Analyzing Dengue Epidemics Using Deterministic and Stochastic Models With Optimal Control Strategies

ABSTRACT Dengue fever remains a major public health concern in tropical and subtropical regions due to its complex transmission dynamics and lack of specific antiviral treatment. In this study, an age‐structured delay differential model is developed to investigate dengue transmission between juvenile and adult human populations and mosquito vectors. Biologically meaningful time delays are incorporated to represent incubation periods and age progression. Both deterministic and stochastic formulations are analyzed to capture average disease dynamics and random environmental effects. Global stability of the disease‐free equilibrium for the deterministic model is established using Lyapunov functional techniques, while conditions for disease extinction and the existence of a stationary distribution are derived for the stochastic system. Numerical simulations based on the Milstein method validate the theoretical findings and illustrate the influence of noise intensity on disease persistence. Sensitivity analysis identifies key parameters governing transmission dynamics. Additionally, optimal control strategies targeting juvenile and adult humans and mosquito populations are formulated using Pontryagin's Maximum Principle (PMP) and solved via a forward–backward sweep algorithm. The results demonstrate that optimal interventions significantly reduce infection levels and control costs, highlighting the effectiveness of integrated modeling and control strategies for dengue prevention.