In a frightening new paper, Philip Munz, Ioan Hudea, Joe Imad, and Robert J. Smith say NO! It’s such scary news that the BBC covered it.
In their model, Susceptible (S) humans can turn into Zombies (Z) with probability β if they meet each other. But Zombies can also rise from dead susceptibles or the so-called Removed R at rate ς. In a mixed population with no birth, S will definitely shrink. Even if S kill Z at rate α, Z can always re-appear from R and never die off. Hence, we end up in a pure Zombie equilibrium. There is no channel for S to grow and there is a channel for Z to grow and there you have it.
Of course, if there is birth then things change. In their model, the authors look at the case where the (exogenous) birth rate Π is zero. But the birth rate should also depend on the fractions of S and Z in the population. If S is large then there should be frequent S-S encounters. Assume away gender issues for simplicity and these S-S encounters should lead to progeny. Even if the birth rate is low, it is multiplies by S-squared the chance of an S-S meeting while the zombie production rate βSZ + ςR is close to ςR if Z is close to zero. If S is large, so ΠS > ςR, this stabilizes a good S equilibrium where a small fraction of zombies does not eventually take over.
This is a small trivial extension but with a good title (“Make Love to win the Zombie War”), it would be an interesting sequel.
There is another solution: cremation is better than burial. I’m not an expert on zombies but I strongly suspect a cremated body cannot reappear in zombie form. Then, if we can kill of zombies fast enough (high α), we should be fine. Phew. But while the human race is safe, all individuals are in danger. I will not sleep well tonight.
(Hat Tip: PLL)