Transmission Dynamics of Dengue Disease Incorporating Treatment, Mass Awareness, and Wolbachia Intervention - Rafika Nanda Agustina; Budi Priyo Prawoto (Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang, 2026)
Dengue Hemorrhagic Fever (DHF) remains a serious global public health threat, with its transmission dynamics strongly influenced by vector control strategies and human behavior. This study constructs and analyzes a mathematical model based on a system of differential equations to investigate the transmission dynamics of DHF by integrating three control strategies: treatment, public awareness, and the release of Wolbachia-infected mosquitoes. The basic reproduction number (R0) is derived using the Next Generation Matrix (NGM) method and serves as a threshold parameter for disease spread. Numerical simulations show that when R0 < 1, the system converges to the disease-free equilibrium, indicating that the disease will eventually die out. Conversely, by adjusting the parameter δ such that R0 > 1, the system becomes stable at the endemic equilibrium, implying the persistence of the disease within the population. These findings highlight the importance of controlling key parameters through integrated intervention strategies to reduce R0 below unity.