Batik Parang Harmoni Epidemi: Mathematical Modeling of Dengue Hemorrhagic Fever Transmission Incorporating Social Awareness (Analysis and Simulation)

Abstract

Dengue Hemorrhagic Fever (DHF) is an infectious disease caused by the dengue virus and transmitted through the bites of Aedes aegypti and Aedes albopictus mosquitoes. This disease remains a major public health problem in tropical regions, including Indonesia. This study examines the influence of social awareness factors on DHF transmission through the development of a mathematical model describing the interaction between the human and mosquito populations. The model divides the human population into six compartments susceptible , aware , exposed , infected , hospitalized , and recovered and the mosquito population into three compartments susceptible , exposed , and infectious . The analysis uses the Next Generation Matrix approach to determine the basic reproduction number ,followed by sensitivity analysis and numerical simulation to study the effects of parameters on disease dynamics. The results show that increasing social awareness significantly reduces the value of , while higher human  and mosquito  transmission rates increase the epidemic risk. When , the system approaches a disease-free equilibrium, whereas  leads to an endemic state. Moreover,the rate of declining awareness (aaa) plays

an important role in determining the intensity and timing of infection peaks. As an artistic interpretation, the findings are embodied in the Batik Parang Harmoni Epidemi artwork, which visualizes the connection between science, social behavior, and cultural values. This work symbolizes the harmony between science and culture in addressing epidemic challenges and emphasizes that enhancing social awareness is a key factor in sustainable DHF control.