简介：ThispaperconsidersanSIRSepidemicmodelthatincorporatesconstantimmigrationrate,ageneralpopulation-sizedependentcontactrateandproportionaltransferratefromtheinfectiveclasstosusceptibleclass.Athresholdparameteraisidentified.Ifσ≤1,thedisease-freeequilibriumisgloballystable.Ifσ＞1,auniqueendemicequilibriumislocallyasymptoticallystable.Fortwoimportantspecialcasesofmassactionincidenceandstandardincidence,globalstabilityoftheendemicequilibriumisprovedprovidedthethresholdislargerthanunity.Somepreviousresultsareextendedandimproved.

简介：ThepaperestablishestwostochasticSIRSmodelswithjumpstodescribethespreadofnetworkvirusbycyberwar,terrorismandothers.First,addingrandomperturbationsproportionallytoeachvariable,wegetthedynamicpropertiesaroundthepositiveequilibriumofthedeterministicmodelandtheconditionsforpersistenceandextinction.Second,givingarandomdisturbancetoendemicequilibrium,wegetastochasticsystemwithjumps.BymodifyingtheexistingLyapunovfunction,weprovethepositivesolutionofthesystemisstochasticallystable.

简介：研究了一类非线性随机非自治SIRS传染病模型的动力学行为.首先,利用Lyapunov函数方法得到了疾病灭绝的充分条件.然后,通过Has′minskii的周期解理论,分成3个区域证明了该系统至少存在1个非平凡的正周期解.最后,利用Matlab进行了数值模拟来说明理论结果.