Original title: The Zombie Infection Model
Stein Andreas Bethuelsen, Erik Broman, Samuel Modée · July 2026
Scientists want to understand how unusual outbreaks spread through connected networks. In this paper, researchers study the Zombie Infection Model, a mathematical process inspired by zombie outbreaks. Each point on a network starts as susceptible, infected, or removed. A healthy point catches the infection at rate λ multiplied by its infected neighbors. At the same time, an infected point gets removed at rate 1 multiplied by its healthy neighbors, meaning healthy individuals can fight back. This setup produces surprising results. The researchers analyzed whether an outbreak can survive indefinitely. On branching tree networks, raising the infection rate λ always increases or maintains the chance of indefinite spread. However, on certain bounded networks, this probability changes continuously but does not steadily rise as λ increases.
Imagine passing a note in a crowded classroom. Normally you want the note to travel faster, so you hand it to more people and expect it to go further. But the teacher snatches any note that is currently being passed around, so handing it to more people can get it confiscated sooner and stop it before it reaches the far side. In this paper, making the spread faster is like handing the note to more people, while an illness-carrier disappears faster when it still has many people around it who could catch it, and that can make the outbreak die out sooner instead of lasting forever.
The model is simple enough to analyze but produces rich, counterintuitive behavior: on some network shapes, making an infection spread faster can make it less likely to persist forever. That warns against trusting simple intuitions about transmission rates in epidemic models. Network structure can change not just how fast something spreads, but whether it spreads indefinitely.
The abstract doesn't say what happens outside the cases it names; it proves monotonicity on trees, gives a bounded-degree counterexample, and reserves exact results for complete graphs, regular trees, and the d-dimensional integer lattice. Arbitrary graphs receive only bounds.
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The Zombie Infection Model — Stein Andreas Bethuelsen, Erik Broman, Samuel Modée
Abstract licence: CC0
Explanation generated by Synthesis from the abstract — it is not the original paper. This is a preprint, so it hasn't necessarily been peer reviewed.