SIMIODE

Hsu, Sze-Bi. 2014. Mathematical Modelling In Biological Science. Department of Mathematics,
Tsing-Hua University TAIWAN. Class Notes. 67 pages.

Table of Contents

Introduction

1 Continuous population model for single species 1

1.1 Logistic equation               1

1.2 Delayed logistic equation             2

1.3 Time-delay models from physiology          3

2 Continuous Models for Interacting Populations 9

2.1 Predator-Prey models              9

2.2 Realistic Predator-Prey Model           11

2.3 Competition Models              20

3 Chemical Reaction Kinetics 25

3.1 Enzyme Kinetics               25

3.2 Autocatalysis                31

3.3 Biological Oscillators: Monotone cyclic feedback systems    34

3.4 Biological Oscillators: Belousov-Zhabotinskii reaction     37

4 Nerve Conduction 43

4.1 Electrical Circuit model of the cell membrane       43

5 Reaction diffusion equations 51

5.1 Simple random walk and derivation of the diffusion equation   51

5.2 Reaction diffusion equations            53

5.3 Chemotaxis                 53

Researchers should cite this work as follows:

• Brian Winkel (2020), "2004-Hsu, Sze-Bi - Mathematical Modelling In Biological Science. Class notes," https://simiode.org/resources/7305.

  BibTex | EndNote

1. biology
2. cell
3. circuit
4. compete
5. delay
6. kinetics
7. logistic
8. predator