Modelling and Analysis of the Role of Vaccination and Isolation on the Spread of Infectious Diseases

Abstract

In this paper, a four dimensional SIS epidemic nonlinear model with immigration is proposed and analyzed to study the role of vaccination and isolation on the spread of an infectious diseases. The model has been analyzed by using stability theory of differential equations and simulation. The model has two equilibria namely, disease free and non-trivial endemic equilibrium. It is shown that the disease free equilibrium is always unstable and the endemic equilibrium, if exists, becomes locally as well as nonlinearly stable under certain conditions. This analysis also implies that as the rate of vaccination of susceptible human population density or the rate of isolation of severely infected human population density increases, the spread of infectious disease decreases. A numerical analysis of the model is also performed which supports the analytical results.