Modeling and Stability Analysis for a Varicella Zoster Virus Model with Vaccination

Abstract

In this paper, a deterministic mathematical model for transmission dynamics of Varicella Zoster Virus (VZV) with vaccination is formulated. The effective reproduction number is computed in order to measure the relative impact for individual or combined intervention for effective disease control. The effective reproductive number, is defined as the number of secondary cases that one infected individual will cause through the duration of the infectious period. The disease-free equilibrium is computed and proved to be locally asymptotically stable when < 1 and unstable when > 1 .It is proved that there exists at least one endemic equilibrium point for all > 1. In the absence of disease-induced death, it is proved that the transcritical bifurcation at R = 1 is supercritical (forward). Sensitivity analysis is performed on the basic reproduction number and it is noted that the most sensitive parameters are the probability of transmission of the disease from an infectious individual to a susceptible individual per contact, , per capita contact rate ,c, per capita birth rate, and the progression rate from latent to infectious stage, . Numerical simulations of the model show that, the combination of vaccination and treatment is the most effective way to combat the epidemiology of VZV in the community.