The present paper investigates the dynamical behaviors of a stochastic SIRS epidemic model with telegraphic noise and Le ́vy noise. First, we establish the existence of a unique global positive solution for stochastic model. Furthermore, by constructing some suitable Lyapunov functions, we show that if R0 ≤ 1 and under some conditions on the parameters, then the solution of stochastic system fluctuates around the disease-free equilibrium, and if R0 > 1 the solution of stochastic system fluctuates around the disease- endemic equilibrium of the deterministic model. Finally, we present numerical simulations to support the theoretical results
Digital Object Identifier (DOI)
El Koufi, Amine; Bennar, Abdelkrim; and Yousfi, Noura
"Dynamics Behaviors of a Hybrid Switching Epidemic Model with Le ́vy Noise,"
Applied Mathematics & Information Sciences: Vol. 15:
2, Article 4.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol15/iss2/4