The Contact Process with switching
MathematicS In Action, Volume 12 (2023) no. 1, pp. 135-154.

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.

Published online:
DOI: 10.5802/msia.35
Classification: 60K35, 92D25, 92D30
Keywords: Contact Process, Coupling, Dormancy, Random environment, Switching
Jochen Blath 1; Felix Hermann 1; Michel Reitmeier 1

1 Goethe-Universität Frankfurt am Main, Robert-Mayer Str. 10, 60629 Frankfurt, Germany
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Jochen Blath; Felix Hermann; Michel Reitmeier. The Contact Process with switching. MathematicS In Action, Volume 12 (2023) no. 1, pp. 135-154. doi : 10.5802/msia.35.

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