# An ancient disease, a scar, and classroom mathematics

How are a 10,000-year-old disease, the scar on your arm (if you are over 25 and born in the UK), and the mathematics you learnt at school related? If you are under 25, where is your scar? My research uses mathematics to understand the role of Bacillus Calmette–Guérin (BCG) vaccine in preventing Tuberculosis (TB) in England and forecast the impact of current policies.

TB is one of the oldest human diseases, with recorded cases in ancient Egypt, renaissance Europe, and in the modern day across the globe. The disease is spread through the air, when people with active TB cough, spit, speak, or sneeze. Classic symptoms include a chronic cough with fever, night sweats, and weight loss. After an initial infection, an individual may immediately develop active TB or enter a latent stage from which active TB may develop years later.

It is thought that roughly one-third of the world’s population has been infected with TB, with 1% of the world’s population being infected annually. However, the vast majority of these cases will never develop active disease. This reservoir of disease presents a challenge for control and eradication as, even if transmission can be halted, new cases will still occur for many years to come. While many people might consider TB to be a problem of the past in England, in 2015 there were 5,758 notified cases, the majority of which occurred in vulnerable communities; where incidence rates can be as much as 15 times higher than in the general population.

The BCG vaccine was developed in 1921 and was introduced to the UK in 1953. Globally, it has been shown to offer variable protection that may reduce over time. However, there is strong evidence that BCG offers high levels of protection for children, and more generally within the UK born population. It remains the only TB vaccine with over 100 million doses given globally each year. Serious side effects are very rare but scarring commonly occurs at the site of injection.

In 2005, the UK withdrew the universal BCG program for those at school age and introduced a targeted program of vaccination for babies that were deemed to be at high risk. This was motivated by several years of declining transmission, the evidence of high levels of protection in children and a belief that other control measures would be more cost-effective. Since this change in policy, declining incidence appears to support this decision. However, due to TB’s complex dynamics, the long-term effects are difficult to predict. More recently there has been a global shortage of the vaccine, which has led to some at risk children not being vaccinated; the potential effects of which are unknown.

The availability of data is revolutionising the way we view the world; in few other areas has this revolution been felt more than in public health. In 2000, Public Health England launched a routine surveillance system for TB, which records demographic, clinical, and microbiological information on all notified cases. This dataset allows us to study the details of TB epidemiology in England more easily than ever before. Whilst this information would present much of interest by itself, by combining it with other datasets we can adjust for the changing demographics of the English population to study the trends in TB over time.

My research has two strands. The first of these is aimed at understanding the current impact of BCG on TB in England. This involves investigating evidence that suggests BCG vaccination may improve outcomes for those who have developed active TB and estimating the direct effects of the 2005 change in vaccination policy. These results will enable policy makers to gain a greater understanding of the role of BCG vaccination in England and hopefully facilitate future decision making.

The second strand uses the power of simple mathematical systems to reproduce complex dynamics. Examples of these techniques can be seen in modelling the weather and understanding the shoaling behaviour of fish. In infectious diseases, mathematical models have been used for over 100 years but have recently become increasingly data driven. By developing simple models, harnessing secondary school level mathematics, I am attempting to explain some of the patterns in TB incidence that have been observed in England over the last 15 years, in the context of changing vaccination policy. The simplicity of these models means that hypothetical scenarios can be explored, via simulation, and forecasts of future TB trends made.

Science is nothing if not a collaborative process. Whilst mathematical models provide a powerful analytical approach, without expert knowledge and good data they can produce meaningless results. While my focus is BCG vaccination, the key lesson from my PhD has been the importance of working across disciplines in order to access expert knowledge and unlock the power of mathematics to solve real world problems.