Asian Research Journal of Mathematics 2021-10-15T13:53:58+00:00 Asian Research Journal of Mathematics Open Journal Systems <p style="text-align: justify;"><strong>Asian Research Journal of Mathematics (ISSN: 2456-477X)</strong> aims to publish high-quality papers (<a href="/index.php/ARJOM/general-guideline-for-authors">Click here for Types of paper</a>) in all areas of ‘Mathematics and Computer Science’. By not excluding papers on the basis of novelty, this journal facilitates the research and wishes to publish papers as long as they are technically correct and scientifically motivated. The journal also encourages the submission of useful reports of negative results. This is a quality controlled, OPEN peer-reviewed, open access INTERNATIONAL journal.</p> Modeling Co-infection of Bovine Brucellosis and Tuberculosis 2021-10-01T02:54:59+00:00 Paride O. Lolika Mohamed Y. A. Bakhet Ben Saliba Lagure <p>Bovine tuberculosis and bovine brucellosis continue to cause serious economic and public health burden in low-income countries, especially in many regions of sub-Saharan Africa where the&nbsp;diseases are co-endemic. The economic burden of the two infections in low-income countries trigger&nbsp;important questions about the optimal intervention strategies in co-endemic regions. Hence, the&nbsp;need for comprehensive modelling studies to address such questions is therefore essential, yet&nbsp;only a limited of such studies exist to date despite the power of models to predict the future and,&nbsp;most importantly, to quantify the uncertainty in these predictions. Here, we develop a brucellosistuberculosis&nbsp;co-infection modelling framework that incorporates all relevant biological factors and&nbsp;culling of infectious animals-as the sole intervention strategy. We performed an optimal control&nbsp;study to assess the impact of culling infectious animals on controlling the prevalence of the two&nbsp;infections. Two objective functions have been considered, a linear and a quadratic.&nbsp;Existence and the characterization of the optimal control has been determined. Numerical results are carried out to illustrate the main findings. Our findings highlight the importance of optimal&nbsp;culling on controlling the spread of two infections.</p> 2021-09-28T00:00:00+00:00 ##submission.copyrightStatement## Existence of Positive Solution For a Fourth-order Differential System 2021-10-05T03:48:00+00:00 B. Kov´acs <p><span class="fontstyle0">Existence of Positive Solution For a Fourth-order&nbsp;Differential System&nbsp;</span></p> <p><span class="fontstyle0"><img src="/public/site/images/sciencedomain/Capture7.PNG">&nbsp;&nbsp; where <span class="fontstyle2">µ &gt; </span>0 is a constant, and the nonlinear terms <span class="fontstyle2">f, g </span>may be singular with respect to the time&nbsp;and space variables. By fixed point theorem in cones, the existence is established for singular&nbsp;differential system. The results obtained herein generalize and improve some known results&nbsp;including singular and non-singular cases. <br> </span></p> 2021-10-01T00:00:00+00:00 ##submission.copyrightStatement## Picard and Adomian Solutions of a Nonlocal Cauchy Problem of a Delay Dierential Equation 2021-10-11T02:50:20+00:00 E. A. A. Ziada <p>In this paper, two methods are used to solve a nonlocal Cauchy problem of a delay differential equation; Adomian decomposition method (ADM) and Picard method. The existence and uniqueness of the solution are proved. The convergence of the series solution and the error analysis are studied.</p> 2021-10-07T00:00:00+00:00 ##submission.copyrightStatement## Admissible Inversion on Γ1 Non-Deranged Permutations 2021-10-15T13:53:58+00:00 M. S. Magami M. Ibrahim <p>Some further theoretic properties of scheme called Γ<sub>1</sub> non deranged permutations, the permutation which fixes the first element in the permutations were identified and studied in relation to admissible inversion in this paper. This was done first through some computation on this scheme using prime number p ≥ 5, the admissible inversion descent <em>aid (ω<sub>p-1</sub>)</em> is equi-distributed with descent number <em>des&nbsp;(ω<sub>p-1</sub>) </em>and also showed that the admissible inversion set <em>Ai&nbsp;(ω<sub>i&nbsp;</sub>) </em>and admissible inversion set&nbsp;<em>Ai&nbsp;(ω<sub>p-i&nbsp;</sub>)</em> are disjoint.</p> 2021-10-12T00:00:00+00:00 ##submission.copyrightStatement## Mathematical Modeling of Transmission Dynamics with Periodic Contact Rate and Control by Different Vaccination Rates of Hepatitis B Infection in Ghana 2021-10-15T02:33:33+00:00 Ali Abubakar Reindorf Nartey Borkor Anas Musah Frank Kofi Owusu <p>The paper evidenced that Hepatitis B infection is the world's deadliest liver infection and Vaccination is among the principal clinical strategies in fighting it. These have encouraged a lot of researchers to formulate mathematical models to accurately predict the mode of transmission and make deductions for better health decision-making processes. In this paper, an SEIR model is used to model the transmission of the Hepatitis B infection with periodic contact rate and examine the impact of vaccination. The model was validated using estimated data in Ghana and simulated in a MATLAB environment. The results showed that the vaccination rate has a great impact on the transmission mode of the Hepatitis B infection and the periodic contact rate may lead to a chaotic solution which could result in an uncontrolled spreading of the infection. It is concluded that even if the vaccination rate is 70%, the infection rate would reduce to the minimum barest so more newborns must be vaccinated.</p> 2021-10-14T00:00:00+00:00 ##submission.copyrightStatement##