PEMODELAN MATEMATIKA PENYEBARAN PENYAKIT DEMAM BERDARAH DENGUE DENGAN LARVASIDA SEBAGAI PARAMETER INTERVENSI - Ekaristi, Mita; Prihandono, Bayu; Noviani, Evi (Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat, 2025)
Dengue Hemorrhagic Fever (DHF) remains a public health threat in Indonesia. This study aims to analyze the effectiveness of larvicides in controlling DHF through a mathematical modeling approach. This study developed an SIR-ASI model that considers the aquatic phase of mosquitoes. The model was formulated as a system of nonlinear differential equations by integrating the parameter of larval mortality due to larvicides . The basic reproduction number is derived using the Next Generation Matrix method. The stability of the system around the equilibrium point is analyzed using the Routh-Hurwitz criterion, which proves that the disease-free equilibrium point is locally asymptotically stable when . Numerical simulations indicate that increasing larvicide intensity significantly reduces from 3.19051 (without intervention) to 0.68281 (with intervention), equivalent to a 78.60% reduction. Sensitivity analysis identified u as one of the key parameters controlling along with mosquito bite frequency and mosquito mortality . The results of this study prove that larvicide intervention is effective in breaking the DHF transmission cycle by suppressing the vector population, thus making it a consideration in vector control strategies