Open Access Original Research Article

Parametric Bootstrapping Predictive Estimator for Logistic Regression

Kunio Takezawa

Journal of Advances in Mathematics and Computer Science, Page 1-15
DOI: 10.9734/jamcs/2019/v32i530154

This paper proposes a method for constructing a predictive estimator for logistic regression. We make a provisional assumption that the predictive estimator is given by multiplying the maximum likelihood estimators by constants, which are estimated using a parametric bootstrap method. The relative merits of the maximum likelihood estimator and the predictive estimator produced by this method are determined by cross-validation. The results show that the predictive
estimators derived by this method lead to a smaller deviance than that obtained by the maximum likelihood estimator in many instances.

Open Access Original Research Article

Forecasting Maternal Mortality with Modified Gompertz Model

Samuel Essamuah Assabil

Journal of Advances in Mathematics and Computer Science, Page 1-7
DOI: 10.9734/jamcs/2019/v32i530155

The Gompertz model is one of the earliest most influential mortality models. The model dominated for more than 100 years and is still one of the most important models in the field of mortality. Even though the model was designed exclusively for human mortality, it has found its application in many fields. However, the model has not solely been applied to maternal mortality. The work, therefore, fit a modified form of Gompertz model to Ghana’ maternal mortality data (2016-2018) and the fit looks quite good. We also forecast with the model and the result shows that Ghana is far from achieving the Sustainable Development Goal (SDG) objective of reducing maternal mortality by 68 percent in the next 11 years. That is, the work shows that there will be an annual reduction of 2.9 percent in maternal mortality rate for the next 11 years. This reduction, however, is not enough to achieve the Sustainable Development Goal (SDG) objective of a 6 percent annual reduction. To make the SDG objective a reality, Ghana needs a further reduction of 3.1 percent annually in its maternal mortality rate. This calls for intensifying programmes that improve maternal health and reduces maternal mortality.

Open Access Original Research Article

Homotopy Analysis Decomposition Method for the Solution of Viscous Boundary Layer Flow Due to a Moving Sheet

S. Alao, R. A. Oderinu, F. O. Akinpelu, E. I. Akinola

Journal of Advances in Mathematics and Computer Science, Page 1-7
DOI: 10.9734/jamcs/2019/v32i530157

This paper investigates a new approach called Homotopy Analysis Decomposition Method (HADM) for solving nonlinear differential equations, the method was developed by incorporating Adomian polynomial into Homotopy Analysis Method. The Adomian polynomial was used to decompose the nonlinear term in the equation then apply the scheme of homotopy analysis method. The accuracy and efficiency of the proposed method was validated by considering algebraically decaying viscous boundary layer  flow due to a moving sheet. Diagonal Pade approximation was used to get the skin friction. The obtained results were presented along with other methods in the literature in tabular form to show the computational efficiency of the new approach. The results were found to agree with those in literature. Owing to its small size of computation, the method is not aected by discretization error as the results are presented in form of polynomials.

Open Access Original Research Article

Construction of Stable High Order One-Block Methods Using Multi-Block Triple

I. J. Ajie, K. Utalor, M. O. Durojaiye

Journal of Advances in Mathematics and Computer Science, Page 1-13
DOI: 10.9734/jamcs/2019/v32i530158

This paper deals with the construction of l-stable implicit one-block methods for the solution of stiff initial value problems. The constructions are done using three different multi-block methods. The first multi-block method is composed using Generalized Backward Differentiation Formula (GBDF) and Backward Differentiation Formula (BDF), the second is composed using Reversed Generalized Adams Moulton (RGAM) and Generalized Adams Moulton (GAM) while the third is composed using Reversed Adams Moulton (RAM) and Adams Moulton (AM). Shift operator is then applied to the combination of the three multi-block methods in such a manner that the resultant block is a one-block method and self-starting. These one-block methods are up to order six and  with at order ten. Numerical experiments show that they are good for solving stiff initial problems.

Open Access Original Research Article

Analysis and Modeling of Tuberculosis Transmission Dynamics

Rodah Jerubet, George Kimathi, Mary Wanaina

Journal of Advances in Mathematics and Computer Science, Page 1-14
DOI: 10.9734/jamcs/2019/v32i530159

Mycobacterium tuberculosis is the causative agent of Tuberculosis in humans [1,2]. A mathematical model that explains the transmission of Tuberculosis is developed. The model consists of four compartments; the susceptible humans, the infectious humans, the latently infected humans, and the recovered humans. We conducted an analysis of the disease-free equilibrium and endemic equilibrium points. We also computed the basic reproduction number using the next generation matrix approach. The disease-free equilibrium was found to be asymptotically stable if the reproduction number was less than one. The most sensitive parameter to the basic reproduction number was also determined using sensitivity analysis. Recruitment and contact rate are the most sensitive parameter that contributes to the basic reproduction number. Ordinary Differential Equations is used in the for­mulation of the model equations. The Tuberculosis model is analyzed in order to give a proper account of the impact of its transmission dynamics and the effect of the latent stage in TB transmission. The steady state's solution of the model is investigated. The findings showed that as more people come into contact with infectious individuals, the spread of TB would increase. The latent rate of infection below a critical value makes TB infection to persist.   However, the recovery rate of infectious individuals is an indication that the spread of the disease will reduce with time which could help curb TB transmission.