Analysis of an SQEIAR epidemic model with media coverage and asymptomatic infection

An SQEIAR model with media coverage and asymptomatic infection is proposed for populations with a certain level of immunity. Firstly, we discuss the extinction and persistence for the diseases of the model by using basic reproduction number $ \mathcal{R}_C $. Then the parameter threshold is analyzed and the effect of parameters on the basic reproduction number is discussed. Furthermore, the optimal media coverage strategy and quarantine strategy for optimal problems under quadratic cost function are derived by applying Pontryagin's Maximum Principle.