An epidemic model with age structured of rubella virus: threshold and stability

Abstract

This study aimed to explore the dynamic behaviour of rubella virus model which considers age-structured. It was not only to figure out the stability analysis of the model but also the judgement of the result through numerical simulation. Firstly, we constructed model for the disease spread based on the characteristic of rubella virus. The basic model of the disease spread (SEIR) had been used as a fundamental model. In the beginning, human population have been divided into two age groups; children and adults. Furthermore, based on the characteristic of rubella, we separated each group into four sub populations, i.e., Susceptible, Exposed, Infected, and Recovered. The transmission routes of the disease were formulated mathematically based on the real problem. In the second step, two disease equilibrium points had been obtained. There were a disease-free equilibrium and an endemic equilibrium. Moreover, by using Next Generation Matrix method, the basic reproduction number also had been determined. Finally, stability analysis had been done to explore the persistence of the disease. This results also had been supported by the numerical simulation.