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.
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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).