Global analysis of an SEIR model with varying population size and vaccination

An SEIR model with varying population size and vaccination strategy is investigated. Three threshold parameters R0,R^0,R¯0 and R∼0 are obtained to govern the disease eradication, which involve the total number of infectives and their proportion in the population. Parameter conditions on the uniform persistence, the global stability of the disease – “free” equilibrium and the “endemic” equilibrium are derived. The global dynamics of model in population size are studied. The correlations of the two systems in terms of disease eradication, endemicity and disease explosion are summarized and compared. We conjecture that substantially low product of vaccination rate and low vaccine efficacy may lead to complicated dynamics for the system in question.