1. A cooperation model. Consider the following two-species model. where , and are positive constants. Under what circumstances is there a positive coexistence equilibrium? In the case where there exists a positive equilibrium, find ALL equilibria, determine their stability and sketch the phase plane. What does the phase plane look like when there is noContinue reading “MathBio HW6, due Wed April 16”

# Category Archives: Methods in Mathematical Biology

## MathBio: Gearing up for Test 2

If you a looking for problems to work on to prepare for Midterm 2, this post will be the place to look. This will be updated several times over the next few days. Challenge problems for discrete-time systems. Solutions to the important parts of the Horseshoe Crab project are written up here: Horseshow crabs 1a Continue reading “MathBio: Gearing up for Test 2”

## MathBio: Midterm 2, Wednesday, April 2

Our second midterm will be Wednesday April 2. The test will cover topics from Chapters 3 and 4. More details will be posted soon, but the main theme is: Qualitative Analysis of two-dimensional systems in both discrete and continuous time. A non-exhaustive list of topics includes: Biological Modeling concepts Age-structured models (e.g., Juvenile-Adult) Epidemic modelsContinue reading “MathBio: Midterm 2, Wednesday, April 2”

## Reminder: No office hours today, Tuesday 3/18

## MathBio: Supplemental Notes for Systems of ODEs

These notes will be updated as we progress through Chapter 4 in the book. Please keep an eye on this entry for the latest version. Systems of ODEs (pdf). Version 1, current as of March 17.

## MathBio: Homework 5, due Wed March 19

For the following assignment, you may work in groups but the homework you turn in should be your own. Homework 5 (pdf) If you have questions or comments, please use the comments section of this page. UPDATE (3/17, 3:30 pm): For 1(b) you may set and determine the stable age structure.

## MathBio: The Basic Horseshoe Crab Model

During the last class before spring break, we were visited by Daniel Sasson from the Biology Department, a horseshoe crab expert and mathematical modeling enthusiast. We presented several versions of our models for the “Blood Harvest” we discussed in Wednesday’s class and he advised us on some parameter values that make sense. Our general conclusionsContinue reading “MathBio: The Basic Horseshoe Crab Model”

## MathBio: R Code for Linear Structured Systems

Code for simulating linear 3d systems: linear3d.R

## MathBio: Horseshoe Crabs and the Blood Harvest

On Wednesday my friend Daniel Sasson passed along a fascinating story from The Atlantic, The Blood Harvest, about the blood of horseshoe crabs. I will leave it to the article to explain the why’s, but it turns out that scientists regularly capture horseshoe crabs, drain them of 30% of their blood, and then return themContinue reading “MathBio: Horseshoe Crabs and the Blood Harvest”

## MathBio: Homework 4, Due Wed Feb 26

One problem, due Wed Feb 26 ————————————————— (Logan and Wolesenksy, 3.3 #2) In 1998, van der Meijden described the following model connecting the cinnabar moth and ragweed. The life cycle of the moth is as follows. It lives for one year, lays its eggs on the plant, and dies. The eggs hatch the next spring.Continue reading “MathBio: Homework 4, Due Wed Feb 26”