Hybrid Euler method and Pontryagin Principle in fractional dengue model with sex classification and optimal controls - Herdicho, Faishal F.; Fatmawati; Alfiniyah, Cicik; Chukwu, Chidozie W. (Statistics, Optimization & Information Computing, 2025)
This study develops a fractional epidemiological model to investigate the dynamics of dengue transmission, incorporating biological and behavioral differences between male and female human populations. The model utilizes fractional calculus to capture memory effects, which are essential for understanding the long-term behavior of infectious diseases. Control variables representing fumigation and preventive measures are introduced to evaluate intervention strategies, formulating a fractional optimal control problem. To solve the model, Euler’s method is employed for numerical approximation of the fractional differential equations, while Pontryagin’s Minimum Principle and a forward-backward numerical approach are applied to determine optimal strategies. Numerical simulations reveal that the combined control strategy, employing both fumigation and preventive measures, is the most effective in minimizing infection levels and system costs. The results also demonstrate that higher fractional orders enhance the efficiency of system dynamics. This research provides a robust framework for modeling dengue transmission and designing cost-effective public health interventions, with potential extensions to account for additional real-world complexities.