The Zika virus is most commonly spread to people by the bite of an infected Aedes species mosquito. It can also be spread through sex from a person who is infected with Zika virus to their sexual partner(s). Zika virus can be passed from a pregnant woman to her fetus. Infection during pregnancy can cause certain birth defects. Zika virus typically occurs in tropical and subtropical areas of Africa, the Americas, Southern Asia, and the Western Pacific. There is currently no vaccine to prevent or medicine to treat Zika.  It is therefore important to understand the dynamics of the Zika virus and develop strategies to control the spread of this virus. In this work, bifurcation analysis and multiobjective nonlinear model predictive control is performed on two dynamic models involving Zika transmission. Bifurcation analysis is a powerful mathematical tool used to deal with the nonlinear dynamics of any process. Several factors must be considered, and multiple objectives must be met simultaneously.  . The MATLAB program MATCONT was used to perform the bifurcation analysis. The MNLMPC calculations were performed using the optimization language PYOMO   in conjunction with the state-of-the-art global optimization solvers IPOPT and BARON. The bifurcation analysis revealed the existence of a branch point in the first model and a Hopf bifurcation point and a limit point in the second. The Hopf bifurcation point, which causes an unwanted limit cycle, is eliminated using an activation factor involving the tanh function. The branch and limit points (which cause multiple steady-state solutions from a singular point) are very beneficial because they enable the Multiobjective nonlinear model predictive control calculations to converge to the Utopia point (the best possible solution) in the models.