Stationary distribution and extinction of a stochastic epidemic model with isolation

Time: 09:00 to  10:30 Ngày 21/05/2021

Venue/Location: C101, VIASM

Speaker: PGS. Nguyễn Thanh Diệu (Vinh University)

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