An introduction to undergraduate research in computational and mathematical biology : from birdsongs to viscosities /: from birdsongs to viscosities. (2020)

• Record Type: Book
• Further Information: Note: Hannah Callender Highlander, Alex Capaldi, Carrie Diaz Eaton, editors.
• Other Names: Highlander, Hannah Callender; Capaldi, Alex; Eaton, Carrie Diaz
• Contents: Intro -- Series Preface -- Introduction -- Contents -- Building New Models: Rethinking and Revising ODE Model Assumptions -- 1 Introduction -- 2 Techniques for Analyzing ODE Models -- 2.1 ODEs as Mean Field Models -- 2.2 Equilibrium Stability Analysis -- 2.3 Bifurcation Analysis -- 2.4 A Few Comments on Approximation -- 2.5 Fast-Slow Analysis of Systems with Multiple Time Scales -- 2.6 Computing Numerical Solutions to ODEs -- 2.6.1 Euler's Method -- 2.6.2 Numerical Solutions in R -- 2.6.3 Keeping Numerical Solutions Positive: The Log-Transform Trick -- 2.7 ODEs as Statistical Models 2.7.1 A Brief Overview of Key Statistical Concepts -- 2.7.2 Likelihood Based Parameter Estimation -- 2.7.3 Likelihood Framework for ODEs -- 2.7.4 Parameter Estimation as an Optimization Problem -- 2.7.5 Recognizing Identifiability (Estimability) Problems -- 2.7.6 Practical Identifiability Analysis -- 2.7.7 Structural Identifiability Analysis -- 2.7.8 Statistical Analyses Beyond Parameter Estimation -- 2.7.9 Alternative Approaches to Parameter Estimation and Uncertainty Quantification -- 2.7.10 Closing Remarks on Fitting ODE Models to Data -- 3 Identifying and Modifying Model Assumptions 3.1 Autonomous ODEs to Non-autonomous ODEs -- 3.2 Deriving Deterministic Discrete-Time Models -- 3.3 Deriving Stochastic Models -- 3.3.1 Continuous-Time, Discrete-State Stochastic Models -- 3.4 Stochastic Differential Equations (SDEs) -- 3.4.1 Numerical Solutions to SDEs -- 3.5 Distributed Delay Equations -- 3.5.1 Integral and Integro-Differential Equations -- 3.5.2 Linear Chain Trick -- 3.5.3 Mathematical Foundations of the Linear Chain Trick -- 3.5.4 Delay Differential Equations -- 3.6 Individual Heterogeneity -- 3.7 Spatially Explicit Models -- 4 Choosing a Research Project 4.1 Additional Project Topics -- 5 The Importance of Publishing -- Appendix -- Getting Started Writing in LaTeX and Programming in R -- Installing and Using LaTeX -- Installing and Using R -- References -- A Tour of the Basic Reproductive Number and the Next Generation of Researchers -- 1 Introduction -- 1.1 Overview -- 1.2 What Is the Basic Reproductive Number and Why Is It Important? -- 1.2.1 Definitions of R0 -- 1.2.2 Methods of Finding R0 -- 1.3 Additional Reading -- 2 An Introductory Example: Student-Teacher Ratio -- 2.1 The Model -- 2.2 Finding R0 with the Next Generation Matrix 2.2.1 The Intuition Behind the NGM Strategy -- 2.2.2 The Mathematical Approach -- 2.3 Interpreting R0 -- 2.4 Sensitivity Analysis -- 2.5 Other Full Examples -- 3 Challenges in the of the Next Generation Matrix -- 3.1 Defining the Infected Class: Infected but Not Infectious -- 3.2 Defining the Infected Class: Multiple Levels of Infection -- 3.3 Unclear Which Eigenvalue Is Largest: Co-infection -- 4 Challenges in Interpreting R0 -- 4.1 Multiple Infection Pathways: The Case of SARS -- 4.2 The Maximum of Two Reproductive Numbers: Co-infection -- 4.3 Two Thresholds and Backwards Bifurcations
• Publisher Details: Cham : Birkhäuser
• Publication Date: 2020
• Extent: 1 online resource (479 pages)
• Subjects: 570.285; Computational biology -- Research; Biomathematics -- Research; Biomathematics -- Research; Electronic books; Electronic books
• Languages: English
• ISBNs: 9783030336455
• Related ISBNs: 303033645X; 9783030336448
• Notes: Note: Print version record.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.