Analysis of a hybrid SIR epidemic model driven by dual white noises and Markovian switching

This work investigates a stochastic SIR epidemic model driven by two independent white noises and Markovian regime switching. The system’s dynamics, particularly the conditions for disease elimination and long-term persistence, are rigorously investigated through the analysis of a mean-reverting process incorporating multiplicative noise and regime-switching dependent parameters. The key contribution of this work is the explicit derivation of the stationary and ergodic probability density function for this process, a result that has not been previously achieved. These findings provide novel and significant insights into the behavior of stochastic epidemic systems, offering advanced analytical tools to characterize the long-term dynamics of infectious diseases in environments subject to random fluctuations and abrupt changes. To provide credible confirmation of the theoretical results obtained, we will rely on numerical simulations of the solution trajectories, along with numerical verification of stationarity and ergodicity of the mean-reverting process with telegraph noise and multiplicative white noises.