How to fight Cholera: A mathematical model

Published online 9 January 2009 Nature doi:10.1038/news.2009.11
(Borrowed from original article by R. Kwok in Nature News Alerts 13 Jan 2009,
Modified By A.J. Tamhankar)
Fighting cholera by the numbers : New model for best course of Action
A new mathematical model could help to determine the best strategy for controlling outbreaks of cholera, a deadly bacterial disease that has recently taken hold in Zimbabwe.
The model, presented at a mathematics conference this week in Washington DC, calculates which combination of vaccination, sanitation and antibiotic treatment levels will most effectively reduce the number of lives lost and the cost of intervention. Although the work has been used only to simulate past epidemics, cholera experts say it could offer a step towards better-informed decisions during an outbreak.
The bacterium responsible for cholera, Vibrio cholerae, spreads mainly through water and food and can easily contaminate the water supply in developing countries, where sanitation is poor. The Zimbabwe outbreak, which began in August 2008, has so far caused about 33,000 suspected infections and more than 1,600 deaths.
Rachael Neilan, a graduate student in mathematics at the University of Tennessee in Knoxville, and her colleagues developed a set of equations to describe the likely spread of cholera. The model takes into account the infectiousness of the bacterium, which is more likely to cause disease when it is first shed, as well as the distinction between symptomatic and asymptomatic patients.
Past predictions
Although the disease-outbreak model builds on previous work, the team has introduced equations to determine the best, most cost-effective intervention schedule. The model predicts how much of, and for how long, each treatment should be applied. As a test, the researchers simulated a cholera outbreak that swept the Bay of Bengal in the early 1900s, when modern treatments were not available. For one district, the model recommended quickly ramping up antibiotics treatment to 275 people in the first few weeks, then gradually reducing treatment. It also suggested that vaccination and sanitation should be intensively applied at the outset but stopped after 20 days.
"This is the very first optimal-intervention strategy model," says Neilan, who presented the work at the Joint Mathematics Meetings of the American Mathematical Society and the Mathematical Association of America. According to the simulation, the suggested treatments would have reduced the number of deaths from 31 to 9 and cut the peak number of infections by more than half.
Currently, the simulations begin with the first day of infection and rely on knowledge of certain factors, such as the ratio of asymptomatic to symptomatic patients. But Neilan says it should be possible to tweak the model so that it can be used partway through the epidemic instead. Making decisions mid-outbreak could add complications: in Zimbabwe, for example, the World Health Organization is not recommending vaccination because of the logistical difficulty of delivering doses and the time lag before the vaccine takes effect.
The researchers plan to incorporate data on the age of patients so they can give more specific suggestions about whom to vaccinate. O. Colin Stine, a geneticist at the University of Maryland School of Medicine in Baltimore, says that the model also assumes that all cholera is the same, but his research in Bangladesh suggests outbreaks are caused by multiple genetic forms of cholera, each of which may each require a different model.
"There is a lot of work that needs to be done to fine-tune the parameters before it's something we're going to want to use as a practical tool," says Glenn Morris, director of the Emerging Pathogens Institute at the University of Florida in Gainesville, who has worked with the Tennessee team. "But it's a start."