Is the total population of birds on the islands growing or shrinking? . Each year, the total population is multiplied by what factor?
If you let $a_t$ be the population size in the first island and time $t$ and $b_t$ be the population size in the second island at time $t$, then the dynamical system determining the dynamics of the populations is $a_{t+1} = $ $b_{t+1} = $
In matrix form, the dynamical system is
The eigenvalues of this matrix are $\lambda = $ and $\lambda = $ .
The dominant eigenvalues is $\lambda_{max} = $ .
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Suppose you decide to use a metapopulation to model the fraction of chicken farms that currently have a bird flu infection as $\frac{dp}{dt} = C - E$ where $p$ is the proportion of farms that are infected, $C$ is the rate at which new infections occur and $E$ is the rate as which farms are able to eradicate influenza. Time $t$ is measured in months.
From some preliminary assessments it appears that new infections occur when chickens are being imported from outside Minnesota (rather than new infections arising from chickens being transported from an infected Minnesota farm to an uninfected farm). Infected chickens are imported from outside farms at a rate of $0.1$ per month.
What form should the infection rate $C$ take? $C=$
Your plan to control bird flu is to eradicate the disease from infected farms at a monthly rate $x$, meaning $x$ is the fraction of infected farms from which the flu is eradicated per month. What form should the extinction rate $E$ take? $E =$
Find all the equilibria: $p = $ (If multiple answers, separate by commas.)
Is it possible to completely eradicate the disease from Minnesota chicken farms? yes no
If so, how fast must you be eradicating the disease from individual infected farms to be able to completely eradicate the disease from Minnesota? (Your expression should be an inequality involving $x$.) If it is not possible, enter 'impossible'.