A Mathematical Model of Effect of Bacillus Calmette-Guerin Vaccine and Isoniazid Preventive Therapy in Controlling the spread of Tuberculosis in Nigeria

Abstract

In this study, we modelled the effect of combining Immunization with latent tuberculosis treatment in controlling the spread of tuberculosis. The administration of BCG vaccines administered at birth protects children from early infection of the disease but the effect of these vaccines expires with time. Hence, detection and treatment of Latent tuberculosis infections by administering isoniazid preventive therapy prevents the break down of latent infections into infectious cases this however, reduces greatly the rate of spread of the disease since, only members of the Infectious class can spread the disease to others. We established the existence of equilibrium states and analyse the disease free equilibrium state for stability using Routh-Hurwitz theorem. The disease free equilibrium state (i.e., the state of total eradication of tuberculosis) will be stable if effort is intensified in bringing down both the contraction rate and the rate of break down to infectious tuberculosis