Dynamics of the deterministic and stochastic SIQS epidemic model with non-linear incidence q

摘要

The deterministic and stochastic SIQS models with non-linear incidence are introduced. For deterministic model, the basic reproductive rate R_0 is derived. Moreover, if R_0 ≤ 1, the disease- free equilibrium is globally asymptotically stable and if R_0 > 1, there exists a unique endemic equilibrium which is globally asymptotically stable. For stochastic model, sufficient condition for extinction of the disease that is regardless of the value of R_0 is presented. In addition, if the intensities of the white noises are sufficiently small and R_0 > 1, then there exists a unique stationary distribution to stochastic model. Numerical simulations are also carried out to confirm the analytical results.