##### Modelling Vaccination and Treatment of Childhood Pneumonia and Their Implications

Cyrus Gitonga Ngari

Journal of Advances in Mathematics and Computer Science, Page 1-24
DOI: 10.9734/JAMCS/2018/41772

This paper presents a deterministic model for pneumonia transmission and uses the model to assess the potential impact of the vaccination, treatment and efficacy of vaccination drugs in lowering the public health impact of the pneumonia disease. The model is based on the Susceptible-Vaccinated-Infected- Treated compartmental classes of children less than five years. There is possibility of the non-severely infected recovering from natural immunity. Model analysis indicates the system lie in the positive region, solution is bounded and there exist unique positive endemic equilibrium point whenever control reproduction number is greater than unity. Important epidemiological thresholds such as the basic and control reproduction number are determined. Disease-free point equilibrium points are determined. Local and Global stability of equilibrium points will be investigated. Sensitivity analysis of the reproduction numbers indicated higher vaccination drug efficacy vaccination, treatment and recoveries from natural immunity hold great promise in lowering pneumonia impact. Estimated numerical result indicated impact of treatment is positive. Numerical simulation was carried to predict the dynamics of the system.

##### Fuzzy Risk Measure for Operational Risk

Assem Tharwat, Ramadan A. ZeinEldin, Hamiden Abd El-Wahed Khalifa, Ahmed M. Saleim

Journal of Advances in Mathematics and Computer Science, Page 1-17
DOI: 10.9734/JAMCS/2018/42625

Operational risk is one of the most hazardous types of risk banks face. Banks must take caution and reserve capital to meet these risks. Value at Risk (VaR) and Expected Shortfall (ES) used to measure operational risk and estimate the required capital to meet it. Value at Risk is not sub-additive and measure risk at specific point in risk position, i.e. does not measure the risk in the tail, while Expected Shortfall examines only the left tails of the loss distribution. At the same time, to apply VaR or ES banks must have enough historical data. On the other hand, banks need an early warning indictor to monitor the movement of the capital needed to meet operational risk and take correction action in appropriate time. In this paper we will introduce new risk measure based on fuzzy numbers. The main advantage of the new risk measure is that the banks can use it as an early warning indictor to monitor the capital required to meet risk. At the same time can be used as an alternative to VaR but have more desirable properties. The application of the proposed risk measure shown that, the obtained results are more reliable and accurate at the same time the proposed risk measure have more desirable properties than VaR and ES.

##### Influence of Chemical Reaction, Viscous Dissipation and Joule Heating on MHD Maxwell Fluid Flow with Velocity and Thermal Slip over a Stretching Sheet

I. G. Baoku

Journal of Advances in Mathematics and Computer Science, Page 1-20
DOI: 10.9734/JAMCS/2018/42481

A numerical integration scheme involving a fourth-fifth Runge-Kutta-Fehlberg method (RKF45) with shooting technique is employed to investigate a steady laminar incompressible forced convective flow of an upper-convected Maxwell fluid which is subjected to a transversely uniform magnetic field past a stretching sheet. Taking into account the velocity and thermal slip boundary conditions, the chemically reactive Maxwell fluid is examined in the presence of viscous dissipation and Joule heating. Using the similarity transformations, the momentum, energy and species concentration equations are transformed into a set of coupled nonlinear ordinary differential equations while the continuity equation is satisfied. The RKF45 solutions are obtained; verified with other results by homotopy analysis method that have been previously published in the literature and are found to be in good agreement. This close agreement supports the present analysis and accuracy of the numerical computations. The effects of the emerging flow parameters on the dimensionless velocity, temperature and species concentration distributions have been presented graphically and discussed. This article also includes a representative set of numerical results for local skin friction coefficient, Nusselt and Sherwood numbers in tables for various values of the governing parameters. It is concluded that the thermal boundary layer thickness is increased by increasing values of Hartmann number, Eckert number and thermal slip parameter while the local Nusselt and Sherwood numbers are enhanced by increments in the values of suction and stretching parameters.

##### Two-Step Hybrid Block Method for Solving First Order Ordinary Differential Equations Using Power Series Approach

G. Ajileye, S. A. Amoo, O. D. Ogwumu

Journal of Advances in Mathematics and Computer Science, Page 1-7
DOI: 10.9734/JAMCS/2018/41557

In this paper, we consider the derivation of hybrid block method for the solution of general first order Initial Value Problem (IVP) in Ordinary Differential Equation. We adopted the method of Collocation and Interpolation using power series approximation to generate the continuous formula. The properties and features of the methods are analyzed and some numerical examples are also presented to illustrate the accuracy and effectiveness of the method.

##### Adaptive Robust Profile Analysis of a Longitudinal Data

Gabriel Asare Okyere, Silverius Kwasi Bruku, Richard Tawiah, Gilbert Biney

Journal of Advances in Mathematics and Computer Science, Page 1-18
DOI: 10.9734/JAMCS/2018/42361

This paper uses nine winsorized scores in the adaptive test of Hogg, Fisher and Randles and deals with its extension to hypothesis testing in profile analysis of a balanced longitudinal data. Simulation studies are conducted to evaluate the efficiency of the adaptive test procedure relative to the traditional ANOVA-F test for different non-normal data sets. To illustrate the feasibility of the test, we analyzed a real data set from the study of tumor sizes in mice.