The epidemiological study of tuberculosis (TB) has been ongoing for several decades,
but the most effective control strategy is yet to be completely understood. The basic
reproduction number, R₀, has been found to be plausible indicator for TB control
rate. The R₀ value is the average number of secondary TB cases produced by a typical
infective individual in a completely susceptible population during its entire infectious
period. In this study we develop two SEIR models for TB transmission; one involving
treatment of active TB only, with the second incorporating both active TB treatment
and post-exposure prophylaxis (PEP) treatment for latent TB. Using the next generation
matrix method we obtain R₀. We determine the disease free equilibrium (DFE)
point and the endemic equilibrium (EE) point. Global stability conditions of DFE are
determined using the Castillo-Chavez theorem. Through model analysis of the reproduction
number, R₀, we find that for R₀ < 1, the infection will die out. The value of
R₀ > 1 implies that the disease will spread within the population. Through stability
analysis, we show that the model exhibits backward bifurcation, a phenomenon allowing
multiple stable states for fixed model parameter value. MATLAB ode45 solver
was used to simulate the model numerically. Using the Latin Hypercube Sampling
technique the model is sensitive to treatment and disease transmission parameters,
suggesting that to control the disease, more emphasis should be placed on treatment
and on reducing TB transmission. For the second model, which incorporated treatment
with post-exposure prophylaxis for latently infected individuals, by means of
simulations, we found that treatment of latently infected individuals may reduce R₀.
Numerical simulations on the latter model also showed that it may be better to introduce
a hybrid of active treatment and post-exposure treatment of the latent class.
The force of infection was found to reduce when this hybrid control strategy is present.
Contour plots and PRCC values highlighted the important parameters that influence
the size of the Infective class. The implications of these findings are that TB control
measures should emphasise on treatment. Our simplified models assume that there is
homogeneous mixing. The model used have not been validated against empirical data. / M.Sc. University of KwaZulu-Natal, Pietermaritzburg 2014.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:ukzn/oai:http://researchspace.ukzn.ac.za:10413/11320 |
| Date | 20 October 2014 |
| Creators | Sithole, Hloniphile. |
| Contributors | Sibanda, Precious., Mwambi, Henry G. |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | English |
| Type | Thesis |
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