G-SIRS Model with Logistic Growth and Nonlinear Incidence

الملخص EN

We present the stochastic SIRS model in the G-expectation space as follows: dXt=rX1−X/K−βXY/1+αY+δZdBt+σ¯1XdBt, dYt=βXY/1+αY−ρ+ϑ+γYdBt+σ¯2YdBt, dZt=γY−μ+δZdBt+σ¯3ZdBt, where σ¯1,σ¯2,σ¯3 are three intensities of the G-Brownian motion and disturb the three variables, and B1 follows G-Normal distribution, namely, B1∼N0,π¯2,π¯2.

For any initial condition X0,Y0,Z0∈D∗, we prove the new model admits a unique solution Xt,Yt,Zt for t≥0 and the solution Xt,Yt,Zt satisfies vω:Xt,Yt,Zt∈R+3,t≥0=1.