Stochastic analysis of a two delayed epidemic model incorporating Lévy processes with a general non-linear transmission

Abstract

In this paper, the qualitative analysis of a stochastic two delayed epidemic model incorporating Lévy processes with a general non-linear incidence transmission is considered. Our analysis show that the proposed model is mathematically and biologically well-posed. Moreover, we develop a mathematical method to present the sufficient conditions for extinction and persistence in the mean of disease. Numerical simulations are realized to show the performance and effectiveness of the theoretical results. Keywords Epidemic model; Lévy process; General non-linear transmission; Two delays.

Keywords:

• Epidemic model
• Lévy process
• General non-linear transmission
• Two delays

Acknowledgements

The authors are grateful to the anonymous referees and to the editors for their helpful comments and suggestions to improve the manuscript. The authors are also thankful to the Faculty of Sciences, Ibn Tofail University-Kenitra for their help and support.