The Mathematics of Patterns, Symmetries, and Beauties in Nature: In Honor of John Adam

Preface
Acknowledgments
Contents
Contributors
Introduction: Nature and Its Mathematics
A Mathematical Model of Thermography with Application to Tungiasis Inflammation of the Skin
	1 Introduction
	2 Mathematical Model
	3 Results and Discussion
	4 Conclusion
	References
Mathematics of COVID-19
	1 Introduction
	2 Development of the Vaccine
		2.1 Structure of the Virus and How It Enters Human Cells
		2.2 Immuno-Response to the Virus
		2.3 The Vaccine
	3 The Basic SIR Model
	4 R0 and Herd Immunity
		4.1 Numerical Solution with Euler's Method
	5 Modifications of the Basic Model
		5.1 Susceptible-Exposed-Infectious-Recovered-Deceased (SEIRD) Model
		5.2 SEIRD Model with Vaccination
		5.3 SEIRDv Model with Reinfection
	References
Application and Modeling of a Tick-Killing Robot, TickBot
	1 Introduction
	2 Parameter Estimation Studies
		2.1 Permethrin Potency
		2.2 TickBot 2016
		2.3 Dry Ice Attraction Study
		2.4 TickBot 2017
	3 The Model
		3.1 Purpose
		3.2 Entities, State Variables, and Scales
			3.2.1 Agents/Individuals
			3.2.2 Spatial Units
			3.2.3 Environment
		3.3 Process Overview and Scheduling
		3.4 Design Concepts
			3.4.1 Basic Principles
			3.4.2 Sensing
			3.4.3 Interaction
			3.4.4 Stochasticity
			3.4.5 Observation
		3.5 Initialization
		3.6 Input Data
		3.7 Submodels
			3.7.1 Process Passage of Time
			3.7.2 Process Tick Life Cycle
			3.7.3 Process Host Mortality and Movement
			3.7.4 Process TickBot
		3.8 Scenarios
	4 Results
		4.1 Number of Ticks Killed
		4.2 Maximum Density of Questing Ticks
		4.3 Sum of Questing Ticks
		4.4 Sum of All Ticks
		4.5 Cost of Effort
	5 Conclusions
	References
Simulations of Social Distancing Scenarios and Analysis of Strategies to Predict the Spread of COVID-19
	1 Introduction
	2 Materials and Methods
		2.1 Data
		2.2 Models Description
			2.2.1 Discrete-Time SIR Model
			2.2.2 Continuous SEIR Model
		2.3 Parameter Estimation Framework
		2.4 Model and Parameter Setups
			2.4.1 Model Parameters
			2.4.2 Delay Scheme
			2.4.3 Social Distancing Scheme
			2.4.4 Parameter Setting
	3 Results and Discussion
		3.1 Analysis on the Effect of Social Distancing
		3.2 Comparison of Strategies to Simulate the Effect of Latency
	4 Conclusions
	References
Mathematical Modelling of the Evolution Dynamics of the Coronavirus Disease 2019 (COVID-19) in Burkina Faso
	1 Introduction
	2 Mathematical Model
	3 Basic Properties
	4 Data
	5 Numerical Simulations
		5.1 Situation Without Public Policies
		5.2 Situation with Public Policies
	6 Conclusion
	Appendix A. Tables of Data
	References
Spatio-Temporal Modelling of Progression of the COVID–19Pandemic
	1 Introduction
	2 The Dataset
		2.1 Preliminary Analyses
	3 Statistical Models and Results
		3.1 Conditional Autoregressive Bayesian Disease Mapping Models for Full Data
		3.2 Output and Results
	4 Discussion: Conclusion
	5 Data Availability Statement
	References
Archimedean and Non-Archimedean Approaches to Mathematical Modeling
	1 Introduction
		1.1 Cultural Approaches to Mathematics
		1.2 Artificial Mathematics
		1.3 Qualitative Mathematics
	2 The Non-Archimedean or Ultrametric/p-adic Approach
		2.1 p-adic Mathematical Physics
		2.2 Mathematically Thinking p-adically
		2.3 p-adic Mental Spaces
	3 The Archimedean or Euclidean Approach
		3.1 Signed Qualitative Modeling: An Example
		3.2 Jacobian Feedback Loops
		3.3 Loops and Jacobian Spectrum
		3.4 Qualitative existence of Multiple Equilibria
		3.5 Applications and Examples
			3.5.1 Thomas Conjectures
			3.5.2 Eisenfeld Qualitative Stability
			3.5.3 Loop Analysis in the Plane
			3.5.4 Biochemical Application: Two-Component Oscillators
			3.5.5 Two-dimensional Model for Electrochemical Corrosion
			3.5.6 A Loop Analysis of the Lorenz System
			3.5.7 A Loop Analysis of the Rossler System
		3.6 Summary
			3.6.1 Research Directions
	References