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Math Help - S-I-R epidemic Model

  1. #1
    Newbie
    Joined
    Aug 2009
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    16

    S-I-R epidemic Model

    For this model you have the following three equations.
    dS/dt=-BSI
    dI/dt=BSI-vI
    dR/dt=vI
    S` is the number of Susceptibles a time t
    I` is the number of Infectives at time t
    R` is the number who have recovered at time t
    B is the disease transmission rate
    v is the recovery rate

    My question is, if the population is to be assumed constant, why can you neglect the third equation?
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  2. #2
    Senior Member
    Joined
    Mar 2010
    Posts
    280
    You wrote "... if the population is to be assumed constant ..."
    but there is no definition of population.
    If population is P=S+I+R=const then
    dP/dt=dS/dt+dI/dt+dR/dt=0 and dR/dt may be found to be
    dR/dt=-dS/dt-dI/dt.
    Or there is another definition of population?
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