Stationary distribution and extinction of a stochastic epidemic model with isolation

Thời gian: 09:00 đến 10:30 Ngày 21/05/2021

Địa điểm: C101, VIASM

Báo cáo viên: PGS. Nguyễn Thanh Diệu (Vinh University)

Tóm tắt:
The aim of this talk is to give sufficient conditions, very close to the necessary one, to classify the stochastic permanence of SIQS epidemic model with isolation via a threshold value R. Precisely, we show that if R < 1 then the stochastic SIQS system goes to the disease free case in sense I(t), Q(t) converge to 0 at exponential rate and the density of susceptible class S(t) converges almost surely at exponential rate to the solution of boundary equation. In the case R > 1, the model is permanent. We show the existence of a unique invariant probability measure and prove the convergence in total variation norm of transition probability to this invariant measure. Some numerical examples are also provided to illustrate our findings