Influenza remains one of the major infectious diseases that target humankind, therefore, understand transmission mechanisms and control strategies can help us obtain more accurate predictions. There are many control strategies, one of them is vaccination. In this paper, our purpose is to extend the incidence rate of a two-strain flu model with a single vaccination, which includes a wide range of incidence rates among them, some cases are not monotonic nor concave, which may be used to reflect media education or psychological effect. Our main aim is to mathematically analyze the effect of the vaccine for strain 1, the general incidence rate of strain 1 and the general incidence rate of strain 2 on the dynamics of the model. Four equilibrium points were obtained and the global dynamics of the model are completely determined via suitable Lyapunov functions. We illustrate our results by some numerical simulations. Our results showed that the vaccination is always beneficial for controlling strain 1, its impact on strain 2 depends on the force of infection of strain 2. Also, the psychological effect is always beneficial for controlling the disease.
