Open Access Short Research Article

Asymptotic Behavior of the System of Second Order Nonlinear Difference Equations

Hongmei Bao

Journal of Advances in Mathematics and Computer Science, Page 1-8
DOI: 10.9734/JAMCS/2017/35842

This paper deals with dynamics of the solutions to the system of second order nonlinear difference equations

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where112.PNG Moreover we use the known results to determine the rate of convergence of the solutions of this system. Finally, we give some numerical examples to justify our results.

Open Access Original Research Article

Modeling and Simulation of the Population Dynamics of Biomphalaria tenagophila, Snails in Tres Palmeras, Salta, Argentina

Juan Carlos Rosales, Dora A. Davies

Journal of Advances in Mathematics and Computer Science, Page 1-14
DOI: 10.9734/JAMCS/2017/34591

Aims/ objectives: We have analyzed the parasitic infections, and the population dynamics of Biomphalaria tenagophila snails. The population under study lives in water bodies formed by tributaries of the river Arias in the Tres Palmeras zone in Salta, Argentina.
Study Design: Longitudinal and Cross-sectional studies.
Place and Duration of Study: Department of Mathematic and School of Biology for Studies of the Diversity of Invertebrates. National University of Salta, Argentina, from January 2005 to December 2007.

Methodology: Samples were collected at least twice per season in the period under study, and taken to the laboratory for further analysis. Snails were observed daily during 7 days to detect emergence of cercariae. In negative cases, snails were dissected to search for hidden infections. Data was analyzed using the techniques of power spectrum, exploratory analysis, and estimation of parameters by linear fit for a logistic model. Simulation tests were also carried out in order to qualitatively describe the present dynamic model.
Results: The highest prevalence corresponded to Echinostomatidae gen sp. III (2.99%), followed by Australapatemon magnacetabulum (1.44 %), while no infections by Schistosoma mansoni were found. Data showed that the most important infection frequencies were detected in the following order: 12, 18 and 3 months. Density-dependent parameters for the net growth rate were estimated as r ≈ 0:32, s ≈ 2:07. The corresponding carrying capacity was K ≈ 1069 for the annual case.
Conclusion: The most important frequency being at 12 months was the parameter that best described the situation observed in the field. This frequency could explain the annual variation, and the opportunistic growth pattern of the species. The function corresponding to density-dependent net growth rate provides an estimation of the growth coefficient and so-called “crowding coefficient”. However, data showed oscillations in the fit curve. The same pattern was observed in the simulations that would be explained with the generalized logistic model. Another possible explanation for the oscillations would be a sinusoidally-variable carrying capacity. Moreover, simulations described qualitatively the annual population dynamics.

Open Access Original Research Article

Ruin Probabilities in a Discrete Semi-Markov Risk Model with Random Dividends to Shareholders and Policyholders

Cui Wang

Journal of Advances in Mathematics and Computer Science, Page 1-9
DOI: 10.9734/JAMCS/2017/36012

The discrete semi-Markov risk model is modified by the inclusion of dividends paying to shareholders and policyholders. When surplus is no less than the thresholds a1 and a2, the company randomly pays dividends to shareholders and policyholders with probabilities q1,q2 respectively. Recursive formulae for ruin probabilities are derived. Finally, a numerical example is given to illustrate the effect of the related parameters on the ruin probabilities.

Open Access Original Research Article

Hypertension Prediction System Using Naive Bayes Classifier

Babajide O. Afeni, Thomas I. Aruleba, Iyanuoluwa A. Oloyede

Journal of Advances in Mathematics and Computer Science, Page 1-11
DOI: 10.9734/JAMCS/2017/35610

Hypertension is an illness that often leads to severe and life-threatening diseases such as heart failure, coronary artery disease, heart attack and other severe conditions if not promptly diagnosed and treated. Data Mining the use of a variety of techniques to smoothen information discovery or decision-making knowledge in the database and extracting these in a way that they can put to use in areas such as predictions, forecasting and estimation. This research has developed hypertension predictive system using data mining modelling technique, namely, Naïve Bayes. Medical profiles such as age, sex, blood pressure, chest pain and blood sugar it can predict the likelihood of patients getting a hypertension. This work was implemented in WEKA environment as an application which takes medical test’s parameter as an input. The 10-fold cross validation method was used to train the developed predictive model and the performance of the models evaluated. This paper presents a model for predicting hypertension with 83.69%. The naïve Bayes’ classifier proved to be an effective algorithm for predicting the diagnosis of hypertension in Nigerian patients. It can serve a training tool to train nurses and medical students to diagnose patients with hypertension.

Open Access Original Research Article

Finite Time Blow-up, Extinction and Non-extinction of Solutions for an Evolutionary Problem

Zhen Zhi, Zuodong Yang

Journal of Advances in Mathematics and Computer Science, Page 1-14
DOI: 10.9734/JAMCS/2017/35755

In this paper we consider a class of p-biharmonic parabolic equation with nonlocal nonlinearities and Neumann boundary condition. By constructing suitable auxiliary functions and using differential inequalities, we give blow-up criterion of solutions as well as extinction and nonextinction.
In addition, we derive similar results for a different equation.