by Chijioke J. Nweke, George C. Mbaeyi, Kelechi C. Ojide and Chukwunenye I. Okonkwo
Original Research
We present an empirical approach to changes in some fertility measures using multivariate profile analysis to determine level, trend and differences in fertility measures in Nigeria. ASFR, TFR and MNCEB was studied with respect to residency for three time points. Results obtained showed strong evidence of mean differences in TFR across zones with both ASFR, TFR and MNCEB showing no interaction with respect to residency. Various profile plots and tests showed evidences of parallelism for all the fertility measures considered. Some implications and suggestions with regards to policy formulation were also given.
American Journal of Applied Mathematics and Statistics. 2019, 7(6), 231-236. DOI: 10.12691/ajams-7-6-5
Pub. Date: December 17, 2019
8046 Views1491 Downloads1 Likes
by Bachioua Lahcene
Original Research
In this article, the Normal Inverse Gaussian Distribution model (NIGDM) is extended to a new Extended Normal Inverse Gaussian Distribution (ENIGDM) and its derivate models find many applications. The author proposes a new model ENIGDM, which generalizes the models of normal inverse Gaussian distribution. This class of ENIGDM is to approximate an unknown risk-neutral density. The paper discusses different properties of the ENIGDM. In particular, the applicability of this new general model with five parameters is well justified by more results which represent mixtures of inverse Gaussian distributions. Then a discussion is begun of the potential of the normal inverse Gaussian distribution and Lévy’s process for modeling and analyzing statistical data, with a particular reference to extensive sets of observations and applications in wide varieties.
American Journal of Applied Mathematics and Statistics. 2019, 7(6), 224-230. DOI: 10.12691/ajams-7-6-4
Pub. Date: December 10, 2019
3585 Views1777 Downloads
by Tormitim Terdoo Timothy, Aboiyar Terhemen, Kimbir Anande Richard and Emmanuel Olumuyiwa Onifade
Original Research
Mathematical modeling of many biological systems leads to ordinary differential equations (ODEs), which are often too complicated to solve exactly. Acquire Immune Deficiency Syndrome (AIDS) is one of the greatest health challenges of this millennium and it is caused by a virus called Human Immunodeficiency Virus (HIV). This work is a nonlinear mathematical model of HIV/AIDS dynamics considering Counseling and Anti-Retroviral Therapy (ART) which was developed in the form of differential equation. Three sub-models of the general model considered were the sub-model without ART, the sub-model with only infected males receiving ART and the sub-model with only infected females receiving ART. The general model and the sub-models with various parameter values are solved using the Variational Iteration Method (VIM), which is a semi analytical method. The VIM is used to obtain solutions of both nonlinear and linear functional equations without discretizing the equations or approximating the operators. The solution when it exists is found in a rapidly converging series form. The VIM provided continuous solutions to the model which can be used for further analysis like differentiation and integration and can be used to compute prevalence rates. Solutions of the model, presented in graphical form and the results revealed that VIM is an alternative method for the fourth-order Runge Kutta method. It was also observed that for effective counseling and ART to lead eradication, it necessary that the same proportion of males and females should be involved in ART. The existence of the disease free equilibrium state of the general model is investigated and shown to be locally and asymptotically stable (LAS).
American Journal of Applied Mathematics and Statistics. 2019, 7(6), 205-223. DOI: 10.12691/ajams-7-6-3
Pub. Date: November 28, 2019
9123 Views1486 Downloads
by Peter Gachoki, Moses Mburu and Moses Muraya
Original Research
Breast cancer is the leading type of cancer among women worldwide, with about 2 million new cases and 627,000 deaths every year. The breast tumors can be malignant or benign. Medical screening can be used to detect the type of a diagnosed tumor. Alternatively, predictive modelling can also be used to predict whether a tumor is malignant or benign. However, the accuracy of the prediction algorithms is important since any incidence of false negatives may have dire consequence since a person cannot be put under medication, which can lead to death. Moreover, cases of false positives may subject an individual to unnecessary stress and medication. Therefore, this study sought to develop and validate a new predictive model based on binary logistic, support vector machine and extreme gradient boosting models in order to improve the prediction accuracy of the cancer tumors. This study used the Breast Cancer Wilcosin data set available on Kaggle. The dependent variable was whether a tumor is malignant or benign. The regressors were the tumor features such as radius, texture, area, perimeter, smoothness, compactness, concavity, concave points, symmetry and fractional dimension of the tumor. Data analysis was done using the R-statistical software and it involved, generation of descriptive statistics, data reduction, feature selection and model fitting. Before model fitting was done, the reduced data was split into the train set and the validation set. The results showed that the binary logistic, support vector machine and extreme gradient boosting models had predictive accuracies of 96.97%, 98.01% and 97.73%. This showed an improvement compared to already existing models. The results of this study showed that support vector machine and extreme gradient boosting have better prediction power for cancer tumors compared to binary logistic. This study recommends the use of support vector machine and extreme gradient boosting in cancer tumor prediction and also recommends further investigations for other algorithms that can improve prediction.
American Journal of Applied Mathematics and Statistics. 2019, 7(6), 196-204. DOI: 10.12691/ajams-7-6-2
Pub. Date: November 26, 2019
14604 Views1294 Downloads
by Nasser A. El-Sherbeny
Original Research
The Minimum Cost Flow Problem (MCFP) is a well-known combinatorial optimization and a logical distribution problem. The MCFP is an NP-hard problem with many applications in logistic networks and computer networks. The Fuzzy Minimum Cost Flow Problem with Fuzzy Time-Windows (FMCFPFTW) is an extension of the MCFP. The goal of the problem is to find the minimum amount of the fuzzy flow from the source to the sink that satisfies all constraints of the fuzzy shortest dynamic f-augmenting path with the fuzzy dynamic residual network. We consider a generalized fuzzy version of the MCFP of the fuzzy network. We propose the mathematical model of the FMCFPFTW. Finally, a new algorithm of the FMCFPFTW is presented.
American Journal of Applied Mathematics and Statistics. 2019, 7(6), 191-195. DOI: 10.12691/ajams-7-6-1
Pub. Date: November 25, 2019
5100 Views1157 Downloads