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SIS disease Model

  1. Feb 9, 2010 #1
    The following problem is an SIS disease problem:

    Calling: I(t) = number of infectives at time t
    N = the total population (assumed constant)
    b = infection rate (here, a positive constant)
    v = recovery rate (also, a positive constant)

    a model for this disease is given bu the following:

    dI/dt = bI(N-I) - vI

    And since the population is assumed constant, we can just take S(t) to be N -I(t). Derive a condition for when the number of infectives goes to zero.

    Is there anyone out there than can help me, even if it's just a little bit?
  2. jcsd
  3. Feb 9, 2010 #2
    The equation is separable. Just integrate
    [tex]dx=dI \frac{1}{I(bN-v-bI)}[/tex]
  4. Dec 18, 2010 #3
    it's a Bernoulli equation...I have to solve the same as you...did u solve it?
    Last edited: Dec 18, 2010
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