-Tanner Model with complete and incomplete information
Biomath Communications Supplement, 2018
The inverse problem of parameter identification of nonlinear system of ordinary differential equa... more The inverse problem of parameter identification of nonlinear system of ordinary differential equations are considered in the case complete and incomplete information about functions of Holling-tanner Model. In the case of incomplete information it is possible to eliminate unknown function from the system of equations. Obtained equation for the known function is linear with respect to a new set of unknown parameters. These parameters functionally depend on six original unknown parameters. It's shown that only five of the original unknown parameters can be identified in the case when only one of the functions is known. Moreover, it's shown that additional knowledge of the second function at one point makes it possible to find all six unknown parameters and completely restore the unknown function. The methods developed in the present report are used for prediction and extrapolation of the system behaviour.
Parameters estimation of a constrained predator prey dynamical model with incomplete data
The Effect of Social Networking on the Behavior of SEC. Sch. in Lagos
The path to great influence and impactful life and living is the ability to understand self contr... more The path to great influence and impactful life and living is the ability to understand self control and divert all energies to a positive dispense. The effect of social punching and phone addiction has diverted the energy of our present day students and youth into a vain dispense of knowledge, reducing their logical senses into nothing or almost nothing. Their strength of reasoning has been engulfed into an atmosphere of getting them lazy, most of the students within the perimeter of Lagos have been able to spend most of their time in social minding and their senses do not have enough capacity to think abstractly. Reading this book would help understand the statistical effect of the social network in the positive and negative sphere within Lagos at large and other places by forecasting.
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Papers by ADEJIMI A ADENIJI