1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Differentials: Population moving model

  1. Jan 22, 2010 #1
    1. The problem statement, all variables and given/known data
    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
    stability condition.

    2. Relevant equations
    R' = −mR + nU
    U' = mR − nU.


    3. 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.
     
  2. jcsd
  3. Jan 23, 2010 #2
    the fraction of people who live in the rural area should be
    Z(t) = R(t) /(R(t)+U(t))
     
  4. Jan 23, 2010 #3
    Z' = -mZ + n(1-Z)

    you can take from here
     
  5. Jan 23, 2010 #4

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Welcome to PF!

    Hi missavvy! Welcome to PF! :smile:

    You're confusing totals with proportions.

    R and U are totals, Z is only a proportion …

    so just ask yourself, what two things is it a proportion of? :wink:
     
  6. Jan 23, 2010 #5
    ah sorry i meant z= r/r + u!
    thanks tiny-tim! yeah that's what i had thought but I wasn't sure, thanks for clarifying that :)
     
  7. Jan 23, 2010 #6
    Just wondering how did you derive the Z(t)?
    Did you derive Z(t) = R(t) / R(t) + U(t), and then just plug in the R' and U' for those values?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Differentials: Population moving model
  1. Population Model (Replies: 2)

  2. Population model (Replies: 1)

Loading...