Stochastic Epidemic SEIRS Models with a Constant Latency Period

Xavier Bardina, Marco Ferrante, Carles Rovira

Research output: Contribution to journalArticleResearchpeer-review


© 2017, Springer International Publishing AG. 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.
Original languageEnglish
Article number179
JournalMediterranean Journal of Mathematics
Issue number4
Publication statusPublished - 1 Aug 2017


  • SEIRS model
  • perturbations
  • stability
  • stochastic delay differential equations

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