Threshold dynamics for an age‐structured heroin epidemic model with distributed delays

Abstract

We introduce, in this paper, a delayed hybrid epidemic model describing the evolution of heroin addiction in a given population. The main objective of our mathematical analysis will be to provide the global behavior of the solutions. To the best of our knowledge, there are no results about the global dynamics of such a model containing both age structure and distributed time delay. We will prove that our model has threshold dynamics in terms of the basic reproduction number . It will be established that for , the addiction‐free equilibrium is globally stable and for , the endemic equilibrium is globally stable. The theoretical results are checked numerically. Especially, we focus on the influence of the addiction rate on the population dynamic.

Analysis of global behavior in an age‐structured epidemic model with nonlocal dispersal and distributed delay

“…In recent years, the age structure of a host cell has become an important tool in modeling cell dynamics which allows an understanding of the behavior of epidemic classes. Since the pioneering work of Kermack and McKendrick which explained infection by the age-infection of individuals, towards after-age infection, has taken place in many works to explain the time that has elapsed since infection; see, for example, earlier studies [9,[32][33][34][35][36][37][38][39][40] and the reference therein.…”