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PreprintCC BY 4.0arXiv

The contact process with social clusters and asymptomatic states

  • Karima Belatreche
  • Lamia Belhadji
  • Nicolas Lanchier
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Abstract

This paper is concerned with a natural variant of the contact process that places a social cluster of individuals, rather than a single individual, at each lattice point, and distinguishes between symptomatic and asymptomatic individuals. In particular, the epidemic model depends on four infection parameters: the external (inter-cluster) and internal (intra-cluster) infection rates for both symptomatic and asymptomatic individuals. Newly infected individuals begin as asymptomatic before transitioning to the symptomatic state at a spontaneous mutation rate, and infected individuals recover at a baseline rate of one. We study the phase structure of the deterministic nonspatial mean-field model when each cluster reduces to a pair of individuals, and prove that the stochastic spatial model exhibits the same phase transitions with respect to the four infection rates for all cluster sizes. We also prove the existence of a phase transition driven by the cluster size itself for the spatial model.

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Cite

BibTeXRIS
BibTeX
@misc{belatreche2026contact,
  title = {{The contact process with social clusters and asymptomatic states}},
  author = {Karima Belatreche and Lamia Belhadji and Nicolas Lanchier},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.04323},
  eprint = {2610.04323},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.04323},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The contact process with social clusters and asymptomatic states
AU  - Karima Belatreche
AU  - Lamia Belhadji
AU  - Nicolas Lanchier
PY  - 2026
DA  - 2026/10/03
PB  - arXiv
DO  - 10.48550/arxiv.2610.04323
UR  - https://arxiv.org/abs/2610.04323
AB  - This paper is concerned with a natural variant of the contact process that places a social cluster of individuals, rather than a single individual, at each lattice point, and distinguishes between symptomatic and asymptomatic individuals. In particular, the epidemic model depends on four infection parameters: the external (inter-cluster) and internal (intra-cluster) infection rates for both symptomatic and asymptomatic individuals. Newly infected individuals begin as asymptomatic before transitioning to the symptomatic state at a spontaneous mutation rate, and infected individuals recover at a baseline rate of one. We study the phase structure of the deterministic nonspatial mean-field model when each cluster reduces to a pair of individuals, and prove that the stochastic spatial model exhibits the same phase transitions with respect to the four infection rates for all cluster sizes. We also prove the existence of a phase transition driven by the cluster size itself for the spatial model.
ER  -