Modelling the Effect of DOTS and Isolation on TB Transmission Dynamics

Abstract

A deterministic model for the transmission dynamics of Tuberculosis (TB) under Direct Observation Therapy Strategy (DOTS) and Isolation in Nigeria is developed and rigorously analysed. The model, consisting of mutually-exclusive epidemiological compartments representing the number of undetected, detected and isolated individuals who are treated under DOTS programme and those who developed Multi-drug resistance. The model has a disease free equilibrium (DFE), which is locally asymptotically stable, whenever the maximum of the associated reproduction numbers of the model (denoted by Rc) is less than unity. Furthermore, the model undergoes a backward bifurcation, where the disease-free equilibrium co-exists with a stable endemic equilibrium. Numerical simulations, using epidemiological and demographic data relevant to Nigeria obtained from WHO and USAID [35,36,38], shows that provided the rate at which the undetected individuals with active TB recovered exceeded a critical values, then DOTS, the STOP TB initiative programme of WHO can lead to effective elimination of TB in Nigeria. This suggest that the detection rate plays significant role in the elimination of TB. Furthermore, it is shown that if the progress or rate of individuals who are susceptible to TB is low, it can also lead to elimination of the disease in Nigeria. The results also shows that if the effective contact rate (  ) for TB infection remains below certain critical value (0.187), the disease can be eliminated.