Epidemiology: An SIRS Model with Births/Deaths by Mike Martin

On this page, plots of three different populations, susceptible (S), infected (I), and recovered (R), are generated. We assume that an infected individual can recover and will become susceptible again after some time recovering. The recovery rate is parameterized by γ and recovered individuals become susceptible again at a rate of v β is the average number of adequate contacts made by an infected individual per time. The parameter b is the birth rate or death rate (which are assumed to be equal). There is a constant total number, N, of susceptible, infected, and recovered individuals:

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

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

R ' ( t ) = γ I (t) - b R (t) - v R (t)

S(0) = S_{0} I(0) = I_{0} R(0) = R_{0}

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

β =

γ =

v =

b =

S (0) =

I (0) =

R (0) =

0 ≤ t ≤

≤ S ≤

≤ I ≤

References:

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