How Do You Solve the SIS Disease Model Equation?

[tactical]

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?

 

[gato_]

The equation is separable. Just integrate
dx=dI \frac{1}{I(bN-v-bI)}

 

[memmepit]

it's a Bernoulli equation...I have to solve the same as you...did u solve it?