ARTICLE
Threshold Parameters of Stochastic SIR and SIRS Epidemic Models with Delay and Nonlinear Incidence
- Partial Differential Equations and Applications , 420 : 281-293
Lien de l'article :
https://doi.org/10.1007/978-3-031-27661-3_11
Discipline :
Mathématiques
Auteur(s) :
TRAORE Ali
Auteur(s) tagués :
TRAORE Ali
Renseignée par : TRAORE Ali
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