EXTINCTION AND STATIONARY DISTRIBUTION OF A HEROIN EPIDEMIC MODEL WITH LÉVY JUMPS AND MARKOV SWITCHING

This paper endeavors to construct and embark on a rigorous investigation of a heroin epidemic model, subject to influences from both Lévy jumps and regime-switching. The primary objective is to conduct an in-depth analysis of the dynamical behaviors of this complex system. Firstly, we establish sufficient conditions for both the persistence in the mean and the extinction of the heroin epidemic model. Subsequently, under some certain conditions, we demonstrate the existence of a unique stationary distribution for this system. Finally, some numerical examples and figures are presented to illustrate and validate the theoretical results in an intuitive manner.