Sensitivity and Stability Analysis of a SEIR Epidemic Model with Information

Abstract

In this paper, the construction and stability analysis of a SEIR epidemic model with information are discussed. This model contains information about how to prevent the spread of infectious diseases which is transmitted by infected individuals to susceptible individuals. Furthermore, the dynamical analysis of the model which includes determination of equilibrium points terms of existence, stability analysis of the equilibrium points and sensitivity analysis are observed. Local stability of the equilibrium point is determined by linearizing the system around the equilibrium point and checking for the eigenvalue sign of Jacobian matrix at each equilibrium point. Sensitivity analysis is performed by using a sensitivity index to measure the relative change of basic reproduction number on each parameter. Based on the analysis result, there are two equilibrium points namely disease-free equilibrium point and endemic equilibrium point. The disease-free equilibrium point always exists and is locally asymptotically stable if the basic reproduction number is less than one. Moreover, the endemic equilibrium point exists and is locally asymptotically stable under certain conditions. From sensitivity analysis, it is found that the rate of mortality is the most sensitive parameter and the least sensitive parameter is the rate of exposed individual becomes infected individual. Finally, numerical simulation is conducted to support the analysis result.

Keywords: Epidemic, information, sensitivity analysis, SEIR, stability analysis.