##### A Mathematical Model for the Control of the Spread of Ebola Virus Disease in West Africa – A Disease-free Equilibrium Approach

A. U. Kalu, N. Agbanyim Akuagwu, I. A. Agwu

Journal of Advances in Mathematics and Computer Science, Page 1-9
DOI: 10.9734/BJMCS/2016/21930

The current Ebola Virus disease outbreak in West Africa is so far, the worst outbreak of the disease in any part of the world. It began in Guinea in December 2013 and then spread to Liberia, Sierra-Leone, Nigeria, Mali and Senegal. It has already claimed so many thousand lives and threatening those of so many others. In order to help control the spread or even completely eradicate the disease in West Africa in particular, we present a mathematical model based on the standard SEIR model. The disease-free equilibrium point of the model was established and its stability analysis carried out using the Routh-Hurwitz criteria. From the stability analysis it was found out that the necessary and sufficient condition for the control or possibly total eradication of the disease in West Africa is that the product of total break-down of the susceptible and latent classes must be less than the product of the total removal rates from both the latent and the infectious classes. We made recommendations on what should be done in order to meet the established condition.

##### Method of Finding Initial Solution for the Geometric Programming Problem

A. Yatsko, W. Susłow

Journal of Advances in Mathematics and Computer Science, Page 1-10
DOI: 10.9734/BJMCS/2016/21873

The paper proposes a new method for finding an initial solution in the problem of geometric programming. The paper describes the conditions, under which the geometric programming problem of obtaining a positive solution of the matrix equation is solved. This equation describes the orthogonality and normalization conditions. The authors gave an example of application of the method in case of solving the problem of minimizing the risk of the object safety violation for the level crossing (technical object with safety requirements).

##### A Twin Prime Analog of Goldbach’s Conjecture

A. Dinculescu

Journal of Advances in Mathematics and Computer Science, Page 1-4
DOI: 10.9734/BJMCS/2016/22064

Starting from the observation that the ratio of the number of twin primes to the number of primes up to a given number n, is similar to the ratio of the number of primes to the number of positive integers in the same interval, and from Goldbach’s conjecture that any even integer greater than 2 can be expressed as the sum of two primes, it is conjectured that any even integer strictly larger than a prime P is the sum of two twin ranks or, equivalently, any prime number is the sum of two twin ranks minus 1. This conjecture was verified up to the 10000th prime, and no counterexample was found.

##### Perfect-Mail: A Secure E-mail Protocol with Perfect Forward Secrecy

Baoyuan Kang, Danhui Xu

Journal of Advances in Mathematics and Computer Science, Page 1-11
DOI: 10.9734/BJMCS/2016/21889

With the rapid development of Internet, e-mail has become an essential communication tool. But, the security of e-mail communications is an important issue. Recently, Chen et al. [6] proposed a new protocol of wide use for e-mail. Chen et al. claimed that the proposed protocol is skillfully designed to achieve perfect forward secrecy and end to end security as well as to satisfy the requirements of confidentiality, origin, integrity and easy key management. But, in this paper, we show that Chen et al.’s protocol suffers from the e-mail server impersonation attack, mail content confidentiality attack and replay attack. Moreover, we give an improvement on Chen et al.’s protocol to overcome its security weaknesses, and propose the perfect-mail, a secure e-mail protocol with perfect forward secrecy. It is concluded by analysis that the improved protocol provides the perfect forward secrecy and resists replay attack, impersonation attack, and mail content confidentiality attack. But the communication cost of improved protocol is equal to that of Chen et al.’s protocol, and the computing cost of improved protocol is only added by two signature verification.

##### Improvement Results for Oscillatory Behavior of Second Order Neutral Differential Equations with Nonpositive Neutral Term

R. Arul, V. S. Shobha

Journal of Advances in Mathematics and Computer Science, Page 1-7
DOI: 10.9734/BJMCS/2016/20641

In this paper we obtain new criteria for the oscillation of all solutions of second order neutral differential equations with nonpositive neutral term, which improve some of the results in [1]. Examples are provided to illustrate the main results.

##### On Eccentric Adjacency index of Several Infinite Classes of Fullerenes

Journal of Advances in Mathematics and Computer Science, Page 1-11
DOI: 10.9734/BJMCS/2016/20567

In theoretical chemistry, molecular structure descriptors are used for modeling physio-chemical, pharmacologic, toxicological, biological and other properties of chemical compound. The eccentric adjacency index of a graph G is defined as

where S(u) denotes sum of degrees of vertices adjacent to the vertex u and ε (u) is defined as the maximum length of any minimal path connecting u to any other vertex of G. Fullerenes are molecules in the form of cage-like polyhedra, consisting solely of carbon atoms bonded in a nearly spherical con guration. In this paper we calculate the eccentric adjacency index for several infinite classes of fullerenes.

##### On Cyclic Associative Abel-Grassman Groupoids

M. Iqbal, I. Ahmad, M. Shah, M. Irfan Ali

Journal of Advances in Mathematics and Computer Science, Page 1-16
DOI: 10.9734/BJMCS/2016/21867

A new subclass of AG-groupoids, so called, cyclic associative Abel-Grassman groupoids or CA- AG-groupoid is studied. These have been enumerated up to order 6. A test for the verification of cyclic associativity for an arbitrary AG-groupoid has been introduced. Various properties of CA- AG-groupoids have been studied. Relationship among CA-AG-groupoids and other subclasses of AG-groupoids is investigated. It is shown that the subclass of CA-AG-groupoid is di erent from that of the AG*-groupoid as well as AG**-groupoids.