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Stochastic Epidemic SEIRS Models with a Constant Latency Period

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Abstract

In this paper, we consider the stability of a class of deterministic and stochastic SEIRS epidemic models with delay. Indeed, we assume that the transmission rate could be stochastic and the presence of a latency period of r consecutive days, where r is a fixed positive integer, in the “exposed” individuals class E. Studying the eigenvalues of the linearized system, we obtain conditions for the stability of the free disease equilibrium, in both the cases of the deterministic model with and without delay. In this latter case, we also get conditions for the stability of the coexistence equilibrium. In the stochastic case, we are able to derive a concentration result for the random fluctuations and then, using the Lyapunov method, to check that under suitable assumptions the free disease equilibrium is still stable.

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Authors and Affiliations

  1. Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193, Bellaterra, Spain

    Xavier Bardina

  2. Dipartimento di Matematica, Università di Padova, Via Trieste 63, 35121, Padova, Italy

    Marco Ferrante

  3. Departament de Matemàtiques i Informàtica, Universitat de Barcelona, Gran Via 585, 08007, Barcelona, Spain

    Carles Rovira

Authors
  1. Xavier Bardina
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  2. Marco Ferrante
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  3. Carles Rovira
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Corresponding author

Correspondence to Carles Rovira.

Additional information

X. Bardina is partially supported by the Grant MTM2015-67802-P from MINECO/FEDER. M. Ferrante is partially supported by the Grant 60A01-8451 from Università di Padova. C. Rovira is partially supported by the Grant MTM2015-65092-P from MINECO/FEDER, UE and by Visiting Professor Program 2015 of the Università di Padova.

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Bardina, X., Ferrante, M. & Rovira, C. Stochastic Epidemic SEIRS Models with a Constant Latency Period. Mediterr. J. Math. 14, 179 (2017). https://doi.org/10.1007/s00009-017-0977-8

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  • DOI: https://doi.org/10.1007/s00009-017-0977-8

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