Journal of Mathematical Biology

, Volume 73, Issue 1, pp 91–121 | Cite as

The deterministic SIS epidemic model in a Markovian random environment

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Abstract

We consider the classical deterministic susceptible-infective-susceptible epidemic model, where the infection and recovery rates depend on a background environmental process that is modeled by a continuous time Markov chain. This framework is able to capture several important characteristics that appear in the evolution of real epidemics in large populations, such as seasonality effects and environmental influences. We propose computational approaches for the determination of various distributions that quantify the evolution of the number of infectives in the population.

Keywords

SIS epidemic model Random environment Number of infectives Markov chain Markovian switching Color noise Telegraph noise Steady-state distribution Embedded distribution 

Mathematics Subject Classification

34F05 60J25 92D30 
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Notes

Acknowledgments

Financial support for this work was provided by the Government of Spain (Ministry of Economy and Competitiveness) and the European Commission through the Project MTM-2011-23864.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of AthensAthensGreece
  2. 2.Faculty of Statistical StudiesComplutense University of MadridMadridSpain

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