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    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?
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    (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.
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    (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?
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    (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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