A susceptible-infected-vaccinated epidemic model with proportional vaccination and generalized nonlinear rate is formulated and investigated in the paper. We show that the stochastic epidemic model admits a unique and...A susceptible-infected-vaccinated epidemic model with proportional vaccination and generalized nonlinear rate is formulated and investigated in the paper. We show that the stochastic epidemic model admits a unique and global positive solution with probability one when constructing a proper C2-function therewith. Then a sufficient condition that guarantees the disappearances of diseases is derived when the indicator R0< 1. Further, if R0> 1, then we obtain that the solution is weakly permanent with probability one. We also derived the sufficient conditions of the persistence in the mean for the susceptible and infected when another indicator R0> 1.展开更多
文摘A susceptible-infected-vaccinated epidemic model with proportional vaccination and generalized nonlinear rate is formulated and investigated in the paper. We show that the stochastic epidemic model admits a unique and global positive solution with probability one when constructing a proper C2-function therewith. Then a sufficient condition that guarantees the disappearances of diseases is derived when the indicator R0< 1. Further, if R0> 1, then we obtain that the solution is weakly permanent with probability one. We also derived the sufficient conditions of the persistence in the mean for the susceptible and infected when another indicator R0> 1.
