Mathematics behind Ebola epidemic decoded

Researchers have calculated new benchmark figures to precisely describe the raging Ebola epidemic in West Africa from a mathematical perspective, an approach that may help health authorities to contain the virus.
Health authorities want to know how the epidemic will develop and, above all, how to prevent it from spreading further, researchers said.
Certain parameters help them to determine this, such as the reproductive number, which is the average number of infections caused by a single infected individual.
The incubation and infectious periods are also highly relevant; ie the time from infection to the onset of symptoms and the time from onset of symptoms to the clearance of the pathogen.

A team led by Tanja Stadler, professor of computational evolution in the Department of Biosystems Science and Engineering at ETH Zurich in Basel, has now calculated these parameters based on the gene sequence of the virus in various patient samples, using a statistical computer programme developed by the group.
The virus sequences were obtained by American, British and Sierra Leonean researchers from blood samples taken from patients in Sierra Leone in the first few weeks after the epidemic migrated to the country from neighbouring Guinea in May and June 2014.

Newer sequences are currently not publicly available, said Stadler.
From the data, the researchers calculated a viral reproductive number of 2.18. This value is in the range of the previous estimated values based on the incidence and prevalence of the disease, which are between 1.2 and 8.2.

"A major benefit of our method is that we can use it to calculate unreported cases and therefore the true scale of the epidemic," said Stadler.
Official patient figures only take into account those cases reported to the health authorities. The actual number of infected persons is generally significantly higher.
Using the data made available to them, the ETH researchers were able to calculate an unreported case rate of 30 per cent (ie patients of which blood samples were not taken).
"However, this applies only to the situation analysed in Sierra Leone in May and June. We do not have any blood samples since June at all," said Stadler.

The researchers were also able to calculate the incubation period for Ebola (five days - this value is subject to significant uncertainty) and the infectious time. Patients can pass on the virus from 1.2 to 7 days after becoming infected.
Researchers hope the new sequences of the currently circulating Ebola virus become available.
"Our programme is ready. If we are given access to current Ebola sequences, we will be able to gain a detailed insight into the spread of the epidemic literally overnight," said Stadler.