Frontiers in Mathematical Modelling Research

390 Pages·2022·42.544 MB·English

by  M. Haider Ali Biswas, M. Humayun Kabir

Mathematics Research Developments

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Mathematics Research Developments

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M. Haider Ali Biswas and
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Frontiers in Mathematical
Modelling Research
Copyright © 2022 by Nova Science Publishers, Inc.
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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.