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Invariant Measures for Contact Processes with State-Dependent Birth and Death Rates

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Abstract

We consider contact processes on locally compact separable metric spaces with birth and death rates that are heterogeneous in space. We formulate conditions on the rates that ensure the existence of invariant measures of contact processes. One of the crucial conditions is the so-called critical regime condition. To prove the existence of invariant measures, we use the approach proposed in our preceding paper. We discuss in detail the multi-species contact model with a compact space of marks (species) in which both birth and death rates depend on the marks.

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Funding

This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.

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Authors and Affiliations

  1. Kharkevich Institute for Information Transmission Problems of the Russian Academy of Sciences, Moscow, Russia

    E. A. Zhizhina & S. A. Pirogov

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  1. E. A. Zhizhina
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  2. S. A. Pirogov
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Correspondence to E. A. Zhizhina.

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Translated from Problemy Peredachi Informatsii, 2023, Vol. 59, No. 2, pp. 63–82. https://doi.org/10.31857/S0555292323020055

Dedicated to Vadim Alexandrovich Malyshev, a great mathematician, who clearly saw mathematics in biology

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Zhizhina, E.A., Pirogov, S.A. Invariant Measures for Contact Processes with State-Dependent Birth and Death Rates. Probl Inf Transm 59, 128–145 (2023). https://doi.org/10.1134/S0032946023020059

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  • DOI: https://doi.org/10.1134/S0032946023020059

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