This paper describes a co-infected two-strain Dengue model with bilinear infection rate. Three efforts, namely awareness efforts to protect human from mosquitoes bites, treatment efforts for infected human and mosquitoes killing efforts are considered to eradicate the infections. The treatment reproduction number R of the model is derived, which provides whether Dengue can persist or not. The existence and the stability analysis of different equilibrium points have been investigated. Sotomayor theorem is employed to prove the existence of transcritical bifurcation of the model. The sensitivity analysis has been performed to identify the most effective parameter for controlling the Dengue infection. The model is also used as an optimal control problem as all the three efforts are considered as time dependent functions. The Pontryagin’s maximum principle has been used to characterize the optimal control. Numerical results show the positive impacts for implementing three controls to reduce the Dengue infections. Finally efficiency analysis is carried out, which shows that awareness efforts to protect human from mosquitoes bites along with treatment is more effective than the mosquitoes killing efforts along with treatment. © 2020, Springer Nature India Private Limited.