Neglected diseases get the mathematical treatment

26 Jan 2010

Tatum Anderson

Source: TropIKA.net

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Professor Sir Roy Anderson.

Mathematical modelling is about to become a key tool in the fight against neglected tropical diseases. That’s the prediction of Professor Sir Roy Anderson, chair in Infectious Disease Epidemiology, and expert in theoretical epidemiology at Imperial College, London.

Credited with transforming this relatively new discipline in biology and medicine over the last 30 years, Anderson is best known for using mathematical models, or equations, to describe infectious diseases, and how they spread. And by calculating the individual effects on millions of inhabitants, as well as the interactions between those people, he can gauge the likely effect of control measures – from closing schools to treating sections of the population with prophylaxis – on an entire population.

Using real-life data and a wealth of clinical evidence – such as how long someone might be infectious – has helped modellers like Anderson mimic the spread of diseases. Imperial’s group has developed models for several diseases already, from syphilis to tuberculosis. Anderson has published several hundred papers on epidemiology, population biology, evolution and pathogens including HIV, BSE, foot and mouth virus, vCJD, and viral and bacterial infections of the respiratory tract.

So powerful are these tools that agencies, from the Centers for Disease Control (CDC) in the US to WHO, use them routinely to predict the movement of emerging infections from SARS to H1N1 and answer key questions, such as what proportion of the population might require vaccinations to halt transmission of a disease, when schools might have to close and who should be treated with prophylaxis.

Modelling and the infectious diseases of poverty

Today, however, agencies from the Bill & Melinda Gates Foundation, to Medical Research Council (MRC) and National Institutes of Health (NIH) are increasingly applying these tools, or the field of theoretical epidemiology, to the infectious diseases of poverty. Imperial’s group has looked at dengue virus, parasitic helminths and protozoa, for instance. Modelling groups around the world are studying tuberculosis, dengue and syphilis.

The idea is that, as well as introducing more scientific rigour, mathematical modelling could help better use the limited funds available to tackle such diseases. They might be used to decide, for instance, the minimum number of times children might be treated for schistosomiasis to make an impact on morbidity and mortality. “We know how to treat [schistosomiasis] but the reason it doesn’t happen is money and infrastructure,” he says. “So, doing simulations about how optimally to use the resources is even more important in the poor diseases of the world. You don’t want to get it wrong and you need to spend your money wisely.”

Mathematical modelling might, therefore, help researchers and policymakers specialising in the diseases of poverty decide whether an intervention that is difficult and expensive to test in real populations, is worth trying. That approach has already been taken in other areas; to test theories on how to control antibiotic resistance, for instance.

It has also been used to disprove a theory that patients could have drug holidays to escape from the nasty side-effects of antiretroviral drugs that treat HIV, says Anderson. Indeed, a group at Imperial predicted that drug holidays would instead promote drug resistance. (However, the idea took a while to catch on he says. “The medics didn’t believe it. But a whole lot of very expensive trials were done that came to exactly that conclusion,” he says.)

And today the department is in a race against Microsoft to create a model for the transmission of malaria that could be used to assess the impact of different control intentions from vaccines to bednets. The groups have been given a year, until June 2010, to deliver. (Anderson is confident that the Imperial team, led by Professor Azra C Ghani will win).

Interestingly, part of the modelling work will also look at simulating intervention trials, which Anderson predicts will become a major part of drug and vaccine development in future. Phase III trials typically cost three-quarters of the total bill to develop new drugs. It is likely that clinical trial designs will be developed using mathematical simulations to calculate the optimal trial size, the number of people selected for trials from different age groups, or the ideal interval for follow up, for instance. Optimising each of these factors could reduce the cost of trials immensely. “The writing is on the wall. We will simulate most trials in the future because it saves money,” he says.

Scepticism

However, modellers say there is sometimes a very unrealistic view of what mathematical simulation can deliver. Of course there will be scepticism; natural enquiry is the basis of science, after all. And of course, like any tool, mathematical modelling can be used well or badly.

But what modelling can and cannot deliver must be better understood says Marc Lipsitch, professor of epidemiology at Harvard School of Public Health, who heads another modelling team which has helped model a range of diseases including swine flu.

“Models of disease transmission can rarely predict the future precisely, because we rarely have enough data or knowledge of biological systems underlying transmission to calibrate the models exactly,” he adds. “Often policy makers want/need predictions of the future, and hope models can provide these – they are commonly disappointed in that hope.”

Others think that models are too dependent on uncertain inputs and hence offer almost no value. “The truth lies in the middle,” he says. “Some decision makers understand that well and I think the pandemic of H1N1 has helped to clarify that a bit.”

One reason for scepticism is that the outcomes of models are not often precise as those from equations associated with other branches of science such as physics and chemistry. That is because by their nature infectious diseases are influenced by a whole manner of variables – from the number of children in a population to the efficaciousness of a vaccine. And many of those variables may have to be estimated if there is little data. The average number of animal vectors in an area, for instance, can complicate calculations for zoonotic infections for instance, because often so little is known about the prevalence of those vectors.

Some diseases are far more difficult to model than others too. Influenza is relatively easy, says Anderson. Malaria, in contrast, is incredibly complicated because it can vary so widely – through recombination, multiple antigenic variations and the number of different genes that can be switched on and off in different certain situations.

Malaria control interventions are complex too. Bednets are used in different ways, they and the new generation of malaria vaccines are likely to have only partial efficacy and may need to be topped up after a few years. These issues add greatly to the complexity of models.

And that is precisely why the use of models by governments and health agencies to set policy on how to deal with outbreaks, epidemics, and even pandemics, can be fraught with controversy. There may be margins of uncertainty, for instance, or even different answers to the same questions.

Take H1N1. Critics have accused WHO of overplaying the pandemic as governments struggle to off-load vaccines bought in expectation of a far more severe effect on their populations. For its part WHO says the science was sound. And of course the decisions that are made on the basis of the models can be controversial too. A Council of Europe investigation is considering whether undue influence by pharmaceutical industry played a role in the way the disease was handled [see TropIKA.net editorial].

Anderson retorts that, while many people are sceptical about mathematical models and margins of uncertainty in biology or medicine, they may not be in other areas. Researchers and policy makers who regularly criss-cross the planet in aeroplanes have already been subject to mathematical modelling because most pilots train on flight simulators, giant mathematical models, he says. Indeed even these kinds of mathematical models sometimes rely on estimations where the science around an area is still a little fuzzy; air turbulence, is an example. “People often think of engineering as precise but there are fuzzy bits of engineering too,” he says.

Different answers?

And as to whether different modellers are likely to come up with different answers to the same question; surprisingly, different academic institutions often independently come up with the same conclusions to modelling questions, in Anderson’s experience. That happens in the case of foot and mouth and SARS he says. And occasionally the same conclusions are reached but with different quantitative data. “So in other words they may say that the optimum thing is to close schools and treat with prophylaxis but there may be differences about timing or what fraction of kids or adults to treat with prophylaxis,” he says.

Scepticism may also abound because modelling is a relatively new branch of medicine and biology, compared with non-infectious disease epidemiology.

It is new for technical reasons; lots of computing power is required to run simulations because computers calculate the effects of several parameters on millions of individuals in a population.

But although computing power has grown exponentially – mobile phone SIM cards are an order of magnitude faster than the computers that guided Apollo missions in the 1960s – it is only in the last 15 to 20 years that such simulations could be carried out on the types of computers that university departments can afford.

Today, Imperial has the computer processing power to carry out simulations of entire populations and is now working on a simulation of the movement and mixing of the entire human race.

The next step is to apply that power to even more complicated biological systems. In the case of infectious diseases of poverty, modellers want to mimic the variations in the genetic make-up of pathogens in a population. “The challenge for modelling is to represent evolution. The beginnings have started but it’s going to be computationally very tough,” he says. “But it’s probably very important for HIV and malaria.”

Other interests

Mathematical modelling is just one of Anderson’s many interests. He holds positions on boards from the Bill and Melinda Gates Foundation’s Grand Challenges fund to chair of the advisory board of the WHO’s Neglected Tropical Diseases (NTD) Department, where he helps WHO look at how best it should spend its limited resources on control and the most pressing research needs.

Today, he is particularly interested in under-researched areas such as the interaction between several existing drugs that combat neglected diseases, such as albendazole and praziquantel for instance. “It would be quite nice if you could give a few tablets at the same time; could you have a single poly-pill which had the active ingredients of three or four treatments?” he asks. “Money is limited. If you are going to a school [to deliver a drug] why not do as much as you possible can on one visit?”

He also plans to develop the Institute for Global Health he has set up at Imperial with ex-UNAIDs head Dr Peter Piot as its first director. Anderson says he plans a world-class Masters programme in global health and public health. “I want it to be interdisciplinary. I don’t want it to focus just on medicine it’s got to be much broader, [including] water and the environment,” he says.

But his position as a non-executive member on the main board of pharmaceutical company GlaxoSmithKline (GSK) remains controversial. In another controversial move, he stepped down as Rector of Imperial College at the end of last year, after overseeing unpopular plans for cuts at the university. “I’ve been a research scientist for my whole life and frankly that interested me more than university administration,” he says.

But he plans to continue the link with GSK, he says, because the company is looking at diseases of the developing world such as HIV and malaria. (As reported in TropIKA.net News, GSK will be putting into the public domain the details of thousands of compounds that might have potential in the treatment of malaria.) “I rather hope I will be able to get them interested in dengue,” he says.