Sensitivity analysis of a model for tuberculosis

Field: Medicine (Health Sciences)

Tuberculosis (TB) is a growing problem worldwide, with an estimated third of the world's population currently infected. Of particular concern is the growing trend of dual epidemics of HIV and TB, with the associated multidrug-resistant TB (MDR-TB). Developed countries which had previously removed TB transmission from communities are being re-infected with the MDR-TB strains. In the USA, Centers for Disease Control & Prevention (2009) estimate that treatment of a single case of MDR-TB costs approximately USD$250,000, with a similar cost expected in Australia.TB is a complicated disease with different rates of progression to, and different aspects of, the clinically active disease. Approximately 5-10% of those infected with TB develop 'fast' TB, and are expected to progress to clinically active TB within 2 years [Porco et al. 2001]. The remainder have 'slow' TB, and remain latently infected, with 5-10% progressing to clinically active TB in 20 years [Blower et al. 1995]. Those with clinically active TB are further divided into extra-pulmonary (non-infectious) and pulmonary (able to infect others). Note those in the 'pulmonary' category may also have extra-pulmonary TB, but the reverse is not true.The control of TB spread is of paramount importance. The main intervention strategy adopted by the World Health Organisation (WHO) Stop TB program is the 'Directly Observed Treatment Short course' (DOTS) [World Health Organisation 2010]. Not all detection occurs under this program, but a significant amount of the treatment does, particularly for high burden countries. Therefore when considering interventions, we concentrate on the DOTS program, and do not consider other interventions here.We develop a population level model for TB transmission, with a focus on incorporating the WHO's DOTS (Directly Observed Treatment Short-course) intervention program. The population is divided into 6 compartments, with 4 describing different stages of the disease (susceptible, latently infected, extrapulmonary, and pulmonary), and 2 for the DOTS intervention program (detection and treatment).This work has applications worldwide, but here we focus on the Torres Strait region where there is a high proportion of multidrug-resistant TB (MDR-TB). In particular, estimates suggest Papua New Guinea (PNG) may have the highest proportion of MDR-TB in the world [Gilpin et al. 2008], and the Torres Strait Islands could potentially act as a gateway for MDR-TB into mainland Australia.A sensitivity analysis is important in terms of both data collection and refinement, and in the context of understanding and informing the control of TB. To perform the sensitivity analysis the model needs to be run many times with different parameter values. Latin hypercube sampling is used to efficiently cover the parameter space, in conjunction with partial rank correlation coefficient to determine which parameters most influence the disease dynamics.The results show the most important parameter for TB in Papua New Guinea (PNG) is the rate of progression from latent to clinically active TB. Therefore, data refinement should concentrate on determining this rate as accurately as possible. The most important intervention parameter is the detection rate for the DOTS intervention program. This suggests an increase in DOTS coverage by even a small margin will result in a significant decrease in the incidence and prevalence of TB in PNG and other high burden countries.