Epidemiology: An SIR Model
by Mike Martin

On this page, plots of three different populations, susceptible (S), infected (I), and recovered , are generated. We assume that an infected individual can recover and not be susceptible after recovering. The recovery rate is parameterized by γ.  There is a constant total number, N, of susceptible and infected individuals:

S (t) + I (t) + R (t) = N

The solutions are also projected into the phase plane along with background stream lines. The equations are of the form:

S ' ( t ) = - (β / N) S (t) I (t)

I ' ( t ) = (β / N) S (t) I (t) - γ I (t)

R ' ( t ) = γ I (t)

S(0) = S0
I(0) = I0
R(0) = R0

The populations, S, I, and R, are usually in units relative to a large population, say in thousands or millions; alternatively, one could normalize the populations and let the two populations represent the percentage of the total population.

The user inputs positive values of the parameters β and γ.  Also, grid bounds, time bounds, and the initial conditions must be specified.  Note that the initial conditions are added together to obtain the value of the total population.

Enter in the value of the parameters and select the plotting bounds, then press the "Plot/Evaluate" button.

β =  

γ =  

S (0) =  

I (0) =  

R (0) =  

0   ≤   t   ≤  

  ≤   S   ≤  

  ≤   I   ≤  


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