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.
