Analysis of a stochastic SIR model with fractional Brownian motion

Abstract

In this article, a stochastic version of a SIR nonautonomous model previously introduced in Kloeden and Kozyakin (2011) is considered. The noise considered is a fractional Brownian motion which satisfies the property of long range memory, which roughly implies that the decay of stochastic dependence with respect to the past is only subexponentially slow, what makes this kind of noise a realistic choice for problems with long memory in the applied sciences. The stochastic model containing a standard Brownian motion has been studied in Caraballo and Colucci (2016). In this paper, we analyze the existence and uniqueness of solutions to our stochastic model as well as their positiveness.