Modelling the transmission of tuberculosis

Doctoral Thesis


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University of Cape Town

Airborne infectious diseases, such as tuberculosis (TB), are spread by airborne infectious particles (viable particles with potential for TB infection) in exhaled air from infectious individuals in enclosed spaces. Exhaled air is the carrier of airborne infectious particles and carbon dioxide is used as a surrogate of this exhaled air. Using carbon dioxide as a surrogate for exhaled air, we modified the Wells-Riley model and the prior modified versions of the model, and obtained a exible but sensitive mathematical model that predicts the risks of airborne infectious diseases, such as TB under steady- state and non-steady-state conditions, without assumptions of well mixed airspace and equilibrium conditions. Applying experimental data from in vivo studies to the mathematical model developed in this study, we explored the probability of exposed guinea pigs acquiring infection in these in vivo stud- ies and quantified the number of surviving airborne infectious particles (infective organisms) required to reach the alveolar to establish infection. Our study shows that the number of infective organisms reported in the in vivo studies might have been markedly underestimated. In this study, we investi- gated TB transmission in congregate settings, such as schools, households, public transport, prisons and health care settings and suggested preventive measures. TB transmission in these locations is attributable to numerous factors, including overpopulation and air pollution, which acts as a carrier of airborne infectious particles. We explored the impact of effective contact rate on TB epidemiology using a mathematical model we developed that consists of five states of susceptible, primary infection, reinfected, active TB and treated individuals. An infectious individual with varying effective contact rate (ranging from 5 to 30 per year) was introduced among 100; 000 fully susceptible individuals and we observed the number of primary infection and reinfected individuals at stability points of a TB epidemic. We found that the number of primary infection individuals decreases at the stability point, while that of reinfected individuals increases with increasing effective contact rate. This implies that a large number of active TB cases might be reinfected individuals. Using an age-structured mathemat- ical model developed in this study that incorporates vaccination, we explored TB disease progression in different age groups (from 0 to ≥ 75 years). We found that TB disease progression is age dependent. High TB notification rate was detected for the age groups [0 - 5); [15 - 25); [45 - 55) and [55 - 65) years, and the lowest TB notification rate was detected in the age group [5 - 15) years. Furthermore, we noted that vaccination decreases active disease progression for the age groups [0 - 5) to [15 - 25) years, while TB notification remains high for the age groups [25-35) to ≥ 75) years. The findings in this study suggest that active disease progression depends on age and average duration of the waning of the vaccine effect.