Stochastic dynamics of feline immunodeficiency virus within cat populations

In this paper, we investigate the basic features of a simple susceptible-infected (SI) epidemic model of Feline immunodeficiency virus (FIV) within cat populations in presence of multiplicative noise terms to understand the effects of environmental driving forces on the disease dynamics. The value of this study lies in two aspects. Mathematically, we propose three threshold parameters, Rsh, R1 and R2 to utilize in identifying the stochastic extinction and persistence. In the case of stochastic persistence, we prove that there is a stationary distribution. Based on the statistical data for rural cat populations Barisey-la-Côte in France, we perform some numerical simulations to verify/extend our analytical results. Epidemiologically, we find that: (1) Large environment fluctuations can suppress the outbreak of FIV; (2) The distributions are governed by Rsh; (3) White noise perturbations of the birth rate for infectious cats (i.e., the vertical transmission) can induce the susceptible-free dynamics.