Open Access Short Research Article

Mathematical Model of the Transmission Dynamics of Lassa Fever with Separation of Infected Individual and Treatment as Control Measures

S. C. Nwasuka, I. E. Nwachukwu, P. C. Nwachukwu

Journal of Advances in Mathematics and Computer Science, Page 1-15
DOI: 10.9734/jamcs/2019/v32i630164

A non–linear deterministic mathematical model is formulated and analysed to study the controllability of lassa fever incorporating separation of infected individuals and treatment measures. The model assumes that humans susceptible acquired the Infection via interaction with the infected rodent populations at a constant rate and also the model assumes that treatment is only given to separated human population. The existence, uniqueness and positivity of the model’s solution have been carried out and the results shows that the solution exist and is unique. Again, the disease – free equilibrium state was obtained and analysed. We obtained an important threshold parameter called the effective reproduction number  using the next generation method. If Reff < 1 the disease-free equilibrium exists and is locally and globally asymptotically stable, implying  that Lassa fever can be controlled and eradicated within the population in a finite time and if the  , the disease invade and become endemic in the population.

Open Access Original Research Article

Perturbation Approach in the Dynamic Buckling of a Model Structure with a Cubic-quintic Nonlinearity Subjected to an Explicitly Time Dependent Slowly Varying Load

A. M. Ette, I. U. Udo-Akpan, J. U. Chukwuchekwa, A. C. Osuji, M. F. Noah

Journal of Advances in Mathematics and Computer Science, Page 1-19
DOI: 10.9734/jamcs/2019/v32i630160

This investigation is concerned with analytically determining the dynamic buckling load of an imperfect cubic-quintic nonlinear elastic model structure struck by an explicitly time-dependent but slowly varying load that is continuously decreasing in magnitude. A multi-timing regular perturbation technique in asymptotic procedures is utilized to analyze the problem. The result shows that the dynamic buckling load depends, among other things, on the first derivative of the load function evaluated at the initial time. In the long run, the dynamic buckling load is related to its static equivalent, and that relationship is independent of the imperfection parameter. Thus, once any of the two buckling loads is known, then the other can easily be evaluated using this relationship.

Open Access Original Research Article

Cramér-Rao Bound of Direction Finding Using a Uniform Hexagonal Array

Grace Wakarima Ndiritu, Dominic Makaa Kitavi, Cyrus Gitonga Ngari

Journal of Advances in Mathematics and Computer Science, Page 1-14
DOI: 10.9734/jamcs/2019/v32i630161

Direction-of-arrival (DOA) estimation is a key area of sensor array processing which is encountered  in many important engineering applications. Although various studies have focused on the uniform hexagonal array for direction finding, there is a scanty use of the uniform hexagonal array in conjunction with Cramer-Rao bound for direction finding estimation. The advantage of Cramér- Rao bound based on the uniform hexagonal array: overcome the problem of unwanted radiation in undesired directions. In this paper, the direction-of-arrival estimation of Cramér-Rao bound based on the uniform hexagonal array was studied. The proposed approach concentrated on deriving the array manifold vector for the uniform hexagonal array and Cramer-Rao bound of the uniform hexagonal array. The Cramér-Rao bound based on the uniform hexagonal array was compared with Cramer-Rao bound based on the uniform circular array. The conclusions are as follows. The Cramer-Rao bound of uniform hexagonal array decreases with an increase in the number of sensors. The comparison between the uniform hexagonal array and uniform circular array shows that the Cramér-Rao bound of the uniform hexagonal array was slightly higher as compared to the Cramér-Rao bound of the uniform circular array. The analytical results are supported by graphical representation.

Open Access Original Research Article

Numerical Solution to One-dimensional Consolidation by the Finite Element Method

E. Nwankwo, O. D. Aluko, S. Iyeke, A. Aladenika

Journal of Advances in Mathematics and Computer Science, Page 1-15
DOI: 10.9734/jamcs/2019/v32i630162

Adequate prediction of structures settlement is of utmost importance in order to prevent future failure of civil engineering structures due to excessive settlement resulting from an inadequate settlement prediction. In this paper, laboratory consolidation test was performed on five different clay samples from different locations to determine the soil consolidation in terms of pore water pressure. A formulation of Finite Element (FE) method was also developed for solving one-dimensional consolidation problem and its validity checked out. The one-dimensional consolidation differential equation was solved using finite element analysis by Rayleigh-Ritz method to obtain an approximate solution and ten elements were used to discretize the domain. MATLAB program was used to write the finite element codes. Considering the graphs generated from the MATLAB program which compares the consolidation behavior of the soil sample from analytical and numerical point of view, it is seen that there is a good agreement between Terzaghi’s exact solution to consolidation behavior of soils and numerical solution using the finite element method.

Open Access Original Research Article

Approximate Solution Technique for Singular Fredholm Integral Equations of the First Kind with Oscillatory Kernels

Vivian Ndfutu Nfor, George Emese Okecka

Journal of Advances in Mathematics and Computer Science, Page 1-9
DOI: 10.9734/jamcs/2019/v32i630163

An efficient quadrature formula was developed for evaluating numerically certain singular Fredholm integral equations of the first kind with oscillatory trigonometric kernels.  The method is based on the Lagrange interpolation formula and the orthogonal polynomial considered are the Legendre polynomials whose zeros served as interpolation nodes. A test example was provided for the verification and validation of the rule developed. The results showed the convergence of the solution and can be improved by increasing n.