This paper considers mathematical modelling and stability analysis of Varicella-Zoster Virus (VZV) disease model in a homogeneous population that is structured as a class of susceptible-exposed-quarantined-infected-hospitalized-recovered with immunity. In this paper, the infectious classes are the exposed, quarantined, infected and hospitalized. The infected class is further subdivided into three subclasses: incubation, prodromal and active classes of VZV. The infectious rate of VZV at the incubation, prodromal, active and hospitalization stages are discussed. The aim of this paper is to determine the significance of having the subclasses of the infected class, and the role these subclasses of the infected class and contact rate play in the spread of chickenpox in the population. The basic reproduction number of our VZV model is obtained. Also, we discuss the global stability of the disease-free equilibrium and the local stability of the endemic equilibrium in the feasible region of the VZV model. Some numerical simulations are carried out to valid the models in this paper, and it is found that the subclasses of the infected class and contact rate play distinct and significant role in the spread of chickenpox in a population.
