Irrespective of whether the test for homogeneity is significant or not, most researchers assume time-homogeneity in analysing Markov chains due to scanty literature on the analysis of time-inhomogeneous Markov chains. Based on the assumption that, for each point in time in the future, a stochastic process will be subjected to a randomly selected transition matrix from an ergodic set of transition matrices the process was subjected to in the recent past, a methodology was proposed for analysing the long-run behaviours of time-inhomogeneous Markov chains. The proposed model was implemented to historical data consisting of the exchange rate of cedi-dollar, cedi-pound, and cedi-euro spanning over 6 years (January 2012 to December 2017). The results show that under certain &#x201C;closeness&#x201D; conditions, the long-run behaviours of the time-inhomogeneous case are almost identical to those of the time-homogeneous case. The paper asserted that even if the Markov chain exhibit time-inhomogeneity, analysing the Markov chain under the assumption of time-homogeneity is a step in the right direction under certain &#x201C;closeness&#x201D; conditions; otherwise, the proposed method is recommended. It was also found that investing in dollars yields better returns than the other currencies in Ghana.

Felix O. Mettle

Lydia Pomaa Boateng

Enoch N. B. Quaye

Emmanuel Kojo Aidoo

Issah Seidu

Analysis of Exchange Rates as Time-Inhomogeneous Markov Chain with Finite States

A maximum dynamic multicommodity flow problem concerns with the transportation of several different commodities through the specific source-sink path of an underlying capacity network with the objective of maximizing the sum of commodity flows within a given time horizon. Motivated by the uneven road condition of transportation network topology, we introduce the dynamic multicommodity contraflow problem with asymmetric transit times on arcs that increase the outbound lane capacities by reverting the orientation of lanes towards the demand nodes. Moreover, a pseudo-polynomial time algorithm by using a time-expanded graph and an FPTAS by using a <span class="nowrap"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.0498209pt" id="M1" height="8.68572pt" version="1.1" viewBox="-0.0498162 -8.6359 8.46388 8.68572" width="8.46388pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><path id="g113-133" d="M600 0V24L339 665L311 657L43 24V0H600ZM497 50H107L303 539L497 50Z"/></g></svg>-</span>condensed time-expanded network are presented.

Shiva Prakash Gupta

Urmila Pyakurel

Tanka Nath Dhamala

Dynamic Multicommodity Contraflow Problem with Asymmetric Transit Times

In this paper, a fishery model for African catfish and Nile tilapia is formulated. This model is used to compare financial profit and biomass outtakes in a two-species system versus single species systems. We consider a stage-structured fish population model consisting of the aforementioned fish species together with two food resources. The model dynamics include cannibalism, predator-prey, feeding, reproduction, maturation, development, mortality, and harvesting. We prove consistency of the model in the sense that the solutions will stay bounded and nonnegative over time. Conditions for local stability of fish-free equilibrium point are established. The simulation results reveal asymptotically stable solutions with coexistence of African catfish, Nile tilapia, and two food resources. The major conclusion from our findings is that fisheries should culture both species to maximize the biomass outtake and financial profit.

L. Nankinga

L. S. Luboobi

J. Y. T. Mugisha

B. Nannyonga

L. Carlsson

A Stage-Structured Fishery Model for African Catfish and Nile Tilapia Feeding on Two Food Resources with Harvesting

In this study, a deterministic mathematical model that explains the transmission dynamics of corruption is proposed and analyzed by considering social influence on honest individuals. Positivity and boundedness of solution of the model are proved and basic reproduction number <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-3.29107pt" id="M1" height="12.5794pt" version="1.1" viewBox="-0.0498162 -9.28833 22.1921 12.5794" width="22.1921pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><path id="g113-41" d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"/></g><g transform="matrix(.013,0,0,-0.013,4.498,0)"><path id="g113-83" d="M610 18C585 26 567 34 540 68C517 97 499 128 476 171C452 215 425 276 413 304C496 332 570 394 570 494C570 555 545 595 509 619S419 650 364 650H139L133 622C216 615 219 612 203 527L129 132C112 40 105 36 23 28L17 0H279L285 28C199 34 194 40 211 132L239 284H284C320 284 334 275 351 236C374 182 394 140 420 93C459 23 495 -1 592 -8H600L610 18ZM480 485C480 424 449 372 403 342C374 323 338 316 293 316H245L291 562C296 589 301 601 311 608S337 618 358 618C432 618 480 575 480 485Z"/></g><g transform="matrix(.0091,0,0,-0.0091,12.584,3.132)"><path id="g50-49" d="M245 635C92 635 37 457 37 312C37 149 91 -12 244 -12C395 -12 449 166 449 312C449 469 395 635 245 635ZM243 598C332 598 358 454 358 312C358 173 334 26 245 26C158 26 128 174 128 313S152 598 243 598Z"/></g><g transform="matrix(.013,0,0,-0.013,17.53,0)"><path id="g113-42" d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"/></g></svg> is computed using the next-generation matrix method. The analysis shows that corruption-free equilibrium is locally and globally asymptotically stable whenever <span class="inline_break"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="24.295pt" style="vertical-align:-3.291101pt" id="M2" height="11.927pt" version="1.1" viewBox="-0.0498162 -8.6359 24.295 11.927"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-83"/></g><g transform="matrix(.0091,0,0,-0.0091,8.086,3.132)"><use xlink:href="#g50-49"/></g><g transform="matrix(.013,0,0,-0.013,16.664,0)"><path id="g117-91" d="M512 -3V55L134 254V256L512 456V514L75 281V230L512 -3Z"/></g></svg><span class="irelop"></span><span class="nowrap"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="6.422pt" style="vertical-align:-3.291101pt" height="11.927pt" version="1.1" viewBox="27.8771838 -8.6359 6.422 11.927"><g transform="matrix(.013,0,0,-0.013,27.927,0)"><path id="g113-50" d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"/></g></svg>.</span></span> Also, the endemic equilibrium point is locally and globally asymptotically stable whenever <span class="inline_break"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="24.295pt" style="vertical-align:-3.291101pt" id="M3" height="11.927pt" version="1.1" viewBox="-0.0498162 -8.6359 24.295 11.927"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-83"/></g><g transform="matrix(.0091,0,0,-0.0091,8.086,3.132)"><use xlink:href="#g50-49"/></g><g transform="matrix(.013,0,0,-0.013,16.664,0)"><path id="g117-92" d="M512 230V281L75 514V456L453 256V254L75 55V-3L512 230Z"/></g></svg><span class="irelop"></span><span class="nowrap"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="6.422pt" style="vertical-align:-3.291101pt" height="11.927pt" version="1.1" viewBox="27.8771838 -8.6359 6.422 11.927"><g transform="matrix(.013,0,0,-0.013,27.927,0)"><use xlink:href="#g113-50"/></g></svg>.</span></span> Then, the model was extended to optimal control, and some numerical simulations with and without optimal control are also performed to verify the theoretical analysis using MATLAB. Numerical simulation of optimal control model shows that the prevention and punishment strategy is the most effective strategy to reduce the dynamic transmission of corruption.

Abayneh Kebede Fantaye

Zerihun Kinfe Birhanu

Mathematical Model and Analysis of Corruption Dynamics with Optimal Control

Heat equation is a partial differential equation used to describe the temperature distribution in a heat-conducting body. The implementation of a numerical solution method for heat equation can vary with the geometry of the body. In this study, a three-dimensional transient heat conduction equation was solved by approximating second-order spatial derivatives by five-point central differences in cylindrical coordinates. The stability condition of the numerical method was discussed. A MATLAB code was developed to implement the numerical method. An example was provided in order to demonstrate the method. The numerical solution by the method was in a good agreement with the exact solution for the example considered. The accuracy of the five-point central difference method was compared with that of the three-point central difference method in solving the heat equation in cylindrical coordinates. The solutions obtained by the numerical method in cylindrical coordinates were displayed in the Cartesian coordinate system graphically. The method requires relatively very small time steps for a given mesh spacing to avoid computational instability. The result of this study can provide insights to use appropriate coordinates and more accurate computational methods in solving physical problems described by partial differential equations.

Endalew Getnet Tsega

Numerical Solution of Three-Dimensional Transient Heat Conduction Equation in Cylindrical Coordinates

Edge detection consists of a set of mathematical methods which identifies the points in a digital image where image brightness changes sharply. In the traditional edge detection methods such as the first-order derivative filters, it is easy to lose image information details and the second-order derivative filters are more sensitive to noise. To overcome these problems, the methods based on the fractional differential-order filters have been proposed in the literature. This paper presents the construction and implementation of the Prewitt fractional differential filter in the Asumu definition sense for SARS-COV2 image edge detection. The experiments show that these filters can avoid noise and detect rich edge details. The experimental comparison show that the proposed method outperforms some edge detection methods. In the next paper, we are planning to improve and combine the proposed filters with artificial intelligence algorithm in order to program a training system for SARS-COV2 image classification with the aim of having a supplemental medical diagnostic.

Gustavo Asumu Mboro Nchama

Leandro Daniel Lau Alfonso

Roberto Rodr&#x00ED;guez Morales

Ezekiel Nnamere Aneke

Asumu Fractional Derivative Applied to Edge Detection on SARS-COV2 Images

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<p><em>Journal of Applied Mathematics</em> publishes original research papers and review articles in all areas of applied, computational, and industrial mathematics.</p>


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<p>Chief Editor, Professor Theodore E. Simos, is based at Ulyanovsk State Technical University, Russia. His main research interest is the numerical analysis of differential equations.</p>


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Journal of Applied Mathematics - Table of contents 2022

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Journal of Applied Mathematics publishes original research papers and review articles in all areas of applied, computational, and industrial mathematics.

Journal of Applied Mathematics