Question

Problem 4: A model of infectious diseases In this problem we'll consider simple models of population dynamics by looking at the example of Australian rabbits. When they were first introduced to the continent, rabbits had no natural predators and an abundant food supply. a) Soon after the release of 24 rabbits in 1859, the population turns out to follow the differential equation $$ \frac{d}{dt}P(t) = 0.00045P^2 $$ Find P(t), and the value of t at which your integrals become improper. b) In 1950, the increasingly desperate Australian government started releasing the rabbit-borne disease myxomatosis in the wild 1. Due to natural selection, the proportion of rabbit susceptible to myxomato- sis went down as time went on. Given that the rabbit population followed the differential equation $$ \frac{d}{dt}P(t) = 0.14P - 0.8te^{-1.4t}P $$ determine P(t). c) Determine how many rabbits died as a result of the Australian government's policy. Do you think this had a lasting impact?

          Problem 4: A model of infectious diseases
In this problem we'll consider simple models of population dynamics by looking at the example of Australian
rabbits. When they were first introduced to the continent, rabbits had no natural predators and an abundant
food supply.
a) Soon after the release of 24 rabbits in 1859, the population turns out to follow the differential equation
$$
\frac{d}{dt}P(t) = 0.00045P^2
$$
Find P(t), and the value of t at which your integrals become improper.
b) In 1950, the increasingly desperate Australian government started releasing the rabbit-borne disease
myxomatosis in the wild 1. Due to natural selection, the proportion of rabbit susceptible to myxomato-
sis went down as time went on. Given that the rabbit population followed the differential equation
$$
\frac{d}{dt}P(t) = 0.14P - 0.8te^{-1.4t}P
$$
determine P(t).
c) Determine how many rabbits died as a result of the Australian government's policy. Do you think this
had a lasting impact?

problem 4 a model of infectious diseases in this problem well consider simple models of population dynamics by looking at the example of australian rabbits when they were first introduced to 63333

Added by Rebecca A.

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