In terms of $p$ and $L$, what fraction of the origin habitat is available for the species to migrate to? Therefore, what is the rate at which new habitat regions are being colonized by this species?
What are the biologically realistic equilibria? If $L \lt$ , the biological realistic equilibria are $p_{eq} = $. If $L \gt $ , the biological realistic equilibria are $p_{eq} = $.
Must all of the habitat of the endangered species be destroyed for it to go extinct? yes no
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'.