Frontiers in Mathematical Modelling Research

Description

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 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. Mathematics Research Developments Frontiers in MathematicalModelling Research Contents Preface Some Key Features of the Book Chapter 1Introduction to MathematicalModelling inApplications Abstract Introduction Types of Mathematical Modelling Approaches Applications of Modelling in Science and Engineering Analysis of MathematicalModel QualitativeAnalysis of a Deterministic Model Lypunov Global Stability Theory LaSalle’s Invariance Principle QualitativeAnalysis of a StochasticModel Existence and Uniqueness Theorem Stability of Equilibrium Solutions for SDE Stochastic Stability Theorem Layout of this Book Chapter 2: Fault Diagnosis of Rotating Machines Based on the Math-ematicalModel of a Rotor Bearing-Mass System Chapter 3: Experimental and Mathematical Modelling to Investigatethe Kinetic Behavior of Plasmid DNA Production by Escherichia ColiDH5 Chapter 4: MathematicalModelling of Robotic Digitalised Production Chapter 5: MathematicalModelling and Simulation of a RobotManipulator Chapter 6: Mathematical Modeling Applied to Control the EmergingDeadly Nipah Fever in Bangladesh Chapter 7: Mathematical Modeling of the Closed-Loop Performanceof a Continuous Bioreactor under a Feedback Polynomial-TypeController Chapter 8: Mathematical Study of Human Movement andTemperature in the Transmission Dynamics ofDengue Disease Between Two Patches Chapter 9: A Numerical Model of Malaria Fever Transmission withOrganized Vector Populace and Irregularity Chapter 10: MathematicalModeling in Food and Agricultural Areas Chapter 11: Mathematical Modelling of Complex Systems usingStochastic Partial Differential Equations: Review and Developmentof Mathematical Concepts Conclusion References Chapter 2Fault Diagnosis of Rotating Machines Basedon the MathematicalModel of a RotorBearing-Mass System Abstract Introduction MathematicalModel of the RBMS Transfer Functions Observability for Unbalance Effects Observability under Misalignment Observability Due to Unbalance and Misalignment RBMS Design Validation Results Conclusion Acknowledgment References Chapter 3Experimental and MathematicalModelling to Investigate the KineticBehavior of Plasmid DNA Production byEscherichia coli DH5 Abstract Introduction Methods Bacterial Strain and Plasmid Medium and Inoculum Cultivation DCW and Glycerol Determination Plasmid DNA Quantification NPT II and Organic Acids Quantification Model Development Thermodynamic Analysis Results pDNA Production Experiments Parametric Identification and Simulations Thermodynamics and the Effect of Temperature on theParameters Conclusion References Chapter 4Mathematical Modelling inRobotic Digital Production Abstract Introduction Analytical Framework Related Work Research Purpose and Objectives Method Section 1. Dynamic and Static Modeling of Processes ofCreation of High-Tech Digital Production Structures Setting the Task of Increasing the Enterprise Potential by CreatingHigh-Tech Structures Development of a Generalized Economic Mathematical Model Prime Cost of Production Analysis and Peculiarities of the Implementation of the EconomicMathematical Model Modification of the Economic Mathematical Model for a Given ProductInnovation Release Program Modification of the Economic Mathematical Model at a Given Level ofAutomation Static Modeling of Processes of Creation of High-Tech Structures Section 2. Discrete Programming Method in the Strategy ofModeling the Output and Capacity Utilization of High-TechDigital Production Structures Optimization of the Production Program of Flexible DigitalManufacturing Organizational and Production Structures Management of Processes of Mastering Production Capacities ofthe Developed Highly Automated Organizational and ProductionStructures Section 3. Modeling of Processes for Selection of EconomicallyExpedient Limits for Robotics of High-Tech Structures inDigital Production Development of an Economic Mathematical Model for DeterminingEconomically Feasible Boundaries for Robotics of Mass Production Development of the Economic Mathematical Model for DeterminingEconomically Feasible Boundaries of Robotics of DiversifiedProduction Section 4. Mathematical Modeling of Solving theCombinatorial Tasks of Minimizing Costs in the Processof Creating High-Tech Digital Production Structures Setting the Task of Modeling the Optimal Composition of HighlyAutomated Production Units Algorithm of Creation of Highly Automated Production Units ofthe High-Tech Organizational and Production Structure Computational Mechanism of Implementation of the Algorithm ofCreation of Highly Automated Production Units of the High-TechOrganizational and Production Structure Results and Discussion Conclusion References Chapter 5Mathematical Modelling and Simulation ofa Robot Manipulator Abstract Introduction MathematicalModelling Forward Kinematics Inverse Kinematics Differential Kinematics Singularities Trajectories Numerical Simulation Acknowledgment Conclusion References Chapter 6MathematicalModeling Appliedto Control the Emerging DeadlyNipah Fever in Bangladesh Abstract Introduction MathematicalModel Formulation Analysis of the Model Boundedness Basic Reproduction Number Equilibrium Analysis Global Stability of the Endemic Equilibrium Point E Incorporating Optimal Control to the Model Characterization of Optimal Controls Numerical Simulations Conclusion Acknowledgments References Chapter 7Mathematical Modelling ofthe Closed-Loop Performance ofa Continuous Bioreactor undera Feedback Polynomial-Type Controller Abstract Introduction Methods ABE Fermentation Model Bifurcation Analysis Stability of the Process Cubic Control Design Results Bifurcation Analysis and Open-Loop Stability Closed Loop Analysis System Stability Analysis Conclusion References Chapter 8Mathematical Studyof Human Movement and Temperaturein the Transmission Dynamics ofDengue Disease between Two Patches Abstract Introduction Model Formulation and Analysis Existence and Stability of Disease Free Equilibrium Point Basic Reproduction Number Numerical Results and Discussion Conclusion References Chapter 9A Numerical Model of Malaria FeverTransmission with Organized VectorPopulace and Irregularity Abstract 1. Introduction 2. Mathematical Model 3. Dynamical Behaviour without Noise 4. Dynamical Behaviour with Noise 5. Numerical Simulations Conclusion Acknowledgments Conflict of Interest References Chapter 10MATHEMATICAL MODELLINGIN FOOD AND AGRICULTURAL AREAS ABSTRACT INTRODUCTION MATHEMATICAL MODELING IN THE FOOD AREA Heat and Mass Transfer Models Heat Transfer Mass Transfer Diffusive Mass Transfer Fick’s Law Maxwell-Stefan Theory Effective Diffusivity Convective Mass Transfer Microbial and Enzymatic Inactivation Temperature Profiles and Thermal Conductivity Coefficient Food Drying Other Food-Related Areas Mathematical Modeling in the Agricultural Area Biochemical Reactions Growth Performance Plants Processes Dynamic Plants Demand Components Other Agricultural-Related Areas Plant Diseases Pest Control Animal Care Conclusion and Future Outlooks References Chapter 11Mathematical Modelling of ComplexSystems Using Stochastic PartialDifferential Equations: Review andDevelopment of Mathematical Concepts ABSTRACT Introduction Models, Mathematics and Modelling Motivation SPDEs and Modelling Development of Polynomial Chaos Expansion One Dimensional PCE Multi-Dimensional PCE Calculation of PCE The Intrusive Projection Method (The GalerkinProjection Method) The Non-Intrusive Projection Method Implementation of Polynomial Chaos Expansion Discretization Scheme in Time and Space Example 1: First Order Stochastic Process Construction of PCE Model of Example 1 Example 2: Stochastic Differential Equation Simulating Sample Realizations of a Brownian Motion (BM) The Euler-Maruyama (EM) Method Example 3: The Stochastic Advection Diffusion Equation (SADE) The Wick Product The Wick Product in Physics The Wick Product in Stochastic Analysis Conclusion and Discussion Appendix A References About the Editors M. Haider Ali Biswas, PhD M. Humayun Kabir, PhD Index Blank Page