A phase transition for a spatial host-parasite model with extreme host immunities on Zd and Td
Abstract
We investigate a model of a parasite population invading spatially distributed immobile hosts on a graph, which is a modification of the frog model.Each host has an unbreakable immunity against infection with a certain probability 1 -p.We show that, on Z d with d ≥ 2 and the d-regular tree T d with d ≥ 3, the survival probability of parasites exhibits a phase transition at a critical value of p c ∈ (0, 1).Also, we show that the value of p c is, in general, not a monotonic function of the underlying graph.Finally, we show that on quasi-vertex-transitive graphs, with probability 1, a fixed vertex is only visited finitely often by a parasite under mild assumptions on the offspring distribution of parasites.
Fields of Study & Subjects
Mathematical and Theoretical Epidemiology and Ecology Models
Stochastic processes and statistical mechanics
Opinion Dynamics and Social Influence
Publication details
- Journal / source
- Latin American Journal of Probability and Mathematical Statistics
- Volume
- 23
- Issue
- 1
- Pages
- 63–63
- Publication date
- 1 January 2026
- Language
- EN