Mathematical modeling and optimal control approaches for dengue

This research explores a continuous-time mathematical model that outlines the transmission dynamics of the dengue virus across different regions, in-volving both human and mosquito hosts. We propose an optimal strat-egy that includes awareness campaigns, safety measures, and health inter-ventions in dengue-endemic areas, with the goal of reducing transmission between individuals and mosquitoes, thus lowering human infections and eliminating the virus in mosquito populations. Utilizing the discrete-time Pontryagin’s maximum principle, we identify optimal control measures and employ an iterative approach to solve the optimal system. Numerical sim-ulations are carried out using MATLAB, and a cost-effectiveness ratio is computed. Through an in-depth cost-effectiveness analysis, we highlight the effectiveness of strategies focused on protecting at-risk populations, pre-venting contact between infected humans and mosquitoes, and promoting the use of quarantine facilities as the most powerful methods for controlling the spread of the dengue virus.