Bifurcation analysis of an age-structured alcoholism model

In this paper, we investigate a new alcoholism model in which alcoholics have age structure. We rewrite the model as an abstract nondensely defined Cauchy problem and obtain the condition which guarantees the existence of the unique positive steady state. By linearizing the model at steady state and analyzing the associated characteristic transcendental equations, we study the local asymptotic stability of the steady state. Furthermore, by using Hopf bifurcation theorem in Liu et al. (Z. Angew. Math. Phys. 62 (2011) 191-222), we show that Hopf bifurcation occurs at the positive steady state when bifurcating parameter crosses some critical values. Finally, we perform some numerical simulations to illustrate our theoretical results and give a brief conclusion.