Stability Analisys of SEIR Epidemiological Models with Nonlinear Incidence:Case Study in the Central Java Province, Indonesia

Abstract

SEIR epidemic models that are described as the system of ordinary differential equations with nonlinear incidence rates are proposed. In the SEIR model, the total population is divided into four classes, i.e., susceptible, exposed, infective, and recovered. The model has two equilibrium states; an infection-free equilibrium and an endemic equilibrium state. Local stability of each equilibrium point is determined by Lyapunov first method. It is found that the infection-free equilibrium is unstable and the endemic equilibrium state is asymptotically stable. Global stability of the endemic equilibrium state is analyzed by Lyapunov second method. Numerical simulations with case study of measles disease are presented. The measles disease data is taken from the Central Java Health Office, Indonesia.