The population of a country is divided in two groups:
People who live in rural areas (R(t)) and people who live in urban areas (U(t)).
People move from rural to urban areas with a rate m and from
urban to rural areas with rate n.
a) Introduce the fraction of people (Z(t)) who live in rural
areas as a new variable and derive an equation for it.
b) Find the steady state(s) of the equation for Z and the
R' = −mR + nU
U' = mR − nU.
The Attempt at a Solution
a) So I don't really get this, but is the fraction Z(t) different from R(t)??
Anyways, I think it goes:
Z(t) = R(t) - U(t) / R(t)
how would i go about deriving it?
I am extremely confused. If anyone can just somehow reword it or something so that I can understand it that would be great.
b) If I could get Z(t) into differential form I can easily find the steady state, by just setting it = to 0.. so my problem really lies in the first part.