Stability of Hybrid SDEs Driven by fBm

In this paper, the exponential stability of stochastic differential equations driven by multiplicative fractional Brownian motion (fBm) with Markovian switching is investigated. The quasi-linear cases with the Hurst parameter H ∈ (1/2, 1) and linear cases with H ∈ (0, 1/2) and H ∈ (1/2, 1) are all studied in this work. An example is presented as a demonstration.

Threshold dynamics for a class of stochastic SIRS epidemic models with nonlinear incidence and Markovian switching

In this paper, we consider a stochastic SIRS epidemic model with nonlinear incidence and Markovian switching. By using the stochastic calculus background, we establish that the stochastic threshold R_{ swt} can be used to determine the compartment dynamics of the stochastic system. Some examples and numerical simulations are presented to confirm the theoretical results established in this paper.