How far does a meme spread on a sparse network when both the audience and the poster can burn out? Exposed contacts, links between an infected and a susceptible person, turn pink on the edge of each outbreak.
Try this Raise network-density from 12 to 30 and press Reset (ties are built at setup). The network goes from about 50 to about 120 ties, peak-infected-count roughly doubles and about twice as many people end fatigued, but most of the audience still never catches the meme.
About this model Where it ends up
A MathPets model of contagion with fatigue, seeded from aggregate X statistics (no post text is used). An audience of audience-size people is wired into a random contact network; you start infected and can re-seed the meme when your posting clock fires. The run lasts one simulated week, one tick per hour.
Each person makes up to four random ties, each with probability network-density percent, and hubs (hub-fraction percent of people) may add one more. Each hour a susceptible person with at least one infected neighbor catches the meme with probability reach-chance + engagement-power/5 percent, 6 points more for hubs. An infected person recovers with probability recovery-chance percent: to fatigued, immune for the rest of the run, with probability fatigue-chance percent, otherwise to recovered, which returns to susceptible at 4% an hour. You re-seed when susceptible or recovered, with a chance scaled from posts-per-day that peaks at peak-hour and drops by night-share before 6 a.m.
Two things dominate the outcome. The network is sparse, about one tie per person at the defaults, so outbreaks stay small and most people never catch the meme. And you are one of the people: in 18 of 20 default runs you became fatigued yourself, on average around hour 55, and never posted again.
