MODIFIKASI MODEL SEIR PADA PENYAKIT CAMPAK

Abstract

The epidemic models Susceptible, Exposed, Infected and Recovered (SEIR) are used for the spread of diseases that have a latent period (incubation period) which one is measles disease. Latent periods are entered into the Exposed class. Measles itself after the incubation period will experience clinical symptoms consisting of three stages, which are prodromal stage, eruption stage and healing stage. Due to these clinical symptoms, the SEIR model can be modified by dividing the Infected class into two classes, which are Infected Prodromal class and Infected Eruption class. While the healing stage enters Recovered class. The spread of measles can be made into an epidemic model with five classes which are 𝑆, 𝐸,𝐼𝑃,𝐼𝐸 and 𝑅. The purpose of this study is to explain the modification of the model, determine and analyze the model's local stability at the equilibrium point of the model and to interpret model simulations with multiple stability-eligible parameter values. The results obtained from this study are modification of 𝑆𝐸𝐼𝑅 model which is 𝑆𝐸𝐼𝑃𝐼𝐸𝑅 model. Based on model, two equilibrium points obtained which are disease-free equilibrium points and endemic equilibrium points, which are locally asymtotics stable with conditions. Model simulations are presented to support an explanation of model stability analysis based on stability-meeting parameters. Keywords: Measles, 𝑆𝐸𝐼𝑅 Model, Modification of 𝑆𝐸𝐼𝑅 Model, Equilibrium Point, Local Stability.