Journal of Mathematical Analysis and Modeling

The solution of fifth and sixth order linear and non linear boundary value problems by the Improved Residual Power Series Method

Muhammad Gul — 2022-03-21

In this paper we solve some fifth and sixth order boundary value problems (BVPs) by the improved residual power series method (IRPSM). IRPSM is a method that extends the residual power series method (RPSM) to (BVPs) without requiring exact solution. The presented method is capable to handle both linear and nonlinear boundary value problems (BVPs) effectively. The solutions provided by IRPSM are compared with the actual solution and with the existing solutions. The results demonstrate that the approach is extremely accurate and dependable.

Completely positive map from M4(C) to M5(C) on positive semidefinite Matrices

Winda C. Akatch — 2022-04-01

Positive maps are essential in the description of quantum systems. However, characterization of the structure of the set of all positive maps is a challenge in mathematics and mathematical physics. We construct a linear positive map from M4 to M5 and state the conditions under which they are positive and completely positive (copositivity of positive).

On Equivalence of the ap-Sequential Henstock and ap-Sequential Topological Henstock Integrals

Victor Odalochi Iluebe — 2022-06-15

Let $X$ be a topological space and $\Omega \subset X$. Suppose $f:\Omega\rightarrow X$ is a function defined in a complete space $ \Omega $ and $ \tau $ is a vector in $ \mathbb{R} $ taking values in $X$. Suppose $ f $ is ap-Sequential Henstock integrable with respect to $\tau$, is $ f $ ap-Sequential Topological Henstock integrable with respect to $\tau$? It is the purpose of this paper to proffer affirmative answer to this question.

Mathematical Modeling: A Study of Corruption among Students of Nigeria Tertiary Institutions

A. O. Adeniran — 2022-06-15

Corruption is a slow poison damaging students and consequently societies and nations, virtually, all students of Nigerian tertiary institutions are exposed to corruption. In this study, an attempt is made to formulate the dynamics of corruption among students of Nigerian tertiary institutions. We describe mathematical modeling of corruption among students using an epidemiological compartment model. The population at risk of adopting corrupt ideology was divided into four compartments: S(t) is the susceptible class, E(t) is the Exposed class, C(t) is the Corrupted class and P(t) is the punished class. The positivity and boundedness of the model were established. The model possesses both corruption-free and endemic equilibrium. Likewise, the model exhibits threshold dynamics characterized by the basic reproduction number R0. The numerical implementation of the model reveals that corruption will persist among Nigeria students if the root cause were not eradicated.

Male Circumcision: A Means to Reduce HIV Transmission between Truckers and Female Sex Workers in Kenya

Ancent M. Kimulu — 2022-06-21

Kenya records over 1.5 million cases of HIV-infected people with a prevalence of 4.8% among adults
in 2019, ranking Kenya as the seventh-largest HIV population in the world. A recent study showed that
55.9% of Kenyan truckers pay for sex in while 46.6% had a regular partner along their trucking route in
addition to a wife or girlfriend at home. The complexity in the sexual network of Truckers, which can be a
conduit for the widespread of HIV, necessitated the need to better understand the dynamics of transmission
of HIV/AIDS between truckers and female sex workers. In this study, a model is formulated for HIV/AIDS
dynamics along the Northern corridor highway in Kenya. The reproduction number, disease-free equilibrium
and endemic equilibrium points were determined and their stabilities were also determined using the nextgeneration
matrix method. The disease-free equilibrium is stable when R0u < 1, R0c < 1 and R0f < 1 while
the endemic equilibrium point is stable when R0u > 1, R0c > 1 and R0f > 1. It is found that circumcision can
be used as an intervention to minimize the infection of HIV among truckers and female sex workers.