
The Mathematics of Patterns, Symmetries, and Beauties in Nature
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This volume honors Dr. John Adam, a Professor at Old Dominion University, USA, for his lifetime achievements in the fields of mathematical modeling and applied mathematics. Dr. Adam has published over 110 papers and authored several books.
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Content
- Intro
- 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
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