Crowd Dynamics, Volume 3: Modeling and Social Applications in the Time of COVID-19 (Modeling and Simulation in Science, Engineering and Technology)

Preface
Contents
Behavioral Human Crowds: Recent Results and New ResearchFrontiers
	1 Introduction
	2 On the Contents of the Edited Book
	3 Research Perspectives
	References
Generalized Solutions to Opinion Dynamics Models withDiscontinuities
	1 Introduction and Summary of Results
		1.1 Mathematical Models and Main Results
	2 Generalized Solutions: Definitions and Basic Facts
		2.1 Solutions to Discontinuous Ordinary Differential Equations
		2.2 Inclusions Between Sets of Solutions
		2.3 P1) Average Preservation
		2.4 P2) Contractivity of the Support
	3 Existence and Uniqueness of Solutions
		3.1 Existence of Solutions
		3.2 Uniqueness for Almost Every Initial Condition
	4 Asymptotic Behavior of Solutions
		4.1 Equilibria and Cluster Points
		4.2 P3) Convergence to Cluster Points
	5 Future Directions
	References
Crowd Behaviour Understanding Using Computer Vision and Statistical Mechanics Principles
	1 Introduction
		1.1 Definition of Crowd
			1.1.1 Crowd Multiple Scales
			1.1.2 Crowd Behaviour Considerations
	2 Crowd Behaviour Detection and Modelling
		2.1 From Motions to Behaviour Understanding
		2.2 Measurement of Crowd
			2.2.1 Crowd Analogies to Physical Systems
			2.2.2 Crowd Representation with Its Holistic Features
			2.2.3 Approach
			2.2.4 Translation Through Flow
			2.2.5 Internal Kinetic Energy
			2.2.6 Structure Through Entropy
			2.2.7 Calculating Entropy
			2.2.8 Approach 1: Preserving the Density Pattern
			2.2.9 Approach 2: Preserving the Density Pattern with Independent Pedestrians
			2.2.10 Pre-processing
			2.2.11 Real-World Pedestrian Locations
			2.2.12 Internal Position Estimation
			2.2.13 Internal Position Density Map
			2.2.14 Normalising Entropy
			2.2.15 Specific Entropy
			2.2.16 Specific Entropy per Unit of Area
	3 Experimental Results
	4 Ongoing Research and Future Perspectives
	References
Applications of Crowd Dynamic Models: Feature Analysis and Process Optimization
	1 Introduction
	2 Congestion Analysis and Alleviation for Managing Crowds During Evacuations
		2.1 Congestion Analysis
		2.2 Congestion Alleviation
	3 Process Optimization in Evacuation Management
		3.1 Group-Based Approaches for Path Planning
			3.1.1 Group-Based Approach Without Navigation
			3.1.2 Optimization of Grouping Behavior with Navigation Knowledge
		3.2 Positive Emotional Contagion During Crowd Evacuation
			3.2.1 Strategies for Utilizing Positive Emotional Contagion
			3.2.2 Optimization of the Positive Emotional Contagion
	4 Summary
	References
Optimized Leaders Strategies for Crowd Evacuation in Unknown Environments with Multiple Exits
	1 Introduction
	2 Control of Pedestrian Dynamics Through Leaders
		2.1 Microscopic Model with Leaders and Multiple Exits
		2.2 Control Framework for Pedestrian Dynamics
	3 Mean-Field Approximation of Follower-Leader System
		3.1 MFMC Algorithms
	4 Numerical Optimization of Leaders Strategies
		4.1 Numerical Experiments
			4.1.1 Test 1: Minimum Time Evacuation with Multiple Exits
			4.1.2 Test 2: Mass Evacuation in Presence of Obstacles
			4.1.3 Test 3: Optimal Mass Splitting over Multiple Exits
		4.2 Discussion and Comparison
	5 Conclusions
	References
The Impact of Physical Distancing on the Evacuation of Crowds
	1 Introduction
	2 Crowd Dynamics and Physical Distancing
		2.1 Changes in Local Densities and Occupant Load
		2.2 Changes in Crowd Movement
		2.3 Route and Exit Choice
		2.4 Group Behaviour
	3 An Experiment on Physical Distancing
	4 Updated Relationships Between Speed/Flow and Density
		4.1 The SFPE Hydraulic Model Considering Physical Distancing
	5 Crowd Evacuation Modelling
	6 Discussion
	7 Conclusions
	References
A Kinetic Theory Approach to Model Crowd Dynamics with Disease Contagion
	1 Introduction
	2 A Kinetic Model for Crowd Dynamics
		2.1 Modeling Interactions
			2.1.1 Interaction with the Walls
			2.1.2 Interaction with Obstacles
			2.1.3 Interactions Between Pedestrians
		2.2 Mathematical Model
		2.3 Full Discretization
		2.4 Numerical Results
	3 Contagion Model in One Dimension
		3.1 Full Discretization
		3.2 Numerical Results
	4 Conclusions
	References
Toward a Quantitative Reduction of the SIR Epidemiological Model
	1 Introduction
	2 Basic SIR Model and Its Quantitative Reduction
	3 Using the Constitutive Law (t)=[(t)]
		3.1 A Direct Short-Time Estimate
		3.2 An Indirect Large-Time Estimate
		3.3 Estimate on the Error of the Reduction Method
	4 Ideas for an Improved Reduced Description
		4.1 An Instance of the Mori–Zwanzig Method
		4.2 Using the Invariant Manifold Method
		4.3 Back to the SIR Model
	5 Conclusion
	References
An Agent-Based Model of COVID-19 Diffusion to Plan and Evaluate Intervention Policies
	1 A Quick Introduction to Our Agent-Based Epidemic Model
		1.1 Why Models? Why Agents? Why Another Model?
		1.2 The Molecular Basis of SARS-CoV-2 Infection
		1.3 Our Model
	2 How S.I.s.a.R. Works
		2.1 Conditional Actions
		2.2 Parameter Definition
		2.3 Agents\' Interaction
	3 Contagion Representation
	4 Exploring Scenarios with Simulation Batches
		4.1 Epidemics Without and With Control Measures
		4.2 Actual Data
	5 Factual and Counterfactual Analyses
		5.1 Spontaneous Second Wave, Without Specific Containment Measures
		5.2 Second Wave, New Infections from Outside, Without Specific Containment Measures
		5.3 Second Wave, New Infections from Outside, with New Specific Containment Measures
		5.4 Calculating the Reproduction Number Without Delays
			5.4.1 Tikhonov Regularization to Smooth the Original Signal
			5.4.2 Do Not Wait for the Symptoms Onset Date
			5.4.3 Residuals
			5.4.4 Deseasoning via Singular Value Decomposition
			5.4.5 Residuals of the Deseasoned Series
			5.4.6 Putting it All Together with Markov Chain Monte Carlo
		5.5 Second Wave, New Infections from Outside, Introducing 20 Days in Advance the New Specific Containment Measures
		5.6 Second Wave, New Infections from Outside, with a Unique Intervention Measure: Stopping Fragile People for 60 Days
		5.7 To Recap
	6 Economic Analysis of the of Interventions
	7 Planning Vaccination Campaigns
		7.1 Some Notes on Vaccines
		7.2 Planning a Vaccination Campaign Using Genetic Algorithms, with Non-pharmaceutical Containment Measures in Action
			7.2.1 Vaccination Groups
		7.3 A Specific Realistic Case
		7.4 Vaccination Quotas, Plain Strategy
		7.5 Vaccination Quotas, Wise Strategy
		7.6 GAs Quotas in the Experiment, with Vaccinated People Spreading the Infection
	8 A New Model and Future Developments
	9 Appendix 1—Parameter Values
	10 Appendix 2—A Gallery of Contagion Sequences
	References