An Invitation to Mathematical Biology

Preface. - 1 Introduction. - 2 Exponential Growth and Decay. - 2. 1 Exponential Growth. - 2. 2 Exponential Decay. - 2. 3 Summary. - 2. 4 Exercises. - 2. 5 References- 3 Discrete Time Models. - 3. 1 Solutions of the discrete logistic. - 3. 2 Enhancements to the Discrete Logistic Function. - 3. 3 Summary. - 3. 4 Exercises. - 3. 5 References- 4 Fixed Points, Stability, and Cobwebbing. - 4. 1 Fixed Points and Cobwebbing. - 4. 2 Linear Stability Analysis. - 4. 3 Summary. - 4. 4 Exercises. - 4. 5 References- 5 Population Genetics Models. - 5. 1 Two Phenotypes Case. - 5. 2 Three Phenotypes Case. - 5. 3 Summary. - 5. 4 Exercises. - 5. 5 References- 6 Chaotic Systems. - 6. 1 Robert May s Model. - 6. 2 Solving the Model. - 6. 3 Model Fixed Points. - 6. 4 Summary. - 6. 5 Exercises. - 6. 6 References- 7 Continuous Time Models. - 7. 1 The Continuous Logistic Equation. - 7. 2 Equilibrium States and their Stability. - 7. 3 Continuous Logistic Equation with Harvesting. - 7. 4 Summary. - 7. 5 Exercises. - 7. 6 References-. - 8 Organism-Organism Interaction Models. -8. 1 Interaction Models Introduction. - 8. 2 Competition. - 8. 3 Predator-Prey. - 8. 4 Mutualism. - 8. 5 Summary. - 8. 6 Exercises. - 8. 7 References- 9 Host-Parasitoid Models. - 9. 1 Beddington Model. - 9. 2 Some Solutions of the Beddington Model. - 9. 3 MATLAB Solution for the Host-Parasitoid Model. - 9. 4 Python Solution for the Host-Parasitoid Model. - 9. 5 Summary. - 9. 6 Exercises. - 9. 7 References- 10 Competition Models with Logistic Term. - 10. 1Addition of Logistic Term to Competition Models. - 10. 2 Predator-Prey-Prey Three Species Model. - 10. 3Predator-Prey-Prey Model Solutions. - 10. 4 Summary. - 10. 5Exercises. - 10. 6References- 11 Infectious Disease Models. - 11. 1 Basic Compartment Modeling Approaches. - 11. 2SI Model. - 11. 3SI model with Growth in S. - 11. 4 Applications using Mathematica. - 11. 5 Applications using MATLAB. - 11. 6 Summary. - 11. 7 Exercises. - 11. 8 References- 12 Organism Environment Interactions. - 12. 1 Introduction to Energy Budgets. - 12. 2 Radiation. - 12. 3 Convection. - 12. 4 Transpiration. - 12. 5 Total Energy Budget. - 12. 6 Solving the Budget: Newton s Method for Root Finding. - 12. 7 Experimenting with the Leaf Energy Budget. - 12. 8 Summary. - 12. 9 Exercises. - 12. 10 References- 13 Appendix 1: Brief Review of Differential Equations in Calculus- 14 Appendix 2: Numerical Solutions of ODEs- 15 Appendix 3: Tutorial on Mathematica- 16 Appendix 4: Tutorial on MATLAB- 17 Appendix 5: Tutorial on Python Programming- Index