In this paper, we introduce a type switching mechanism for the Contact Process. That is, we allow the individual particles/sites to switch between two (or more) types independently of one another, and the different types may exhibit specific infection and recovery dynamics. Such type switches can e.g. be motivated from biology, where “phenotypic switching” is common among micro-organisms. Our framework includes as special cases systems with switches between “active” and “dormant” states (the Contact Process with dormancy, CPD), and the Contact Process in a randomly evolving environment (CPREE) introduced by Broman (2007). The “standard” multi-type Contact Process (without type-switching) can also be recovered as a limiting case.
After constructing the process from a graphical representation, we first establish basic properties that are mostly analogous to the classical Contact Process. We then provide couplings between several variants of the system, obtaining sufficient conditions for the existence of a phase transition. Further, we investigate the effect of the switching parameters on the critical value of the system by providing rigorous bounds obtained from the coupling arguments as well as numerical and heuristic results. Finally, we investigate scaling limits for the process as the switching parameters tend to 0 (slow switching regime) resp. (fast switching regime). We conclude with a brief discussion of further model variants and questions for future research.
Keywords: Contact Process, Coupling, Dormancy, Random environment, Switching
Blath, Jochen 1 ; Hermann, Felix 1 ; Reitmeier, Michel 1
CC-BY 4.0
@article{MSIA_2023__12_1_135_0,
author = {Blath, Jochen and Hermann, Felix and Reitmeier, Michel},
title = {The {Contact} {Process} with switching},
journal = {MathematicS In Action},
pages = {135--154},
year = {2023},
publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
volume = {12},
number = {1},
doi = {10.5802/msia.35},
language = {en},
url = {https://www.numdam.org/articles/10.5802/msia.35/}
}
TY - JOUR AU - Blath, Jochen AU - Hermann, Felix AU - Reitmeier, Michel TI - The Contact Process with switching JO - MathematicS In Action PY - 2023 SP - 135 EP - 154 VL - 12 IS - 1 PB - Société de Mathématiques Appliquées et Industrielles UR - https://www.numdam.org/articles/10.5802/msia.35/ DO - 10.5802/msia.35 LA - en ID - MSIA_2023__12_1_135_0 ER -
%0 Journal Article %A Blath, Jochen %A Hermann, Felix %A Reitmeier, Michel %T The Contact Process with switching %J MathematicS In Action %D 2023 %P 135-154 %V 12 %N 1 %I Société de Mathématiques Appliquées et Industrielles %U https://www.numdam.org/articles/10.5802/msia.35/ %R 10.5802/msia.35 %G en %F MSIA_2023__12_1_135_0
Blath, Jochen; Hermann, Felix; Reitmeier, Michel. The Contact Process with switching. MathematicS In Action, Maths Bio, Tome 12 (2023) no. 1, pp. 135-154. doi: 10.5802/msia.35
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