Using Graph Theory to Analyze the Spread of Tuberculosis in South Africa
In class, we have discussed graph theory and more recently, the small world phenomenon or “six degrees of separation” notion that every person in this world is connected to another person in six or fewer relationships. With the current widespread talk of the Ebola virus, it interesting to note how the concepts of graph theory and of “six degrees of separation” can apply to the spread of viruses and the rise of epidemics. The small world phenomenon can be a frightening notion when relating the interconnectedness of the world to the spread of disease. In such a context, it can be alarming that you are only six handshakes away from contracting communicable diseases like the flu or SARS. A recent study applied the idea of graph theory and such a network perspective to the spread of an extensively-drug resistant (XDR) form of tuberculosis. This type of tuberculosis commonly found in southern Africa is deadly for HIV infected individuals and can cause lethal bacterial lung infections.
In 2012, researchers at the University of KwaZulu-Natal conducted a retrospective, observational study on data acquired from tuberculosis patients at a South African hospital in the Tugela Ferry district of the Kwazulu-Natal province. Data was acquired over a period of 2 years to develop a transmission network analysis. Transmission network graphs were created using the following guidelines. Patients were represented as nodes while the transmission of tuberculosis was shown as edges. Patients were included if they had a epidemiological link to any member (node) of the network, and patients who were diagnosed earlier on were considered to have infected epidemiologically linked patients in the same hospital ward who had later diagnosis dates during the overlap in time period that both patients were in the hospital. For each graph, the component size and network density was calculated.
Researchers were alarmed to find how truly interconnected the transmission graphs were. One male patient was found to be connected to eleven other patients while another female was linked to ten other females in the same ward. The largest component of the graph consisted of fifty-one tuberculosis patients, all of whom were infected with the same ST60/KZN tuberculosis bacterial strain. This high degree of interconnectedness suggests that the outbreak and spread of the disease within the hospital was not a point-source outbreak, but much rather an ongoing spread of multiple generations of the disease. Such data is key to developing a plan to combat the widespread transmission of diseases in third-world hospitals. In the future, factors such as the long duration of hospital stay and highly crowded wards that led to the ongoing spread of tuberculosis (as shown by the interconnectedness of the transmission graphs) could be controlled to diminish the spread of disease.
The study:
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3523793/#__ffn_sectitle