Dynamical behavior of a hybrid switching SIS epidemic model with vaccination and Lévy jumps

Qun Liu; Daqing Jiang; Tasawar Hayat; Ahmed Alsaedi

doi:10.1080/07362994.2019.1575236

Dynamical behavior of a hybrid switching SIS epidemic model with vaccination and Lévy jumps

Qun Liu
, Daqing Jiang
, Tasawar Hayat
, Ahmed Alsaedi

Northeast Normal University
Faculty of Sciences, King Abdulaziz University
King Abdulaziz University

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

In this paper, the dynamical behavior of a hybrid switching SIS epidemic model with vaccination and Lévy jumps is considered. Besides a standard geometric Brownian motion, another two driving processes are taken into account: a stationary Poisson point process and a continuous time finite-state Markov chain. Firstly, we establish sufficient conditions for persistence in the mean of the disease. Then we obtain sufficient conditions for extinction of the disease. In addition, we also establish sufficient conditions for the existence of positive recurrence of the solutions to the model by constructing a suitable stochastic Lyapunov function with regime switching.

Original language	English
Pages (from-to)	388-411
Number of pages	24
Journal	Stochastic Analysis and Applications
Volume	37
Issue number	3
DOIs	https://doi.org/10.1080/07362994.2019.1575236
State	Published - 4 May 2019
Externally published	Yes

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 3 Good Health and Well-being

Keywords

Vaccination; persistence and extinction; positive recurrence; Markov switching; Lévy jumps

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10.1080/07362994.2019.1575236

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abstract = "In this paper, the dynamical behavior of a hybrid switching SIS epidemic model with vaccination and L{\'e}vy jumps is considered. Besides a standard geometric Brownian motion, another two driving processes are taken into account: a stationary Poisson point process and a continuous time finite-state Markov chain. Firstly, we establish sufficient conditions for persistence in the mean of the disease. Then we obtain sufficient conditions for extinction of the disease. In addition, we also establish sufficient conditions for the existence of positive recurrence of the solutions to the model by constructing a suitable stochastic Lyapunov function with regime switching.",

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AU - Jiang, Daqing

AU - Hayat, Tasawar

AU - Alsaedi, Ahmed

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AB - In this paper, the dynamical behavior of a hybrid switching SIS epidemic model with vaccination and Lévy jumps is considered. Besides a standard geometric Brownian motion, another two driving processes are taken into account: a stationary Poisson point process and a continuous time finite-state Markov chain. Firstly, we establish sufficient conditions for persistence in the mean of the disease. Then we obtain sufficient conditions for extinction of the disease. In addition, we also establish sufficient conditions for the existence of positive recurrence of the solutions to the model by constructing a suitable stochastic Lyapunov function with regime switching.

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ER -

Dynamical behavior of a hybrid switching SIS epidemic model with vaccination and Lévy jumps

Abstract

UN SDGs

Keywords

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