Exam 2 Review

Review
• The final exam will be comprehensive.
• It will cover material in the text book from
Chapters 1 – 6.
• It will also cover material not in the text book that was provided to you in the lecture notes.
• Please see the Exam 1 review for what to expect from chapters 1 -- 6.2
– All of that information still applies

Review – Discrete Models
• Exam 1
– Covered some mathematical and graphical aspects of discrete equations
(problem 1)
• Exam 2
– Will likely cover modeling aspects of discrete equations
• Model development, analysis, and interpretation

Review – Continuous Models
• Exam 1
– Covered some model analysis and interpretation for single-species continuous equations (problem 2 - Harvesting)
• Exam 2
– This is also fair game for Exam 2
• Instead of leading you through the mathematics, I may ask you a biological question and you will need to decide what mathematics to do to answer that question

Review – Continuous Models
• Exam 1
– Covered the analysis of a system of two equations (problem 3)
• Exam 2
– This is also fair game for Exam 2
– Some items that were not on Exam 1 that will very likely be included on Exam 2 are:
• Nondimensionalization
• Produce a phase portrait – by hand
• Produce a bifurcation diagram

Review – Continuous Models
• Exam 1
– No model development
• Exam 2
– This is fair game for Exam 2
• From the description of a biological problem, you should be able to derive a system of equations to model it
– We’ve had several group modeling sessions to practice this skill

Review Continuous Models
• Exam 1
– No computational component
• Exam 2
– This is fair game for Exam 2
– Be comfortable writing MATLAB code that solves single ODEs as well as systems of two or more equations
– NO pplane

Review – Specifics
• Chapter 6: 6.1 – 6.4 and 6.6
– Interacting Species
• Predator-Prey (Lab 5, Ch 6.2)
• Competition (Chapter 6.3 Assigned Reading)
– Multiple Species Models
• Lecture notes and chapter 6.4
– SIR Models (Ch 6.6 and lecture notes)
• Be able to recognize, develop, analyze and interpret the results from these types of models

Review - Specifics
• Multispecies Model Analysis
– Jacobian Matrix of Partial Derivatives
– Characteristic Polynomial
– Stability Criteria
• Routh-Hurwitz Criteria – Chapter 6.4 page 234

Review – Specifics
• SIR Models
– Model development
– Model reduction
– Conditions for an epidemic
– Properties of an epidemic
• Severity
• How many get infected
• etc