There are papers studying a zombie outbreak using infectious disease modelling (an SIR continuous-time Markov model): see e.g.

P. Munz et al, When zombies attack!: Mathematical modelling of an outbreak of zombie infection, Infectious Disease Modelling Research Progress, 133-150 (2009)

and the review at https://jgeekstudies.org/2015/05/18/zombie-model/