1. ## Differece equation

A problem from class where we're trying to figure out the spread of disease.

Newly infected Total Infected
0 1
2 3
4 7
9 16
12 28
4 32
0 32

$\displaystyle I_{n+1} = I_{n} + G_{n}$

$\displaystyle G_{n} = aI_{n}(N+I_{n})$

$\displaystyle I_{n+1} = I_{n} + aI_{n}(N+I_{n})$

What happens to the difference equation when everyone is infected?

What happens when no one is infected?

For $\displaystyle G_{n}$, is it possible for $\displaystyle I_{n}$ to decrease?

I don't know where to start.... HELP!!

2. Originally Posted by kl.twilleger
A problem from class where we're trying to figure out the spread of disease.

Newly infected Total Infected
0 1
2 3
4 7
9 16
12 28
4 32
0 32

$\displaystyle I_{n+1} = I_{n} + G_{n}$

$\displaystyle G_{n} = aI_{n}(N+I_{n})$

$\displaystyle I_{n+1} = I_{n} + aI_{n}(N+I_{n})$

What happens to the difference equation when everyone is infected?

What happens when no one is infected?

For $\displaystyle G_{n}$, is it possible for $\displaystyle I_{n}$ to decrease?

I don't know where to start.... HELP!!
What is $\displaystyle N$? Are you sure that your difference equations are correct?

If $\displaystyle G$ denote the number of new cases should not $\displaystyle N$ be the total population and:

$\displaystyle G_{n} = aI_{n}(N-I_{n})$

Then when everyone is infacted $\displaystyle I_{n+1}=I_n$

CB