Mathematics Research Developments No part of this digital document may be reproduced, stored in a retrieval system or transmitted in any form or by any means. The publisher has taken reasonable care in the preparation of this digital document, but makes no expressed or implied warranty of any kind and assumes no responsibility for any errors or omissions. No liability is assumed for incidental or consequential damages in connection with or arising out of information contained herein. This digital document is sold with the clear understanding that the publisher is not engaged in rendering legal, medical or any other professional services. Mathematics Research Developments Partial Differential Equations: Theory, Numerical Methods and Ill-Posed Problems Michael V. Klibanov and Jingzhi Li (Authors) 2022. ISBN: 978-1-68507-592-7 (Hardcover) 2022. ISBN: 978-1-68507-727-3 (eBook) Advanced Engineering Mathematics and Analysis. Volume 2 Rami A. Maher (Author) 2022. ISBN: 978-1-68507-605-4 (Hardcover) 2022. ISBN: 978-1-68507-691-7 (eBook) Outliers: Detection and Analysis Apra Lipi, Kishan Kumar, and Soubhik Chakraborty (Authors) 2022. ISBN: 978-1-68507-554-5 (Softcover) 2022. ISBN: 978-1-68507-587-3 (eBook) Generalized Inverses: Algorithms and Applications Ivan Kyrchei (Editor) 2021. ISBN: 978-1-68507-356-5 (Hardcover) 2021. ISBN: N/A (eBook) Advanced Engineering Mathematics and Analysis. Volume 1 Rami A. Maher (Author) 2021. ISBN: 978-1-53619-869-0 (Hardcover) 2021. ISBN: 978-1-68507-435-7 (eBook) Navier-Stokes Equations and their Applications Peter J. Johnson (Editor) 2021. ISBN: 978-1-53619-967-3 (Softcover) 2021. ISBN: 978-1-68507-162-2 (eBook) More information about this series can be found at https://novapublishers.com/product-category/series/mathematics-research- developments/ M. Haider Ali Biswas and M. Humayun Kabir Frontiers in Mathematical Modelling Research Copyright © 2022 by Nova Science Publishers, Inc. https://doi.org/10.52305/VLST3329 All rights reserved. No part of this book may be reproduced, stored in a retrieval system or transmitted in any form or by any means: electronic, electrostatic, magnetic, tape, mechanical photocopying, recording or otherwise without the written permission of the Publisher. We have partnered with Copyright Clearance Center to make it easy for you to obtain permissions to reuse content from this publication. Simply navigate to this publication’s page on Nova’s website and locate the “Get Permission” button below the title description. This button is linked directly to the title’s permission page on copyright.com. Alternatively, you can visit copyright.com and search by title, ISBN, or ISSN. 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In addition, no responsibility is assumed by the Publisher for any injury and/or damage to persons or property arising from any methods, products, instructions, ideas or otherwise contained in this publication. This publication is designed to provide accurate and authoritative information with regard to the subject matter covered herein. It is sold with the clear understanding that the Publisher is not engaged in rendering legal or any other professional services. If legal or any other expert assistance is required, the services of a competent person should be sought. FROM A DECLARATION OF PARTICIPANTS JOINTLY ADOPTED BY A COMMITTEE OF THE AMERICAN BAR ASSOCIATION AND A COMMITTEE OF PUBLISHERS. Additional color graphics may be available in the e-book version of this book. Library of Congress Cataloging-in-Publication Data ISBN: (cid:28)(cid:26)(cid:27)(cid:16)(cid:20)(cid:16)(cid:25)(cid:27)(cid:24)(cid:19)(cid:26)(cid:16)(cid:27)(cid:23)(cid:24)(cid:16)(cid:23)(cid:11)(cid:72)(cid:37)(cid:82)(cid:82)(cid:78)(cid:12) Published by Nova Science Publishers, Inc. † New York Contents Preface …………………………………………………………. vii Chapter 1 Introduction to Mathematical Modelling in Applications………………………………………….…..1 M. Haider Ali Biswas and M. Humayun Kabir Chapter 2 Fault Diagnosis of Rotating Machines Based on the Mathematical Model of a Rotor Bearing-Mass System ………………………………….……………… 23 Juan L. Mata-Machuca, Ricardo Aguilar-López, Julio Tapia-Reyes and Jorge Fonseca-Campos Chapter 3 Experimental and Mathematical Modelling to Investigate the Kinetic Behavior of Plasmid DNA Production by Escherichia coli DH5 ……………….. 47 Fernando Grijalva-Hernández, María del Carmen Montes-Horcasitas, Jaime Ortega-López, Edgar N. Tec-Caamal and Ricardo Aguilar-López Chapter 4 Mathematical Modelling in Robotic Digital Production………………………………………………75 Marina Batova, Vyacheslav Baranov and Irina Baranova Chapter 5 Mathematical Modelling and Simulation of a Robot Manipulator………………………………………….. 149 Juan L. Mata-Machuca, Ricardo Aguilar-López and Jorge Fonseca-Campos Chapter 6 Mathematical Modeling Applied to Control the Emerging Deadly Nipah Fever in Bangladesh …….. 175 M. Haider Ali Biswas, Mst. Shanta Khatun, M. Nazmul Hasan and M. Humayun Kabir vi Contents Chapter 7 Mathematical Modelling of the Closed-Loop Performance of a Continuous Bioreactor under a Feedback Polynomial-Type Controller ……………. 205 Ricardo Aguilar-López, Edgar N. Tec-Caamal, Juan C. Figueroa-Estrada, Alma R. Domínguez- Bocanegra and María Isabel Neria-González Chapter 8 Mathematical Study of Human Movement and Temperature in the Transmission Dynamics of Dengue Disease between Two Patches ……………... 223 Ganga Ram Phaijoo and Dil Bahadur Gurung Chapter 9 A Numerical Model of Malaria Fever Transmission with Organized Vector Populace and Irregularity …247 Kalyan Das and M. N. Srinivas Chapter 10 Mathematical Modelling in Food and Agricultural Areas …………………………………... 273 Maicon Sérgio N. dos Santos, Carolina E. Demaman Oro, Rogério M. Dallago, Giovani L. Zabot and Marcus V. Tres Chapter 11 Mathematical Modelling of Complex Systems Using Stochastic Partial Differential Equations: Review and Development of Mathematical Concepts……… 333 Parul Tiwari, Don Kulasiri and Sandhya Samarasinghe About the Editors…………………………………………………..…3 73 Index …..………………………………………………………3 77 Preface Mathematical modeling is the process of trying to precisely define a nonmathematical situation, real-life phenomena of changing world and the relationships between the situations in the language of mathematics, and finding out mathematical formulations or patterns within these situations and phenomena. Mathematical modeling in terms of nonlinear dynamic equations is described as a conversion activity of real problems in a mathematical form. The interactions between the mathematical and biological sciences have been increasing rapidly in recent years. Both traditional topics, such as population and disease modeling, and new ones, such as those in genomics arising from the accumulation of DNA sequence data, have made mathematical modeling in biomathematics an exciting field. The best predictions of numerous individuals and scientific communities have suggested that this growing area will continue to be one of the most dominating and fascinating driving factors to capture the global change phenomena and design a sustainable management for a better world. Frontiers in Mathematical Modelling Research provides the most recent and up-to-date developments in the mathematical analysis of real world problems arising in engineering, biology, economics, geography, planning, sociology, psychology, medicine and epidemiology of infectious diseases. Mathematical modeling and analysis are important, not only to understand disease progression, but also to provide predictions about the evolution of the disease and insights about the dynamics of the transmission rate and the effectiveness of control measures. One of the main focuses of the book is the transmission dynamics of emerging and re-emerging infectious diseases and the implementation of intervention strategies. It also discusses optimal control strategies like pharmaceutical and non-pharmaceutical interventions and their viii M. Haider Ali Biswas and M. Humayun Kabir potential effectiveness on the control of infections with the help of compartmental mathematical models in epidemiology. This book also covers a wide variety of topics like dynamic models in robotics, chemical process, biodynamic hypothesis and its application for the mathematical modeling of biological growth and the analysis of diagnosis rate effects and prediction of zoonotic viruses, data-driven dynamic simulation and scenario analysis of the spread of diseases. Frontiers in Mathematical Modelling Research will play a pivotal role as helpful resource for mathematical biologists and ecologists, epidemiologists, epidemic modelers, virologists, researchers, mathematical modelers, robotic scientists and control engineers and others engaged in the analysis of the transmission, prevention, and control of infectious diseases and their impact on human health. It is expected that this self-contained edited book can also serve undergraduate and graduate students, young scholars and early career researchers as the basis for meaningful directives of current trends of research in mathematical biology. Some Key Features of the Book  Offers analytical and numerical techniques for dynamic models of nonlinear differential equations covering diverse area of applications  Discusses mathematical modeling and their applications in treating infectious diseases or analyzing their spreading rates  Covers the application of differential equations for analyzing robotic problems in systems and control engineering  Examines fault diagnosis of rotating machines by mathematical model of a rotor bearing-mass system  Focuses on the bioreactor mathematical model to simulate the non- linear behavior of the reactor in chemical process.