In setting up the model, the birth rate is given as a constant (capital pi). Clearly the birth rate should be proportional to the number of survivors S.<p>This doesn't materially alter the thrust of the argument, which presupposes a short outbreak with pi := 0 anyway, but does negate the conclusion of the first section, that "an outbreak of zombies will lead to the collapse of civilisation, as large numbers of people are either
zombified or dead."<p>In reality, the first ODE just states that the sum of (living+zombies+dead) only increases when new humans are born.