Modeling the impact of optimized treatment patterns on dengue transmission dynamics

Dengue fever continues to pose a severe public health threat, especially in tropical and subtropical regions. Its rapid transmission through Aedes mosquitoes has led to recurrent outbreaks with devastating social, economic, and health consequences worldwide. Despite significant efforts by governments and health agencies, the disease remains endemic in many regions and poses a persistent global challenge. In response, this study develops a nonlinear dynamical model to analyze the transmission dynamics of dengue, focusing on key risk factors, disease progression, and long-term impacts. Using analytical mathematical methods, we examine how the system behaves at two primary equilibrium states by setting specific conditions on the threshold parameter. The examination proves the existence and uniqueness, positivity, boundedness, and local and global asymptotic stabilities. To validate the theoretical results, we implement the Non-standard Finite Difference (NSFD) technique and compare its performance with classical Euler and RK4 (Runge-Kutta method of order 4). Additionally, the numerical simulation NSFD method reveals that increasing treatment efforts using time-invariant control measures can significantly expedite disease eradication. Sensitivity analysis highlights the most influential parameters affecting disease transmission. Furthermore, we formulate and solve an optimal control problem to determine the most effective time-dependent treatment strategies. The obtained results underscore the potential of well-designed treatment intervention to minimize both the spread of infection and associated financial costs. This research develops an extended dengue model by incorporating treatment dynamics, establishing well-posedness, performing bifurcation and sensitivity analysis, and formulating an optimal control framework. The findings provide both rigorous mathematical insights and practical guidelines, highlighting key epidemiological drivers and offering effective strategies for treatment-based dengue management.