The contact process with dormancy

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This talk will be broadcast at 13:30 BST / 14:30 CEST / 15:30 EEST, July 30th, 2025 on MS Teams only.

Meeting ID: 393 527 089 878
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Abstract

The Contact Process with Dormancy (CPD) is an extension of the classical contact process by incorporating a type-switching mechanism, allowing individ- ual particles or sites to alternate independently between two states: active and dormant. The infection and recovery dynamics can differ across these states. We begin by introducing a Markovian framework for this model, where tran- sitions between states are governed by Poisson point processes. Fundamental properties of this model, including the existence of a non-trivial invariant dis- tribution and phase transitions, are discussed to parallel those of the classical contact process. We continue by deriving an asymptotic shape theorem for a broader class of models including the CPD. At the end we leave the Markovian set-up by allowing renewal processes with heavy-tailed inter-arrival distributions to trigger type switches. This variation we call the contact process with renewal dormancy. Inspired by a series of papers about the renewal contact process we can show interesting results like survival on finite graphs and at most logarithmic growth for variants of our model.

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