Mathematical Modeling in the Age of the Pandemic (Textbooks in Mathematics)

One cannot watch or read about the news these days without hearing about the models for COVID-19 or the testing that must occur to approve vaccines or treatments for the disease. The purpose of Mathematical Modeling in the Age of a Pandemic is to shed some light on the meaning and interpretations of many of the types of models that are or might be used in the presentation of analysis. Understanding the concepts presented is essential in the entire modeling process of a pandemic. From the virus itself and its infectious rates and deaths rates to explain the process for testing a vaccine or eventually a cure, the author builds, presents, and shows model testing. This book is an attempt, based on available data, to add some validity to the models developed and used, showing how close to reality the models are to predicting "results" from previous pandemics such as the Spanish flu in 1918 and more recently the Hong Kong flu. Then the author applies those same models to Italy, New York City, and the United States as a whole. Modeling is a process. It is essential to understand that there are many assumptions that go into the modeling of each type of model. The assumptions influence the interpretation of the results. Regardless of the modeling approach the results generally indicate approximately the same results. This book reveals how these interesting results are obtained. Cover Half Title Series Page Title Page Copyright Page Contents Preface About the Author Chapter 1. Modeling as a Process 1.1. Introduction 1.2. Background and the Modeling Process 1.2.1. Overview 1.2.2. The Modeling Process 1.2.3. The Pandemic as a Process 1.2.4. Modeling Steps 1.2.5. Illustrative Examples 1.3. Technology 1.4. Conclusions Chapter 2. Discrete Dynamical System Models 2.1. Introduction 2.2. Introduction to Modeling with Dynamical Systems and Difference Equations 2.3. Modeling Discrete Change 2.4. Equilibrium Values and Long-Term Behavior 2.4.1. Stability and Long-Term Behavior 2.5. Modeling Nonlinear Discrete Dynamical Systems 2.5.1. What Is Herd Immunity? Chapter 3. Modeling Coupled Systems of Discrete Dynamical Systems 3.1. SIR and Other Models 3.2. Chapter Summary Chapter 4. Modeling with Differential Equation 4.1. What Is Social Distancing? 4.1.1. Why Practice Social Distancing? 4.1.2. Tips for Social Distancing 4.2. How Far Does a Cough Travel? Chapter 5. Systems of Differential Equations 5.1. Model of Systems 5.2. Chapter Summary Chapter 6. Probabilistic Models 6.1. Introduction 6.2. Empirical Model and Forecasts 6.3. Markov Chain Models 6.4. Regression Models and Regression Analysis 6.4.1. Curve Fitting Criterion 6.4.2. Diagnostics and Interpretations R2= 1-SSE/SST Residual Plots 6.4.3. Percent Relative Error 6.5. Chapter Summary Chapter 7. Hypothesis Tests 7.1. The P-Value Approach to Test Hypothesis 7.2. Large Samples with σ is Unkown 7.2.1. Large Samples with Proportions Chapter 8. Two Samples Hypothesis Test (Means and Proportions) 8.1. Large Independent Samples (Both Sample Sizes m, n ≥ 30) 8.2. Large Independent Samples [Only One Sample Size (Either m or n) Is ≥30] 8.2.1. Two Sample Tests on Proportions 8.2.2. Tests with Two Independent Samples, Continuous Outcome 8.2.3. Tests with Matched Samples, Continuous Outcome 8.2.4. Tests with Two Independent Samples, Proportions 8.3. Chapter Summary Chapter 9. Agent-Based Model with NetLogo 9.1. Scenario 1 9.2. Scenario 2 Sensitivity Analysis One Chapter 10. Concluding Remarks and Epilogue References Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Index "COVID-19 or the testing that must occur to approve vaccines or treatments for the disease. This book's purpose is to shed some light on the meaning and interpretations of many of the types of models that are or might be used in the presentation of analysis. Understanding the concepts presented is essential in the entire modeling process of a pandemic. From the virus itself and its infectious rates and deaths rates to explain the process for testing a vaccine or eventually a cure, the author builds, presents, and shows model testing. This book is an attempt, based on available data, to add some validity to the models developed and used, showing how close to reality the models are to predicting "results" from previous pandemics such as the Spanish flu in 1918 and more recently the Honk Kong flu. Then the author applies those same models to Italy, New York City, and the United States as a whole. Modeling is a process. It is essential to understand that there are many assumptions that go into the modeling of each type of model. The assumptions influence the interpretation of the results. Regardless of the modeling approach the results generally indicate approximately the same results. This book reveals how these interesting results are obtained"-- Provided by publisher