Understanding the Equation Behind Healthy People

[sara_87]

Homework Statement

# healthy people = # people staying healthy + # new healthy people

The odds of staying healthy are a, so
# people staying healthy = a * # healthy people

New healthy people are sick people who did not stay sick. The odds of staying sick are B, so the odds of NOT remaining sick, i.e. new healthy people is (1-B), so
# new healthy people = (1-B) * # sick people

Homework Equations

The Attempt at a Solution

So if Y is the number of healthy people and X is the number of sick people at a given time,
Y[n+1] = a*Y[n] + (1-B)*X[n]

what would the equation for X[n+1]?
thank you

 

[arildno]

Regard the total population as equalling some constant P.
What is then the relationship between Yn and Xn?

 

[sara_87]

i don't know
??

 

[arildno]

Well, then Xn=P-Yn. Agreed?