On Multi-Group Chickenpox Mathematical Epidemic Models with Effective Vaccination and Re-Infection Challenges

Abstract

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 model. The findings show that age heterogeneity and vaccination rate play prominent roles in the determination of epidemic spread and control of chickenpox disease in the population and also serve as the factors that influenced the basic reproduction number. We found numerically that re-infections have little or no influence on the basic reproduction number but contribute tremendously to the reduction and/or increase in the number of individuals in incubation, prodromal and active stages, as well as treatment compartment of chickenpox infection over time.