Threshold Parameters of Stochastic SIR and SIRS Epidemic Models with Delay and Nonlinear Incidence,
Lien de l'article:
https://doi.org/10.1007/978-3-031-27661-3_11
Auteur(s):
TRAORE Ali
Auteur(s) tagués:
Ali TRAORE ;
Résumé
In this paper, we study stochastic SIR and SIRS epidemic models with delay. A nonlinear incidence function that includes some special incidence rates is also considered. Two thresholds RS0 and R ̃S0 of the two models are derived by using the nonnegative semimartingale convergence theorem. The disease goes extinct when the value of RS0 is below 1 and it prevails when R ̃S0 value is above 1 for any size of the white noise. The comparison between the two thresholds is made.
Mots-clés
delays stochastic SIR model nonlinear incidence extinction persistence in mean