Ergodic stationary distribution of a stochastic nonlinear epidemic model with relapse and cure

Abstract

In this paper, we consider a stochastic general epidemic model with relapse, graded cure and nonlinear incidence rate. We show the existence and uniqueness of a global positive solution for the model under some mild conditions. We also give some sufficient conditions for ensuring the existence of an ergodic stationary distribution for the model. Moreover, we analyse the extinction of the disease described by the model. Finally, we provide some numerical simulations to illustrate our main results.

COMMUNICATED BY:

• M. Fang

Keywords:

• Stochastic epidemic model
• nonlinear incidence rate
• relapse
• stationary distribution

2010 AMS Subject Classifications:

• 34F05
• 60H10
• 92D30

Acknowledgments

The authors are grateful to the editors and reviewers for their constructive comments, which helps us to improve the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (11471230; 11671282).