Open Access Short Research Article

A Mathematical Model for Mycolactone Toxin Reaction and Diffusion in Cell Cytoplasm

Peter Romeo Nyarko, Isaac Kwame Dontwi, Nana Kena Frempong

Journal of Advances in Mathematics and Computer Science, Page 1-11
DOI: 10.9734/JAMCS/2018/41382

The study of mechanisms and transport of proteins inside cells provide understanding of the dynamics of biological systems and give clues to biological effect of drugs on our system. Reaction-diffusion mechanisms inside cells control various cell functions from adhesion, haptotaxis, chemotaxis to cytoskeletal rearrangement. The theoretical model presented in this work aims to model activation of proteins in a biological cell. In our previous paper on mathematical model for mycobacterium invasion of tissues, (Nyarko et. al. 2017), we reported that mycolactone activation of theWASP in the cytoplasm of cells leads to tissue necrosis in the Buruli ulcer disease. We present two approaches to model reaction-diffusion in the cytoplasm: first the system of reaction-diffusion arising from mycolactone and WASP interactions are solved in a 3D domain with mycolactone toxin allowed to diffuse into the cytoplasm through the cell membrane to bind the WASP whiles defining a flux boundary condition on the cell membrane for the mycolactone, and restricting the WASP to the cytoplasm compartment. In the second model, we use the idea of periodicity to develop a topological setup for a layer of tissue that constitutes aggregation of similar cells. The model is solved using the coefficient form of PDE in Comsol Multiphysics. In the numerical simulation we compare the performance of three sparse direct solvers (UMFPACK, SPOOLES and PARDISO) on a 64-bit windows HP-Z1 workstation machine with 16GB RAM. The numerical results show the concentration distribution of mycolactone to be maximum at the center of the cytoplasm. The study shows that, the PARDISO solver performs better than the UMFPACK and SPOOLES solvers in terms of memory requirements and computational time on a fine mesh. The model is a contribution to the understanding of drug diffusion in the cell and most importantly to the understanding of the etiology of Buruli ulcer disease.

Open Access Original Research Article

Heart Disease Diagnosis via Nonparametric Mixture Models

Chipo Mufudza, Hamza Erol

Journal of Advances in Mathematics and Computer Science, Page 1-17
DOI: 10.9734/JAMCS/2018/40440

Aims/Objectives: Effective and efficient heart disease prediction via nonparametric mixture regression models.

Data Source: Data used in this paper is from the UCI database of the Cleveland Clinic Foundation for heart disease. The original data source contains 76 raw attributes with 303 observations each. For the purpose of this paper only 14 attributes were used as explained in section 4.

Methodology: Cluster analysis was applied via mixture models in the form of Nonparametric Density-based models. The clusters were identified using a graph theory based technique. Voronoi diagrams were used and and their distributions were estimated nonparametrically through a mixture model with Gaussian kernels. The optimal number of clusters and components of the identified clusters were determined, analysed and diagnosed using a density based silhouette information criteria. All the data analysis and model diagnosis were performed in R using the PdfCluster package.

Results: Different number of components resulted in different number of clusters when nonparametric mixture are used on heart disease. However, the optimal number of clusters under heart disease risks were found to be represented by two clusters with two components using density based silhouette information criteria. These were both well separated and classified as indicated by lack of spurious clusters and high positive density based silhouette values (See Figs. 2 and 4). Their properties are given in Table 2. The result is irregardless of the flexible conditions which are assumptions free on: shape of the distribution, number of components and number of clusters.

Conclusion: When nonparametric mixture models are used, individuals under risks of heart diseases can be diagnosed either under high or low risk depending on the dominant characteristics on a given individual. Those under high risk have attributes that makes them progress to heart diseases faster compared to those under low risk. Therefore by classifying individuals into these categories, medical personnel can quickly diagonise heart disease and efficiently identify characteristics associated with each category.

Open Access Original Research Article

Mathematical Modeling of TB - HIV Co Infection, Case Study of Tigania West Sub County, Kenya

Grace Gakii Muthuri, David M. Malonza

Journal of Advances in Mathematics and Computer Science, Page 1-18
DOI: 10.9734/JAMCS/2018/41850

TB is one of the leading causes of death among individuals infected with HIV/AIDS. A deterministic model for HIV/TB co-infection is presented and analyzed. The analysis of the model carried out includes the reproduction number, local stability of the disease free equilibrium, unique endemic equilibrium point, bifurcation analysis and sensitivity analysis of the model. The stability of the model shows that the model is stable if R0 < 1 and unstable otherwise. The research seeks to investigate the impact of HIV/AIDS on TB infections. Numerical simulation shows that HIV infection speeds the progression from exposed to infectious/active TB. The two diseases exhibit synergistic relationship where the infection of one disease accelerates the progression of the other. The model also seeks to confirm the need of HIV testing of all TB patients. From the sensitivity analysis and simulation, treatment reduces the spread of TB in the population among the TB infected and HIV/TB infected individuals. Numerical simulation was carried out using data from Tigania West Sub County Hospital.

Open Access Original Research Article

On the Geometry of Complex-Contact Riemannian Submersion

S. Longwap, P. T. Ajai, N. Homti

Journal of Advances in Mathematics and Computer Science, Page 1-12
DOI: 10.9734/JAMCS/2018/40993

This paper gives the structure equations of a complex-contact Riemannian submersion and establish that the fiber of this submersion is a contact metric submanifold of the total space. We investigate the vertical and horizontal distributions and obtain necessary and sufficient conditions for the distributions to be totally geodesic foliations. We also obtain some necessary and sufficient conditions of the submersion to be a totally geodesic map.

Open Access Original Research Article

A Computational Model for Multi-level Quadratically Constrained Quadratic Optimization under Fully Fuzzy Environment

Hawaf AbdAlhakim, O. E. Emam, A. A. Abd El-Mageed

Journal of Advances in Mathematics and Computer Science, Page 1-21
DOI: 10.9734/JAMCS/2018/42263

Fully fuzzy quadratic programming became emerge naturally in numerous real-world applications. Therefore, an effective model based on the bound and decomposition method and the separable programming method is proposed in this paper for solving Fully Fuzzy Multi-Level Quadratically Constrained Quadratic Programming (FFMLQCQP) problem, where the objective function and the constraints are quadratic, also all the coefficients and variables of both objective functions and constraints are described fuzzily as fuzzy numbers. The bound and decomposition method is recommended to decompose the given (FFMLQCQP) problem into series of crisp Quadratically Constrained Quadratic Programming (QCQP) problems with bounded variable constraints for each level. Each (QCQP) problem is then solved independently by utilizing the separable programming method, which replaces the quadratic separable functions with linear functions. At last, the fuzzy optimal solution to the given (FFMLQCQP) problem is obtained. The effectiveness of the proposed model is illustrated through an illustrative numerical example.