Global asymptotic stability of a compartmental model for a pandemic

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⩽1R0⩽1, the disease free equilibrium is globally asymptotically stable; when R0>1R0>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.