##### Mathematical Modeling of Typhoid Fever Disease Incorporating Unprotected Humans in the Spread Dynamics

Julia Wanjiku Karunditu, George Kimathi, Shaibu Osman

Journal of Advances in Mathematics and Computer Science, Page 1-11
DOI: 10.9734/jamcs/2019/v32i330144

A deterministic mathematical model of typhoid fever incorporating unprotected humans is formulated in this study and employed to study local and global stability of equilibrium points. The model incorporating Susceptible, unprotected, Infectious and Recovered humans which are analyzed mathematically and also result into a system of ordinary differential equations which are used for interpretations and comparison to the qualitative solutions in studying the spread dynamics of typhoid fever. Jacobian matrix was considered in the study of local stability of disease free equilibrium point and Castillo-Chavez approach used to determine global stability of disease free equilibrium point. Lyapunov function was used to study global stability of endemic equilibrium point. Both equilibrium points (DFE and EE) were found to be local and globally asymptotically stable. This means that the disease will be dependent on numbers of unprotected humans and other factors who contributes positively to the transmission dynamics.

##### Mathematical Model of Cholera Transmission with Education Campaign and Treatment Through Quarantine

H. O. Nyaberi, D. M. Malonza

Journal of Advances in Mathematics and Computer Science, Page 1-12
DOI: 10.9734/jamcs/2019/v32i330145

Cholera, a water-borne disease characterized by intense watery diarrhea, affects people in the regions with poor hygiene and untreated drinking water. This disease remains a menace to public health globally and it indicates inequity and lack of community development. In this research, SIQR-B mathematical model based on a system of ordinary differential equations is formulated to study the dynamics of cholera transmission with health education campaign and treatment
through quarantine as controls against epidemic in Kenya. The effective basic reproduction number is computed using the next generation matrix method. The equilibrium points of the model are determined and their stability is analysed. Results of stability analysis show that the disease free equilibrium is both locally and globally asymptotically stable R0 < 1 while the endemic equilibrium is both locally and globally asymptotically stable R0 > 1. Numerical simulation carried out using MATLAB software shows that when health education campaign is efficient, the number of cholera infected individuals decreases faster, implying that health education campaign is vital in controlling the spread of cholera disease.

##### Logical Design of n-bit Comparators: Pedagogical Insight from Eight-Variable Karnaugh Maps

Ali Muhammad Ali Rushdi, Sultan Sameer Zagzoog

Journal of Advances in Mathematics and Computer Science, Page 1-20
DOI: 10.9734/jamcs/2019/v32i330146

An -bit comparator is a celebrated combinational circuit that compares two -bit inputs  and  and produces three orthonormal outputs: G (indicating that  is strictly greater than ), E (indicating that  and  are equal or equivalent), and L (indicating that  is strictly less than ). The symbols ‘G’, ‘E’, and ‘L’ are deliberately chosen to convey the notions of ‘Greater than,’ ‘Equal to,’ and ‘Less than,’ respectively. This paper analyzes an -bit comparator in the general case of arbitrary  and visualizes the analysis for  on a regular and modular version of the 8-variable Karnaugh-map. The cases  3, 2, and 1 appear as special cases on 6-variable, 4-variable, and 2-variable submaps of the original map. The analysis is a tutorial exposition of many important concepts in switching theory including those of implicants, prime implicants, essential prime implicants, minimal sum, complete sum and disjoint sum of products (or probability-ready expressions).

##### Integrability of Very Weak Solutions for Boundary Value Problems of Nonhomogeneous p-Harmonic Equations

Yeqing Zhu, Yanxia Zhou, Yuxia Tong

Journal of Advances in Mathematics and Computer Science, Page 1-9
DOI: 10.9734/jamcs/2019/v32i330147

The paper deals with very weak solutions u to boundary value problems of the nonhomogeneous p-harmonic equation. We show that, any very weak solution u to the boundary value problem is integrable provided that r is sufficiently close to p.

##### Aperture Maximization with Half-Wavelength Spacing, via a 2-Circle Concentric Array Geometry that is Uniform but Sparse

Musyoka Kinyili, Dominic Makaa Kitavi, Cyrus Gitonga Ngari

Journal of Advances in Mathematics and Computer Science, Page 1-20
DOI: 10.9734/jamcs/2019/v32i330148

This paper proposes a new sensor-array geometry (the 2-circle concentric array geometry), that maximizes the array's spatial aperture mainly for bivariate azimuth-polar resolution of direction-of-arrival estimation problem. The proposed geometry provides almost invariant azimuth angle coverage and oers the advantage of full rotational symmetry (circular invariance) while maintaining an inter-sensor spacing of only an half wavelength (for non-ambiguity with
respect to the Cartesian direction cosines). A better-accurate performance in direction nding of the proposed array grid over a single ring array geometry termed as uniform circular array (UCA) is hereby analytically veried via Cramer-Rao bound analysis. Further, the authors demonstrate that the proposed sensor-array geometry has better estimation accuracy than a single ring array.