Impulsive epidemic model with differential susceptibility and stage structure

A stage-structured epidemic model with two differential susceptible of susceptibility and pulse vaccination is proposed. We introduce two thresholds R^∗ and R_∗, and further prove that a disease cannot invade the disease-free state if R^∗ is less than unit and can invade if R^∗ is larger than unit. Two numerical simulations are also given to illustrate our main results.