This unique book gathers various scientific and mathematical approaches to and descriptions of the natural and physical world stemming from a broad range of mathematical areas – from model systems, differential equations, statistics, and probability – all of which scientifically and mathematically reveal the inherent beauty of natural and physical phenomena. Topics include Archimedean and Non-Archimedean approaches to mathematical modeling; thermography model with application to tungiasis inflammation of the skin; modeling of a tick-Killing Robot; various aspects of the mathematics for Covid-19, from simulation of social distancing scenarios to the evolution dynamics of the coronavirus in some given tropical country to the spatiotemporal modeling of the progression of the pandemic. Given its scope and approach, the book will benefit researchers and students of mathematics, the sciences and engineering, and everyone else with an appreciation for the beauty of nature. The outcome is a mathematical enrichment of nature’s beauty in its various manifestations.
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.
Author(s): Bourama Toni
Series: STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health
Publisher: Springer
Year: 2021
Language: English
Pages: 156
City: Cham
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
