Dynamics of a stochastic SIR epidemic model driven by Lévy jumps with saturated incidence rate and saturated treatment function

Abstract

In this article, we consider a stochastic SIR model with a saturated incidence rate and saturated treatment function incorporating Lévy noise. First, we prove the existence of a unique global positive solution to the model. We investigate the stability of the free equilibria E₀ by using the Lyapunov method. We give sufficient conditions for the persistence in the mean. We show the dynamic properties of the solution around endemic equilibria point of the deterministic model. Moreover, we display some numerical results to confirm our theoretical results.

Keywords:

• Epidemic model
• saturated treatment function
• Lévy noise
• persistence
• extinction

Acknowledgments

The authors are grateful to the anonymous referees and the editors for their valuable comments and suggestions to develop the manuscript.