A stochastic analysis for a triple delayed SIQR epidemic model with vaccination and elimination strategies

Mohamed El Fatini; Roger Pettersson; Idriss Sekkak; Regragui Taki

doi:10.1007/s12190-020-01380-1

A stochastic analysis for a triple delayed SIQR epidemic model with vaccination and elimination strategies

J Appl Math Comput. 2020;64(1-2):781-805. doi: 10.1007/s12190-020-01380-1. Epub 2020 Jun 26.

Authors

Mohamed El Fatini¹, Roger Pettersson², Idriss Sekkak¹, Regragui Taki³

Affiliations

¹ Département de Mathématiques, Faculté des Sciences, Université Ibn Tofail, BP 133, Kénitra, Morocco.
² Department of Mathematics, Linnaeus University, 351 95 Växjö, Sweden.
³ Chouaib Doukkali University EST Sidi Bennour, El Jadida, Morocco.

Abstract

In this paper, a delayed SIQR epidemic model with vaccination and elimination hybrid strategies is analysed under a white noise perturbation. We prove the existence and the uniqueness of a positive solution. Afterwards, we establish a stochastic threshold $R_{s}$ in order to study the extinction and persistence in mean of the stochastic epidemic system. Then we investigate the existence of a stationary distribution for the delayed stochastic model. Finally, some numerical simulations are presented to support our theoretical results.

Keywords: Delay; Epidemic model; Extinction; Persistence in mean; Stationary distribution; White noise.