Optimal control strategies and parameter estimation with a time delay dengue model using Penang Hospital data

Dengue fever is a mosquito-borne viral disease posing a major health challenge in tropical and subtropical regions, including Malaysia, where the climate supports year-round transmission. It affects millions annually, leading to severe illness and hospitalization, while the lack of specific antiviral treatment and the expanding range of Aedes mosquitoes make dengue a persistent global threat. To overcome this issue, this study develops a time delay SEITR-SEI model incorporating two biologically motivated delays representing the human intrinsic and vector extrinsic incubation periods. Firstly, time delay of intrinsic incubation period (IIP) in system captures the dynamics of dengue with time delay in human. The model's dynamics are examined by identifying dengue free and existing equilibria, evaluating the basic reproduction number, and analyzing local and global stability. The dengue free state is stable when the reproduction number is below one; otherwise, a stable endemic state arises. The second delay in the vector compartment represents a delay in the extrinsic incubation period (EIP), which suppresses dengue transmission while allowing the mosquito population to remain sustainable. The model was fitted using real hospital data from Penang General Hospital. These records correspond to patients admitted to Hospital between 2022 and 2023. The model parameters related to the dengue outbreak in this specific area were estimated using the least squares method. Furthermore, using these estimated parameter values, the equilibrium points of the model were also examined through the nonstandard finite difference (NSFD) scheme to ensure numerical stability and dynamic consistency of the system. In addition, a sensitivity analysis was performed to identify the most influential parameters affecting the transmission dynamics of dengue in Penang. Unlike previous studies on simple dengue fever models, this work applies optimal control to a more realistic double-delay model, where graphical comparison showed NSFD outperforming Euler. Simulation results emphasize the importance of biological control strategies, particularly eco-friendly and sustainable approach to limit dengue transmission without eliminating mosquito populations. All over Malaysia, the spread of dengue is nearly same, so the findings provide theoretical insights and practical guidance for dengue control policies in Malaysia.