Qualitative analysis on a diffusive age-structured heroin transmission model. (August 2020) - Duan, Xi-Chao; Li, Xue-Zhi; Martcheva, Maia
Abstract: In this paper, to understand the impact of spatial heterogeneity of treatment and movement of individuals on the persistence and extinction of heroin spread, we propose a new diffusive heroin transmission model with treatment-dependent age-structure. The basic reproduction number in heterogenous environment R 0 of the system is defined, which is consistent with the one deduced from the next generation operator approach R ( x ) . The threshold dynamics in terms of the basic reproduction number is established: if R 0 ≤ 1, the drug-free steady state is globally asymptotically stable, if R 0 > 1, heroin transmission is uniformly persistent if it is present initially. In particular, when the environment is homogeneous and R 0 > 1, our system has a unique space-independent drug spread steady state and it is globally asymptotically stable. Finally, some numerical simulations are carried out to illustrate the main results.