The COVID-19 pandemic that started in 2019-2020 has led to a gigantic increase in modeling and simulation of infectious diseases. There are numerous topics associated with this epoch-changing event, such as (a) disease propagation, (b) transmission, (c) decontamination, and (d) vaccines. This is an evolving field. The targeted objective of this book is to expose researchers to key topics in this area, in a very concise manner. The topics selected for discussion have evolved with the progression of the pandemic. Beyond the introductory chapter on basic mathematics, optimization, and machine learning, the book covers four themes in modeling and simulation infectious diseases, specifically:
Part 1: Macroscale disease propagation,
Part 2: Microscale disease transmission and ventilation system design,
Part 3: Ultraviolet viral decontamination, and
Part 4: Vaccine design and immune response.
It is important to emphasize that the rapid speed at which the simulations operate makes the presented computational tools easily deployable as digital twins, i.e., digital replicas of complex systems that can be inexpensively and safely optimized in a virtual setting and then used in the physical world afterward, thus reducing the costs of experiments and also accelerating development of new technologies.
Author(s): Tarek I. Zohdi
Publisher: Springer
Year: 2023
Language: English
Pages: 122
City: Cham
Preface
Contents
About the Author
List of Figures
1 Preliminaries: Basic Mathematics, Optimization and Machine-Learning
1.1 Elementary Notation and Mathematical Operations
1.1.1 Vectors, Products and Norms
1.1.2 Basic Linear Algebra
1.1.3 Integral Transformations
1.2 Temporal Discretization Methods
1.2.1 Isolating a Single Particle
1.3 Basic Machine-Learning and Optimization
1.3.1 Gradient-Based Methods
1.3.2 Difficulties
1.4 Genetic-Based Machine-Learning Algorithm
1.4.1 Algorithmic Specifics
2 Part 1: Macroscale Disease Propagation
2.1 Introduction
2.1.1 Classical Basic Models
2.1.2 SIR Sub-population Models
2.1.3 Generalization of the SIR Family of Models
2.1.4 Agent-Based Models and Objectives
2.2 Direct Agent-Based Interaction Models
2.2.1 Agent-to-Agent Interaction and Rules of Engagement
2.2.2 Algorithm
2.2.3 Computational Acceleration
2.3 A Model Problem
2.4 Extensions
2.4.1 An Example of a Swarm Formulation
2.5 An Algorithm for Movement in a Region
2.5.1 Preliminary Numerical Example
3 Part 2: Microscale Disease Transmission and Ventilation System Design
3.1 Introduction
3.2 Analytical Characterization: Simplified Stokesian Model
3.2.1 Analysis of Particle Velocities
3.2.2 Analysis of Particle Positions
3.2.3 Settling (Airborne) Time
3.3 Computational Approaches for More Complex Models
3.3.1 More Detailed Characterization of the Drag
3.3.2 Simulation Parameters
3.4 Ventilation System Design
3.4.1 Assumptions
3.4.2 Incorporation of Masks
3.4.3 Incorporation of Vents
3.4.4 Overall Model
3.5 Genetic-Based Machine-Learning Ventilation Optimization
3.5.1 Model Problem
3.6 Summary and Extensions
4 Part 3: Ultraviolet Viral Decontamination
4.1 Introduction
4.1.1 Objectives
4.2 Electromagnetic Energy Propagation
4.2.1 Beam-Ray Decomposition
4.2.2 Reflection and Absorption of Rays
4.3 Electromagnetic Wave Propagation and Rays
4.3.1 Plane Harmonic Wave Fronts
4.3.2 Natural (Random) Electromagnetic Energy Propagation
4.3.3 Reflection and Absorption of Energy-Fresnel Relations
4.3.4 Reflectivity
4.4 Model Problem and Response Trends
4.4.1 Tracking of Beam-Decomposed Rays
4.4.2 Test Surface
4.5 Numerical/Quantitative Examples
4.6 Summary and Discussion
5 Part 4: Vaccine Design and Immune-System Response
5.1 Introduction
5.1.1 Brief History
5.1.2 Types of Vaccines
5.1.3 Vaccine Efficacy
5.1.4 Objectives of This Work
5.2 A Flexible Immune-Response Digital-Twin
5.3 Rapid Voxel Based Computation
5.4 Numerical Simulation of the Coupled System
5.4.1 Discretization of the c- and s-Fields
5.4.2 Iterative (implicit) Solution Method
5.5 Operation Counts in a Voxel-Based Method
5.6 Numerical Examples
5.7 Genetic-Based Machine-Learning Framework
5.7.1 Algorithmic Settings
5.7.2 Parameter Search Ranges and Results
5.8 Discussion and Summary
Epilogue
Appendix A Artificial Neural Networks
References
