Effects of Vaccine Efficacy on Basic Reproduction Number of a Vaccination Model of Tuberculosis.

Abstract

This paper addresses the effect of vaccine efficacy rate on a vaccination model of tuberculosis (TB) epidemic. Numerical simulations was performed on the model using Maple 15 computation software. Our results showed that as the levels of vaccine efficacy increase, the basic reproduction number, R₀, decreases. This implies that if the protective effect of TB vaccine is increased, it would bring a lower R₀. In consequence, there would be a steady reduction in the number of infectives and susceptibles while eradication of infection would be achieved in finite time. Graphical results are also presented and discussed qualitatively.

Keywords: Mathematical model; tuberculosis; basic reproduction number; vaccine efficacy; equilibrium points; stability.