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A Stochastic SVIR Model with Imperfect Vaccine and External Source of Infection

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Performance Engineering and Stochastic Modeling (EPEW 2021, ASMTA 2021)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 13104))

Abstract

A stochastic SIR (Susceptible - Infected - Recovered) type model, with external source of infection, is considered for the spread of a disease in a finite population of constant size. Our interest is in studying this process in the situation where some individuals have been vaccinated prior to the start of the epidemic, but where the efficacy of the vaccine to prevent infection is not perfect. The evolution of the epidemic is represented by an absorbing three-dimensional continuous-time Markov chain. We focus on analysing the time for a threshold number of individuals to become infected, and carry out a global sensitivity analysis for the impact of varying model parameters on the summary statistic of interest.

Supported by the Government of Spain, Department of Science, Innovation and Universities; European Commission project: PGC2018-097704-B-I00 and Banco Santander and Complutense University of Madrid, Pre-doctoral Contract: CT 42/18-CT43/18.

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Author information

Authors and Affiliations

  1. Faculty of Statistical Studies, Complutense University of Madrid, Madrid, Spain

    Maria Gamboa & Maria Jesus Lopez-Herrero

  2. School of Mathematics, University of Leeds, Leeds, UK

    Martín López-García

Authors
  1. Maria Gamboa
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  2. Martín López-García
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  3. Maria Jesus Lopez-Herrero
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Corresponding author

Correspondence to Maria Gamboa .

Editor information

Editors and Affiliations

  1. University Paris-Saclay, Gif-sur-Yvette, France

    Paolo Ballarini

  2. Telecom Sub Paris, Evry, France

    Hind Castel

  3. University of Patras, Patras, Greece

    Ioannis Dimitriou

  4. Università degli studi della Campania Luigi Vanvitelli, Caserta, Italy

    Mauro Iacono

  5. Faculty of Engineering, Information and Systems, Division of Policy and Planning Sciences, University of Tsukuba, Tsukuba, Japan

    Tuan Phung-Duc

  6. Ghent University, Gent, Belgium

    Joris Walraevens

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Gamboa, M., López-García, M., Lopez-Herrero, M.J. (2021). A Stochastic SVIR Model with Imperfect Vaccine and External Source of Infection. In: Ballarini, P., Castel, H., Dimitriou, I., Iacono, M., Phung-Duc, T., Walraevens, J. (eds) Performance Engineering and Stochastic Modeling. EPEW ASMTA 2021 2021. Lecture Notes in Computer Science(), vol 13104. Springer, Cham. https://doi.org/10.1007/978-3-030-91825-5_12

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  • DOI: https://doi.org/10.1007/978-3-030-91825-5_12

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  • Print ISBN: 978-3-030-91824-8

  • Online ISBN: 978-3-030-91825-5

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