Dynamics of an Age Structured Heroin Transmission Model with Imperfect Vaccination

Abstract

In this paper, we formulate a new-age structured heroin transmission model with respect to the age of vaccination which structures the vaccine wanes rate [Formula: see text] and infection ratio of vaccination individuals [Formula: see text]. The well-posedness and the basic reproduction number [Formula: see text] of our model are first presented. If [Formula: see text], the drug-free steady state [Formula: see text] is locally stable and there will be multiple positive steady states due to the imperfect vaccine. If [Formula: see text], there is a unique drug spread steady state, and our model is uniformly persistent. To reveal the dynamics of our model in detail, we carry out a further analysis in some special cases, including the backward and forward bifurcation results of our model when [Formula: see text] and [Formula: see text], and the unique drug-spread steady state’s stability when [Formula: see text]. Finally, a brief conclusion and discussion are presented.