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SIS disease Model

by tactical
Tags: disease, model
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tactical
#1
Feb9-10, 12:34 AM
P: 6
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?
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gato_
#2
Feb9-10, 04:00 AM
P: 117
The equation is separable. Just integrate
[tex]dx=dI \frac{1}{I(bN-v-bI)}[/tex]
memmepit
#3
Dec18-10, 06:58 AM
P: 1
it's a Bernoulli equation...I have to solve the same as you...did u solve it?


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