LOCAL AND GLOBAL STABILITY ANALYSIS OF MEASLES EPIDEMIC MODEL AT DISEASE-FREE EQUILIBRIUM

Abstract

In this study, a continuous mathematical model for the dynamics of Measles (rubeola) outbreak at constant recruitment rate was formulated. In the model, we partitioned the population into Susceptible (S), Vaccinated (V), exposed (E), Infected (I) and recovered (R) individuals. We analyzed a SVEIR compartmental nonlinear deterministic mathematical model of measles epidemic in a community with constant population. Analytical studies were carried out on the model using the method of linearized stability. The basic reproductive number R0 that governs the disease transmission is obtained from the largest eigenvalue of the next-generation matrix. The disease-free equilibrium is computed and proved to be locally and globally asymptotically stable if R0<1 and unstable if R0 >1 respectively. Finally, we simulate the model system in MATLAB and obtained the graphical behavior of each compartment. From the simulation, we observed that the measles infection was eradicated in the environment when R0<1.