A Delayed Pulse Vaccination Model of Infectious Diseases in Children

Abstract

This study concerns the theoretical determination of a mathematical model of delayed pulse vaccination of infectious diseases that affects children. In this study, a delayed SEIR epidemic model with impulsive effect and the global dynamic behaviors of the model will be analyzed. Using the discrete dynamical systems determined, it’s shown that there exists an ’infection-free’ periodic solution which is globally attractive when the period of impulsive effect is less than certain critical value. The sufficient condition for the permanence of the epidemic model with pulse vaccination is given, which means the epidemic disease is to spread around. The study has concluded that time delay and pulse vaccination brings great effects of shortening ‘infection period’ on the dynamics of the model. The results indicate that a large vaccination rate or a short period of pulsing leads to the eradication of the disease. Numerical simulation has been used together with the analytical results. The result has been presented in tabular and graphical form.