Global dynamics of a stochastic smoking epidemic model driven by Black-Karasinski process

Abstract

In this paper, we develop a stochastic smoking epidemic model, where Black-Karasinski process is for the first time introduced to describe the environmental fluctuations in smoking transmission. By constructing suitable Lyapunov functions and compact sets, we establish sufficient conditions for the exponential extinction of smoking populations and the existence of a stationary distribution (i.e., a reflection of smoking persistence). Our results show that stochastic noise will be conducive to smoking pandemic.