With influenza as a prototype, we propose a compartmental model for a pandemic by
taking into account of recruitment. The model has a threshold dynamics. Precisely, when the basic
reproduction number R0 6 1, the disease free equilibrium is globally asymptotically stable; when
R0 > 1, the disease free equilibrium is unstable and there is a unique endemic equilibrium which
globally attracts all solutions except the trivial one (the disease free equilibrium). These results
are established by applying the LaSalle's invariance principle.