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# SIR Model watch

1. I'm trying to find the fixed points of the SIR model which includes births and deaths:

dS/dt=uN-bSI-uS
dI/dt=bSI-rI-uI
dR/dt=rI-uR
where N=S+I+R
u is the birth rate, death rate is taken to be equal to the birth rate u. r and b are positive constants, any tips how to find the fixed points please?
2. (Original post by Alfie0608)
I'm trying to find the fixed points of the SIR model which includes births and deaths:

dS/dt=uN-bSI-uS
dI/dt=bSI-rI-uI
dR/dt=rI-uR
where N=S+I+R
u is the birth rate, death rate is taken to be equal to the birth rate u. r and b are positive constants, any tips how to find the fixed points please?
The SIR model is simply a system of differential equations, so finding the fixed points amounts to finding where the derivatives concerned vanish. However, in this system there is a little trick: the quantity R is determined when S & I are determined (since N=S+I+R), so you can ignore the third equation in this system! So to proceed, just set dS/dt = dI/dt = 0 and solve.
3. (Original post by Gregorius)
The SIR model is simply a system of differential equations, so finding the fixed points amounts to finding where the derivatives concerned vanish. However, in this system there is a little trick: the quantity R is determined when S & I are determined (since N=S+I+R), so you can ignore the third equation in this system! So to proceed, just set dS/dt = dI/dt = 0 and solve.
Should I change N to be S+I+R in dS/dt to solve this?
4. (Original post by Alfie0608)
Should I change N to be S+I+R in dS/dt to solve this?
No, leave N in there; remember it is a constant in this model.

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