Mathematical Models in Biology
Serving as a basic introduction to concepts in deterministic biological modeling, this text shows how relatively simple mathematics can be applied to a variety of models to draw interesting conclusions.
TABLE OF CONTENTS Mathematical Models in Biology
List of Tables
Chapter 1: The Theory of Linear Difference Equations Applied to Population Growth
- Table 1.1: Changes in a Plant Population over 20 Generations: (a) ?=0.5, ?=0.25, ?=2.0, ?=0.8; (b) ?=0.6, ?=0.3, ?=2.0, ?=0.8
Chapter 3: Applications of Nonlinear Difference Equations to Population Biology
- Table 3.1: Mating Table
- Table 3.2: Offspring Table
Chapter 4: An Introduction to Continuous Models
- Table 4.1: Chemostat Parameters
- Table 4.2: Jacobian Coefficients for the Chemostat
- Table 4.3: Variables in Bolie s (1960) Model for Insulin-Glucose Regulation
Chapter 5: Phase-Plane Methods and Qualitative Solutions
- Table 5.1: Linear Systems of two ODEs
- Table 5.2: Directions of Flow in the NC Plane (Fig. 5.16)
Chapter 6: Applications of Continuous Models to Population Dynamics
- Table 6.1: A Summary of Several Epidemic Models
- Table 6.2: Estimates of the intrinsic reproductive rate R0 for human diseases and the corresponding percentage of the population p that must be protected by immunization to achieve eradication. [Reprinted by permission, American Scientist, journal of Sigma Xi, Parasitic Infections as Regulator of Animal Populations, by Robert M. May, 71:36 45 (1983).]
Chapter 9: An Introduction to Partial Differential Equations and Diffusion in Biological Settings
- Table 9.1: Particles Entering the Box (See Figure 9.4b.)
- Table 9.2: Analogies between Vector and Del Operations
- Table 9.3: Diffusion Coefficients of Biological Molecules
- Table 9.4: Time Taken to Diffuse Through a Given Distance
Chapter 10: Partial Differential Equation Models in Biology
- Table 10.1: Dispersal Rates
Chapter 11: Models for Development and Pattern Formation in Biological Systems
- Table...
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