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Math Help - Differece equation

  1. #1
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    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


    I_{n+1} = I_{n} + G_{n}

    G_{n} = aI_{n}(N+I_{n})

    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 G_{n}, is it possible for I_{n} to decrease?

    I don't know where to start.... HELP!!
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by kl.twilleger View Post
    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


    I_{n+1} = I_{n} + G_{n}

    G_{n} = aI_{n}(N+I_{n})

    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 G_{n}, is it possible for I_{n} to decrease?

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

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


    G_{n} = aI_{n}(N-I_{n})

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

    CB
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