Global analysis for a general epidemiological model with vaccination and varying population

An SIR model with vaccination and varying population is formulated. The global dynamics of this model and its corresponding proportionate system are investigated. The correlations between the two systems in terms of disease eradication and persistence are presented. Three critical vaccination rates ϕ 1 c , ϕ 2 c and ϕ 3 c are obtained. It is found that when ϕ > ϕ 1 c the disease can be eradicated by increasing the vaccination rate until it exceeds ϕ 3 c . When ϕ < ϕ 1 c , the disease can be controlled to an endemic level by taking the appropriate vaccination rate ϕ 2 c .