##### The Impact of Vaccination on Covid-19 Disease Transmission Patterns in a Human Population: A Theoretical Analysis

A. B. Okrinya, C. N. Timinibife

Asian Research Journal of Mathematics, Page 1-14
DOI: 10.9734/arjom/2021/v17i1030332

We construct a Mathematical model that describes the effect of vaccination on the dynamics of the transmission of COVID-19 disease in a human population. The model is a system of ordinary differential equations that describes the evolution of humans in a range of Covid-19 states due to emergence of an index case in a disease free region. The analysis of the model shows that effective vaccination can lead to disease eradication, where in the disease free state is locally asymptomatically stable if the basic reproductive number, and unstable when The numerical simulations suggests the use of other social measures alongside  vaccination in order to avert the possibility of the disease  becoming endemic.

##### Mathematical Logic of the Jones and Homfly Polynomials of Knotted Trivalent Networks

Mohsen Mohammed Almoallem

Asian Research Journal of Mathematics, Page 15-28
DOI: 10.9734/arjom/2021/v17i1030333

Two rational functions are defined logically for special type of knotted trivalent networks as state models of planar trivalent networks. The restriction of these two rational functions reduce to the Jones and Hom y polynomials for non oriented links. Also, these two models are used to define two invariants for this special type of knotted trivalent networks embedded in R3. Finally, we study some congruences of these two polynomials for periodic knotted trivalent networks this generalize the work of periodicity of the Jones and Hom y polynomials on knots to these two rational functions of knotted trivalent networks.

##### Some Properties of Cone Inner Product Spaces over Banach Algebra

Anas Yusuf, Abor Isa Garba

Asian Research Journal of Mathematics, Page 29-37
DOI: 10.9734/arjom/2021/v17i1030334

The aim of this paper is to introduce a concept of a cone inner product space over Banach algebras. This is done by replacing the co-domain of the classical inner product space by an ordered Banach algebra. Some properties such as Cauchy-Schwarz inequality, parallelogram identity and Pythagoras theorem are established in this setting. Similarly, the notion of cone normed algebra was introduced. Some illustrative examples are given to support our findings.

##### Application of Game Theory and Markov Chains on English Premier League (EPL) Scorelines Analysis

Christogonus Ifeanyichukwu Ugoh, Chinwendu Alice Uzuke, Obiora-Ilouno Happiness Onyebuchi, Obi-Okpala Chinelo Ijeoma, Orji gabriel Oyo, Eze Theophine Chinaza

Asian Research Journal of Mathematics, Page 38-50
DOI: 10.9734/arjom/2021/v17i1030335

The aim of this paper is to obtain the optimal strategies of two competitive players using Game Theorem and to make future predictions of games using Markov Chains involving the EPL. All the teams that have participated since 2005/2006 EPL season to EPL 2019/2020 season were considered and the method of proportion of wins was used to select five best teams. Linear programming was employed to select the optimal strategies, while the predictions for seasons 2020/2021 to 2023/2024 are obtained by Markov chain method. The results obtained revealed that Man U is the optimal strategy for Player A, and that Player A has to choose Man U to maximize his profit, meanwhile, Chelsea is the optimal strategy for Player B and he has to choose Chelsea to minimize his loss. The findings of the results also revealed that for Man U or Chelsea to win their home games, it will depend on their current home winning against the team they are playing with.

##### Algebraic Points of Degree at Most 5 on the Affine Curve y$$^{2}$$ = x$$^{5}$$ - 243

EL Hadji Sow, Pape Modou Sarr, Oumar Sall

Asian Research Journal of Mathematics, Page 51-58
DOI: 10.9734/arjom/2021/v17i1030336

In this work, we determine the set of algebraic points of degree at most 5 on the ane curve y2 = x5 - 243. This result extends a result of J.TH Mulholland who described in [4] the set of $$\mathbb{Q}$$- rational points i.e the set of points of degree one over $$\mathbb{Q}$$ on this curve.

##### Bound Estimation of Some Special Functions

Mengxuan Han, Jihong Yan

Asian Research Journal of Mathematics, Page 59-68
DOI: 10.9734/arjom/2021/v17i1030337

This article estimates bounds of several special functions. It also gives mathematical proofs and graphs of the corresponding functions. The results are applicable in aspect of inequalities.