In tropical areas, dengue fever is a significant public health concern. It is caused by the dengue virus, which is transmitted to humans by infected mosquitoes. Effective and efficient strategies must be implemented to minimize the damage, and to do this, we must understand the dynamics of the dengue transmission and implement control methods that are beneficial and cost-effective. 

In this work, bifurcation analysis and multi objective nonlinear model predictive control is performed on two dynamic models involving dengue 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. Bifurcation analysis and multi objective nonlinear model predictive control (MNLMPC) calculations are performed on three oncolytic dynamic models. 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 branch and limit  points in the models. 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 both models.