A class of multi-age group $SEQ_3IHR$ chickenpox epidemic models with effective vaccination in a different subpopulation size, is considered, in this paper. It is assumed that individual members of the subpopulations who recovered from the disease, may be re-infected by the disease. The models comprise of six infectious classes of subclasses and three distinct infected stages of subclasses. We establish that the global dynamics of the epidemic models are determined entirely by the basic reproduction number. In this paper, we determine that the disease-free and endemic equilibrium states, and carry out a stability analysis of the disease-free as well as the endemic equilibrium points of the m... More >