Hybrid Euler method and Pontryagin Principle in fractional dengue model with sex classification and optimal controls

Abstract

This study develops a fractional epidemiological model to investigate the dynamics of dengue transmission, incorporatingbiological and behavioral differences between male and female human populations. The model utilizesfractional calculus to capture memory effects, which are essential for understanding the long-term behavior of infectiousdiseases. Control variables representing fumigation and preventive measures are introduced to evaluateintervention strategies, formulating a fractional optimal control problem. To solve the model, Euler’s method is employedfor numerical approximation of the fractional differential equations, while Pontryagin’s Minimum Principleand a forward-backward numerical approach are applied to determine optimal strategies. Numerical simulationsreveal that the combined control strategy, employing both fumigation and preventive measures, is the most effectivein minimizing infection levels and system costs. The results also demonstrate that higher fractional orders enhancethe efficiency of system dynamics. This research provides a robust framework for modeling dengue transmission anddesigning cost-effective public health interventions, with potential extensions to account for additional real-worldcomplexities.