Mathematics of Planet Earth

You might have heard of a group of diseases called the “Neglected Tropical Diseases”. This isn’t just a generic title for all the forgotten diseases in the world; it’s a specific designation on behalf of the World Health Organization for 13 particular diseases that qualify for neglected status. Collectively, these diseases infect about one sixth of the world’s population.

The diseases in question include three types of worm (hookworm, roundworm and whipworm), a number of helminths (elephantitis, river blindness, Guinea worm disease and schistosomiasis), protozoans (leishmaniasis, Chagas’ Disease, sleeping sickness) and bacterial infections (the Buruli ulcer, leprosy and trachoma). Approximately 4.2 billion people — more than half the population of the Earth — are at risk for hookworm alone, with 807 million currently infected.

What characterizes these particular diseases isn’t that — unlike more sensational diseases like HIV/AIDS, malaria and TB — they kill huge numbers of people (about 530,000 people per year, although that’s still not nothing). Instead, they’re responsible for massive levels of disfigurement and disability, impairing childhood development and economic productivity. They’re found in every tropical country (including Australia) and yet are neglected at the community, national and international levels, largely because they affect the poor, the powerless and the stigmatised.

For example, Chagas’ disease kills 50,000 people a year (far more than West Nile virus, Bird Flu and swine flu combined), but you probably haven’t heard of it because it’s a disease of the poor. If your house is made of sticks, the bugs that carry the disease burrow through your walls and bite you under the eye. But if you can afford plaster, then you’re completely safe. So it’s a widespread disease in poor, rural South America (where the average life of a dog is about two years, thanks to the disease), but doesn’t kill anyone who might be in a position to lobby governments, advocate for medical interventions or mobilize advertising campaigns.

Rather than simply count deaths, the World Health Organization has developed a measure of the number of years of life lost from premature death or disability, or DALYs (Disability-Adjusted Life Years). The number of DALYs per year for HIV/AIDS is 84.5 million. That is, without HIV/AIDS we’d have about 84,500,000 years of healthy life back. But NTDs are collectively the next largest burden on the world, with DALYs of 56.6 (diarrhoeal diseases are third, followed by childhood and vaccine preventable diseases, then malaria and TB). So despite being neglected, the NTDs are one of the largest problems human beings face today.

Treatments exist for some NTDs, although often control occurs through less “sexy” methods, such as mass dewormings in schools, insecticides, safe water and, in some cases, arsenic and amputation. (Seriously. Arsenic is still used to treat sleeping sickness, while the only treatment for the Buruli ulcer is to amputate infected limbs. NTDs ain’t pretty.) Part of the problem is that there’s no money in them: why would a profit-driven pharmaceutical company waste time developing treatments for diseases whose sufferers can’t pay? Of the 1600 drugs developed between 1974 and 2004, only 18 were for tropical diseases (and 3 for TB).

So what’s to be done? Fortunately, there are a couple of success stories. Guinea worm disease has been all but eliminated, despite having no vaccine, no drug and no immunity. Instead, behavior changes (convincing people not to put infected limbs in the water, distributing cloth filters to villages and outfitting nomadic people with drinking pipes) have led to a massive reduction in cases and already eliminated the disease from Asia and the Middle East.

Who made this miraculous feat happen? It’s thanks to the efforts of one man: former president Jimmy Carter, who did the unglamorous but important work of mobilizing public-private partnerships, delivering education messages to remote populations and even negotiating a “Guinea worm ceasefire” in the Sudan civil war so that NGOs could go in and educate those most at risk. As a result, Guinea worm disease has been almost eradicated from the planet. It’s not only going to be the first parasitic disease to be eradicated, it’s also going to be the first to be eliminated using behavior changes alone. That’s an incredible achievement.

Another success story is river blindness, and this is where mathematical modelling comes into the picture. The West African river blindness program was developed as a co-production between the World Health Organization, the World Bank, the UN, and 20 donor countries and agencies in 1974. Mathematical modelling was used at the outset to predict long-term outcomes; by including modelling in the design of the program, sceptical donors were convinced that control was feasible. When the drug ivermectin was made available in the late eighties, mathematical models were able to adapt to its inclusion. After the program was completed, modelling retained a prominent role in subsequent policy discussions.

One of the great advantages of mathematical modelling is that it’s cheap. A lot can be done with a little, so many potential scenarios can be investigated even when data is limited. In a way, this makes NTDs an ideal subject for modelling to tackle. There are a great many problems that urgently need to be solved that mathematical models could help with.

Unfortunately, the NTDs are as neglected by modelling as they are by everyone else. Only sleeping sickness has received any substantial theoretical modelling. There are no models at all for the Buruli ulcer and only one for Guinea worm disease. When models do exist for NTDs, they’re usually confined to one lab and its collaborators per NTD. What we urgently need is a diversity of voices.

Specific problems might include adapting malaria pesticide models for vector control in Chagas’ disease or leishmaniasis. Spatial modelling is critical: access to resources depends critically upon geographical constraints, so models that accounts for distance to hospitals, swamps, mountains and road networks are crucial. Co-infection models — between other NTDs and also major diseases like HIV — are also desperately needed.

Modelling could also help categorize the costs to developing economies of disabling NTDs: if treating NTDs is shown to save more money than it costs in productivity, this will help motivate action. Another, slightly meta, approach might be to model research funding itself: if granting agencies are requiring researchers to provide “at home” benefits, this could be standing in the way of significant work on diseases that might help a very large number of people.

In summary, NTDs require immediate attention. They extract an enormous price in suffering, lack of economic development and the promotion of poverty. Mathematical models can be used to inform policy at minimal cost, solving problems that may not be theoretically complex, but which have the potential to deliver enormous benefits.

NTDs are the low-hanging fruit of mathematical modelling. A great many problems could be solved, relatively easily, by harnessing the power of mathematical modelling. The price — political and otherwise — for such a huge improvement in the quality of life for one sixth of the world’s population is tiny.

Robert Smith?
The Department of Mathematics
The University of Ottawa
585 King Edward Ave
Ottawa, ON K1S 0S1
Canada