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In 2015, WHO estimated there were 9.6 million TB cases and 1.5 TB deaths. Nearly 500,000 of these cases were resistant to two or more of the main drugs used to treat TB. New drugs, and combinations of drugs, are being developed to treat tuberculosis, as are new vaccines that may protect against disease in adults. Quantifying the burden of TB is fundamental to understanding its global epidemiology and for making appropriate resource allocation decisions. Most estimates of new TB case numbers each year rely strongly on the number of cases reported by countries in that year to WHO. Unfortunately, one in three TB cases are thought to go either undetected or unreported, so the number of cases reported underestimates the number of new cases. While one can correct for this, it is hard to know exactly how much to adjust the reported numbers. Some countries have good systems for recording causes of deaths, which can be used to estimate the number of deaths caused by TB. Increasingly, large and expensive prevalence surveys are being used to estimate the number of people with active disease in a population. These estimates are less subject to bias, but measure a different quantity. Little work has explored the best way of combining these three data sources. A major goal of this work is to use mathematical transmission models for burden estimation and provide a unified framework for all data. These models yield the number of new cases, deaths, and also the prevalence of disease. They explicitly represent disease transmission and so introduce a dependence between the number of new cases in different years. These models involve parameters evidenced from previous epidemiological work, but must be calibrated to learn from data on TB reports, deaths and prevalence. Calibration means adjusting imperfectly known model parameters in order to match observed model outputs to the data. This process provides a model that may be used to make predictions about burden, but may also teach us something about the underlying processes. Many of the parameters concerning the epidemiology and disease course of TB are quite uncertain, and this uncertainty is rarely represented fully in models needing calibration, but will be done in this project using statistical techniques that also allow comparison of different models' performance. TB burden estimation and calibration of transmission models are almost always carried out on a country-by-country basis. Many parameters describing disease progression are likely to be similar in different countries, even if their exact values differ for unknown reasons. Hierarchical modelling techniques allow such parameters to be correlated between countries. This can improve precision, particularly for countries with little data, as estimates can be informed by data from neighbouring countries. I will explore these techniques for the transmission model, and also in statistical modelling aiming to account for the observed patterns of drug-resistance. The transmission model will ultimately be extended to include different types of drug resistance. As new treatments and vaccines emerge, those with responsibility for public health will want to understand the potential impact these new technologies can have in terms of gains in health, and changes in spending. Producing cost-effectiveness and budget impact evidence requires a model that includes transmission, in order to account for indirect benefits accrued by avoiding secondary cases. We will use our model to provide guidance to decision-makers seeking to maximise health gain with limited resources. We will also analyse sources of uncertainty in the model to identify future research that would have most value in increasing the precision of burden estimates and in reducing decision uncertainty around the introduction of new interventions.","The Global Challenges Research Fund (GCRF) supports cutting-edge research to address challenges faced by developing countries. The fund addresses the UN sustainable development goals. 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