Mathematical models incorporating ecological data are starting to be deployed on the front line in the battle against infectious disease. Virginia Gewin talks to the number-crunchers who are spearheading the assault.
During Britain's epidemic of foot-and-mouth disease in 2001, the government culled some 4 million cattle, pigs and sheep. These drastic measures were introduced following the advice of a new breed of epidemiologist — those who deploy mathematical models of disease ecology to predict the progress of an outbreak and the probable effectiveness of different control strategies. In this case, the modellers crunched data on the distribution of farms, the size of herds, wind patterns and records of recent animal transport.
Controversy still rages over the decision to rely on culling alone, rather than using vaccination to try and reduce the slaughter1. But the cull did succeed in bringing an end to an epidemic that threatened to send British agriculture into meltdown2. Before the modellers recommended that livestock on infected farms be culled within 24 hours of foot-and-mouth being reported, and animals on neighbouring farms within 48 hours, the disease was spreading completely out of control.
Britain's experience with foot-and-mouth disease is a high-profile example of a growing trend to incorporate ecological models of disease in strategies to protect human and animal health. Ecological factors, experts are realizing, frequently underpin disease outbreaks.
In the future, climate change, encroachment into natural habitats and other consequences of human activity promise to change our exposure to infectious disease. And despite scepticism from some traditional epidemiologists, ecological models are showing up on the front lines of public-health systems all over the world. “Mathematical modelling will be equally as important as anything that comes from the human genome in terms of its utility in public health,” claims Andrew Dobson, an ecologist at Princeton University in New Jersey.
The field first began to attract attention in the late 1970s, thanks to the work of Roy Anderson of Imperial College in London and Robert May, then at Princeton and now president of the Royal Society in London. They created general models of disease spread based on the population dynamics of hosts and pathogens3,4.
Since then, ecological modelling, in particular of the spatial dynamics of disease, has become increasingly robust. Recent models have revealed how outbreaks of both measles5 and dengue fever6 can spread in repeated waves from central foci of infection. In the latter case, researchers led by Donald Burke of the Johns Hopkins Bloomberg School of Public Health in Baltimore, Maryland, showed how waves of dengue infection radiate across Thailand from the capital, Bangkok, every three years or so, moving at a speed of almost 150 kilometres per month.
Dengue, which is a major problem in the tropics of Asia, Africa and North America, provides one of the clearest examples of the value of ecological modelling for public health. The dengue virus is spread by the mosquito Aedes aegypti, which also carries yellow fever. Many mosquito species breed in marsh edges, or in transient puddles such as those in hoofprints, but A. aegypti prefers to lay its eggs in water-storage containers. With this knowledge in hand, Dana Focks, principal scientist at Infection Disease Analysis, a public-health research company in Gainesville, Florida, has developed an accurate method to estimate the size of adult mosquito populations by counting pupae in these containers.
Focks, who used to work with the US Department of Agriculture, has developed models that predict the risk of disease transmission from the availability of suitable mosquito breeding habitats and the degree of immunity to the virus in the regional human population7. These can be used to predict what types of water-storage bins should be covered or drained to keep mosquito populations below the ‘tipping point’, beyond which a dengue epidemic becomes imminent.
Unfortunately, not all diseases have such straightforward, well-documented ecology. Malaria, for instance, is spread by more than 60 species of the Anopheles mosquito — for which there is little high-quality information on population dynamics.
In such cases, ecologists are trying to use secondary means of predicting mosquito distribution and abundance — such as satellite data and hydrological models of surface wetness. David Rogers, an ecologist at the University of Oxford, UK, is using satellite images to correlate seasonal climate parameters, such as annual rainfall and wet-season temperature, with predictions of the distribution of five of the six main mosquito vectors of malaria across Africa8.
Longer-term climate cycles can also influence the prevalence of human disease. For example, the El Niño–Southern Oscillation (ENSO), a periodic disruption in trade winds, ocean currents and sea surface temperatures in the tropical Pacific, has been linked to outbreaks of cholera, dengue and hantavirus — which causes a deadly lung disease. Indeed, a team led by Gregory Glass of the Johns Hopkins Bloomberg School of Public Health has used satellite data to show how increased rainfall in the southwestern United States under ENSO conditions causes an increase in vegetation. This correlates with booms in populations of the deer mouse (Peromyscus maniculatus), which can pass hantavirus to people9. Terry Yates of the University of New Mexico in Albuquerque, a member of Glass's team, is now testing mathematical models designed to predict the risk of hantavirus transmission, which are based on an ecological understanding of where infected rodents are likely to persist even in the absence of ENSO.
But it can be difficult to produce reliable predictions of disease incidence. Focks, for instance, is trying to use information on ENSO to develop dengue early-warning systems for urban Indonesia and Thailand. For Indonesia, unpublished results from his models produced reasonably accurate forecasts over a timescale of up to three months, but predictions for Thailand were not so successful.
Given the looming phenomenon of global warming, ecological modellers would dearly love to increase the reliability of predictions based on changes in climate. But at present, modelling the influence of climate change on the incidence of a disease such as malaria is difficult. Models based on the biology of the mosquito vectors suggest that, with global warming, malaria will spread into regions that are at present too cool to support a permanent mosquito population. Yet models that base their predictions purely on climate forecasts generally indicate that warming will have little impact on malaria prevalence8. “The state of the art of climate and infectious-disease modelling is improving, but hasn't yet reached a point where it could influence decision making,” says Burke.
In other cases, modellers are frustrated by the sheer complexity of host and pathogen population dynamics. When asked by the US Centers for Disease Control and Prevention (CDC) in Atlanta, Georgia, to create a model to describe the spread of West Nile virus, Focks ultimately declined. “There were too many hosts, and not enough known about them, to make models like I did for dengue,” he says. Indeed, West Nile virus, which in recent years has fanned out across most of the United States, has been found in 216 bird species, 30 other vertebrates and 49 species of mosquito.
These limitations may explain why some traditional epidemiologists remain unconvinced of the value of ecological modelling. The sceptics also question the extent to which ecological models can be used to devise viable disease-control strategies, given that decisions to fell forests, divert rivers or change the environment in other ways that may alter disease transmission are rarely made with public-health considerations in mind. “My personal opinion is that mathematical models will rarely be very useful,” says David Morens, a medical epidemiologist at the National Institute of Allergy and Infectious Diseases in Bethesda, Maryland.
Sceptics are particularly concerned by claims from some ecologists, including newcomers to the field, that they can devise models to predict outbreaks of disease. Such claims have won funding from agencies including the US National Science Foundation and the National Institutes of Health.
The problem, according to some public-health experts, is that in few cases are the underlying ecological data good enough to give the resulting models any real predictive power. “It does a disservice to the field to mislead policy-makers that we can use models for predictive capability when we don't have the data,” says Duane Gubler, now at the University of Hawaii in Honolulu, and formerly director of the CDC's Division of Vector-Borne Infectious Diseases.
Gubler argues that ecologists now entering the field should look to emulate Fock's work on dengue. “His models are the best in the business, and the reason they are so good is because he understands the complexities of the ecology that goes into them, and he understands their limitations,” Gubler says.
Despite the doubts, the World Health Organization is embracing a number of ecological models in its efforts to control water- and vector-borne diseases. Following the foot-and-mouth epidemic, Britain's Department of Environment, Food and Rural Affairs has incorporated mathematical modelling into its cadre of tools for protecting the health of livestock. And US institutions are beginning to follow suit. New Mexico's state government is using Yates's model to provide warnings of when environmental conditions may support a hantavirus outbreak.
Whether ecological modelling expands further to become an established public-health tool will depend upon the incorporation of better underlying data. But Burke, a self-proclaimed convert to the power of ecological models, believes that another major impediment to progress in the field is a lack of dialogue between mathematical modellers and traditional epidemiologists. “They don't talk to each other as much as you think they would,” he says. If public-health officials are to meet their ultimate goal of predicting and preventing disease outbreaks, rather than simply responding to mitigate their toll, suggests Burke, this needs to change.
Keeling, M. J., Woolhouse, M. E. J., May, R. M., Davies, G. & Grenfell, B. T. Nature 421, 136–142 (2003).
Woolhouse, M. et al. Nature 411, 258–259 (2001).
Anderson, R. & May, R. M. Nature 280, 361–367 (1979).
May, R. M. & Anderson, R. M. Nature 280, 455–461 (1979).
Grenfell, B. T., Bjornstad, O. N. & Kappey, J. Nature 414, 716–723 (2001).
Cummings, D. T. et al. Nature 427, 344–347 (2004).
Focks, D. A., Brenner, R. J., Hayes, J. & Daniels, E. Am. J. Trop. Med. Hyg. 62, 11–18 (2000).
Rogers, D., Randolph, S. E., Snow, R. W. & Hay, S. I. Nature 415, 710–715 (2002).
Glass, G. E. et al. Proc. Natl Acad. Sci. USA 99, 16817–16822 (2002).
About this article
Telematics and Informatics (2015)
Initial epidemic area is strongly associated with the yearly extent of soybean rust spread in North America
Biological Invasions (2013)
Individual variations in infectiousness explain long-term disease persistence in wildlife populations