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Floquet theory for seasonal environmental forcing of spatially explicit waterborne epidemics

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Abstract

The transmission of waterborne pathogens is a complex process that is heavily linked to the spatial characteristics of the underlying environmental matrix as well as to the temporal variability of the relevant hydroclimatological drivers. In this work, we propose a time-varying, spatially explicit network model for the dynamics of waterborne diseases. Applying Floquet theory, which allows to extend results of local stability analysis to periodic dynamical systems, we find conditions for pathogen invasion and establishment in systems characterized by fluctuating environmental forcing, thus extending to time-varying contexts the generalized reproduction numbers recently obtained for spatially explicit epidemiology of waterborne disease. We show that temporal variability may have multifaceted effects on the invasion threshold, as it can either favor pathogen invasion or make it less likely. Moreover, environmental fluctuations characterized by distinctive geographical signatures can produce diversified, highly nontrivial effects on pathogen invasion. Our study is complemented by numerical simulations, which show that pathogen establishment is neither necessary nor sufficient for large epidemic outbreaks to occur in time-varying environments. Finally, we show that our framework can be used to reliably characterize the early geography of epidemic outbreaks triggered by fluctuating environmental conditions.

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Acknowledgments

The authors wish to thank two anonymous referees for their helpful comments on the manuscript. LM, EB and AR acknowledge the support provided by ERC advanced grant program through the project RINEC-227612 and by the SFN/FNS projects 200021 124930/1 and CR2312 138104/1. MG and AR acknowledge the support from the SFN/FNS project IZK0Z2 139537/1 for international cooperation.

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Authors and Affiliations

  1. Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, 20133, Milan, Italy

    Lorenzo Mari, Renato Casagrandi & Marino Gatto

  2. Laboratory of Ecohydrology ECHO/IIE/ENAC, École Polytechnique Fédérale de Lausanne, 1015, Lausanne, Switzerland

    Lorenzo Mari, Enrico Bertuzzo & Andrea Rinaldo

  3. Dipartimento di Ingegneria Civile, Edile ed Ambientale, Università di Padova, 35131, Padua, Italy

    Andrea Rinaldo

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  1. Lorenzo Mari
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  2. Renato Casagrandi
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  3. Enrico Bertuzzo
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  4. Andrea Rinaldo
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  5. Marino Gatto
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Correspondence to Lorenzo Mari.

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Mari, L., Casagrandi, R., Bertuzzo, E. et al. Floquet theory for seasonal environmental forcing of spatially explicit waterborne epidemics. Theor Ecol 7, 351–365 (2014). https://doi.org/10.1007/s12080-014-0223-y

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