ON THE BEHAVIOR ANALYSIS OF SUSCEPTIBLE, INFECTION, RECOVERY (SIR) MEASLES SPREAD MODEL WITH AGE STRUCTURE

Abstract

This study discusses the behavior analysis model of the Susceptible-Infected-Recovered (SIR) epidemic of the spread of measles based on age structure. The total population is grouped into four age groups, the first age group (0-4 years), the second age group (5-9 years), the third age group (10-14 years), and the fourth age group (> 15 years). The steps in analyzing the behavior of the model can be done by determining the equilibrium point, basic reproduction number, and stability analysis at the equilibrium point. In the measles distribution model with four age groups, where each age group has no interaction with other age groups, sixteen equilibrium points are obtained, which are a combination of the disease-free equilibrium and endemic equilibrium points separately. The stability properties of each equilibrium point can be determined by the value of the basic reproduction number (R_0) which is the product of the basic reproduction number of each age group. The measles disease-free equilibrium point will be locally asymptotically stable when R_0<1, meanwhile the endemic equilibrium point is locally asymptotically stable when R_0>1. This research contributes to providing information to both the government and the public.