Stochastic evolution of bad memes

Dawkins introduced a groundbreaking concept suggesting that humans, similar to other animals, operate as gene-propagating machines. Following in his footsteps, Blackmore posits that humans might distinguish themselves from other animals by also serving as specialized meme-replicating machines. Here we introduce a mathematical model that examines the impact of social conformity on the propagation of bad memes (memes with low intrinsic appeal). We state the meme equations, which give us the number of different kinds of memes living in the population and its total amount. We show that, unlike a virus, bad memes have a very low probability of initially spreading. However, as memes are produced in large numbers, some will eventually experience a stochastic rise and persist for extended periods, aided by social conformism within groups. We develop analytical approximations to calculate the mean time taken for memes to become extinct and the mean time spent in each population state. These approximations enable us to apply the meme equations to conduct a qualitative analysis.