MATHEMATICS MODEL SIRS-SI OF TRANSMISSION DENGUE VIRUS CONSIDERING FUMIGATION, VACCINATION AND TREATMEN IN CASE OF TANGERANG CITY - Utomo, Rukmono Budi; Azizah, Azizah (Lembaga Penelitian dan Pengabdian Masyarakat (LPPM), Institut Teknologi Sumatera, Lampung Selatan, Lampung, Indonesia, 2024)
Abstract: In this paper, we construct a mathematical model SIRS-SI transmission dengue fever considering fumigation, vaccination and treatment in case Tangerang City. Background why this research has to do because in Tangerang City the case of dengue fever is pretty lot. Method in this research is using compartment model and create differential equation system. We also do some analyze the model like determining free disease equilibrium point and endemic equilibrium point. We also determining basic reproduction number and making analyze stability of the model around equilibrium points. We also do simulation of the model and the result; model is local asymptotic stable in area free disease equilibrium point and local asymptotic stable in area endemic equilibrium point. Because R0 <1 for free disease equilibrium point, then there are no endemic disease, but because R0 > 1 for endemic equilibrium point then situation is in endemic dengue fever. Keywords: SIRS, Fumigation, Vaccination, Treatment, Dengue