A stochastic Feline immunodeficiency virus model with vertical transmission

In this paper, we formulate a stochastic Feline immunodeficiency virus (FIV) model with vertical transmission to investigate the effect of environmental fluctuations on the FIV dynamics. We prove that the threshold parameter R0s can be used to identify the stochastic extinction and persistence of the FIV: if R0s<1, the FIV will be extinct a.s., while if R0s>1, the FIV will persist a.s. Epidemiologically, we find that large environmental fluctuations can suppress the outbreak of FIV, and the vertical transmission may be beneficial to the persistence of the FIV. Thus, in order to control the spread of the FIV, we must decrease the vertical transmission.