A recent NPR blog features a few quotes emphasizing a math word that is lamentably absent from many readers’ vocabularies: “It’s spreading and growing exponentially,” President Obama said Tuesday. “This is a disease outbreak that is advancing in an exponential fashion,” said Dr. David Nabarro, who is heading the U.N.’s effort against Ebola. I can’t help but feel sad that the occasion for someone to learn about the term “exponential” might be directly linked to Ebola. I would hope instead that it would pertain to the growth of their earnings in a bank account, or the growth curve of some formerly endangered species as it recovers.
However, it is exciting to see some coverage of the “basic reproduction ratio”, R_0 , and a plethora of graphs aimed at showing the variety of scenarios that might unfold in West Africa. Amy Greer at Math.Epi.Lab is one of the researchers using the IDEA (incidence decay and exponential adjustment) model to regularly update predictions as to when this outbreak will reach its peak.
Evolution of the basic reproduction ratio R_0 and the control parameter d in the IDEA model for incidence
Currently, the IDEA estimate is that in December of this year, the number of cases will peak at around 13,000. Dr. Greer sees the total number of cases due to this outbreak as easily reaching 20,000. In one of her posts, she posts the evolving value of R_0, a nice reminder that this is a dynamic parameter that is estimated using Estimation Theory. In this graphic, the control parameter d “controls” the weight of the mitigating measures in reducing incidence.
Data on Ebola has been provided by the World Health Organization to the general public, and Caitlin Rivers, a computational epidemiologist at Virginia Tech, is making this data more accessible. Ms. Rivers titles her Ebola-related posts #HackEbola, and a quick twitter search shows others using the hashtag as well. World Health Organization more accessible. And her most recent post looks at the data concerning follow-ups with those who have come in contact with someone infected with Ebola.
My favorite math and epidemiology blog so far has been Musings on Infection, in which computational epidemiologist David Hartley ponders various infectious diseases, but especially focuses, in his last half a dozen posts and on his twitter feed, on Ebola. In his post “Epidemiology and behavior in the time of Ebola”, Hartley points us at some great articles, and gives some food for thought, including the possibility that Ebola could become endemic due to the distrust between healthcare workers and the local population. It is interesting to see how different estimates are holding up. Looking back, one of the earlier studies that Hartley references on a September 02 post entitled “Why Model Infectious Disease”, the graphic from physicist Alessandro Vespignani’s paper predicted the number of cases today to be between about four and eleven thousand. Indeed, the current number of cases is 6,500 according to the CDC, which is well within Vespignani’s range.
Alessandro Vespignani’s research as featured in Science Insider on August 31st
The ability to isolate currently infected individuals and follow up with those who have been exposed will play a huge role in determining the evolution of the “effective reproductive number” – the number of individuals that are actually infected by each currently infected person. So I leave you with a tool that you might consider using with your students or just play with for your own edification. The game VAX, developed by Phd candidate Ellsworth Campbell, is a great way to get a feel for how disease can spread through a network depending on the connectivity of the network and the ability to vaccinate those who are healthy (not yet a possibility for Ebola) and quarantine those who are infected.
VAX game screenshot
Hope all of this helps to better inform you as to some of the mathematics involved in helping to analyze the current situation in West Africa. Please let me know if you have a favorite blog that discusses mathematics and epidemiology.