Dynamics and control for a stochastic giving up smoking model

This paper focused on a stochastic giving-up-smoking model with harmonic mean-type incidence rate, in which the population was divided into four types. Firstly, we showed that the model has a unique global positive solution. Then, stochastic permanence of the model was discussed, which means that the population described by the model will not grow wildly or disappear. Next, sufficient conditions for the elimination of smokers (including occasional smokers, chain smokers, and quit smokers) were established. Additionally, sufficient conditions for the existence of an ergodic stationary distribution were derived, meaning that all types of smokers can be persistent. Moreover, we discussed how to control the size of the smoker population from the perspective of economics. Finally, some numerical simulations were introduced.