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Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations
- Publisher
- Springer Journals
- Copyright
- Copyright © Forum D'Analystes, Chennai 2020
- ISSN
- 0971-3611
- eISSN
- 2367-2501
- DOI
- 10.1007/s41478-020-00276-4
- Publisher site
- See Article on Publisher Site
Abstract
In this paper, we study a stochastic epidemic model with relapse, non linear incidence and a random transmission rate. The existence, uniqueness and boundedness of a positive solution are proved for any positive initial value. Using the Lyapunov analysis, we investigate the asymptotic behaviour of the solution. Mainly, we give sufficient conditions for extinction and persistence of the disease. Then, we propose an optimal control for both deterministic and stochastic models. Finally, we give some numerical illustrations to demonstrate our analytical results.
Journal
The Journal of Analysis – Springer Journals
Published: Sep 1, 2021
Keywords: Stochastic epidemic; Stochastic stability; Optimal control; 92B05; 93C10; 93E15