Studi tentang Kestabilan Model Sird-T dengan Kriteria Routh-Hurwitz pada Penyebaran Suatu Penyakit Menular

Abstract

The goal of this investigation is to explore how the SIRD-T mathematical model represents the spread of measles, with a focus on identifying a stable equilibrium comprising disease-free and endemic states. It assesses the equilibrium's stability and performs numerical simulations using parameters affecting measles transmission to mitigate its spread. The Routh-Hurwitz criterion suggests that the infection rate is not rising, indicating asymptotic stability of the system. Consequently, the basic reproduction number R0 < 1 is obtained, meaning that there is no spread of measles, which indicates long-term stability. As a result of Odin's simulation, the Suspectible population will remain in the population because the population is in endemic conditions, and the Infected population will stabilize locally over time.