Skip to main content

Section 20.3 Examples and questions

These are additional examples for reviewing the topic we have covered. When reading each example, try to find your own solution before clicking “Answer”. There are also questions for reviewing the concepts of this section.

The original Lotka-Volterra model assumes that on their own, rabbit population would grow exponentially: \(R' = a R\) leads to \(R(t) = R_0e^{at}\text{.}\) But in reality, population is constrained by available resources (food and habitat). Modify the equation (20.2.1) by replacing \(aR\) with \(aR(1-R/K)\) where \(K\) is the carrying capacity of the population. Adjust the parameters to

d = 0.003;
K = 200;

and solve the system on the interval \([0, 500]\text{.}\)

How could one model the introduction of a vaccine during an epidemic?