Ebola viruses exude from infected cell, photocredit: NIAD creative commons
Nick Cumming-Bruce and Alan Cowell of the New York Times just published Ebola Could Eventually Afflict Over 20,000, W.H.O. Says. `A total of 1,552 have died in four countries. After starting in Guinea, possibly in December of 2013, the Ebola virus has spread to Liberia, Sierra Leone, and Nigeria.
40% of all cases have occurred in the last 21 days. Think about this for a moment. A characteristic of a viral epidemic virus in its unchecked phase, and all other forms of exponential growth caused by a positive feedback loop, is that the "doubling time" remains farily constant. Remember in mathematical terms "positive" does not mean "good" but reinforcing. (It is the sign of the transfer function of the feedback loop in control theory mathematics.)
GENEVA — As the tally of deaths from the worst known outbreak of the Ebola virus continued its seemingly inexorable rise, the World Health Organization said on Thursday that the epidemic was still accelerating and could afflict more than 20,000 people — almost seven times the current number of reported cases — before it could be brought under control.
The dire forecast was made as the W.H.O. reported that the number of known cases and fatalities had risen once again. The organization also acknowledged that in areas of intense transmission “the actual number of cases may be two-to-four times higher than that currently reported.”
The outbreak “continues to accelerate,” the organization said.
According to the latest figures released by the W.H.O. on Thursday, the death toll has risen by more than 100, to 1,552 out of 3,069 cases in four West African countries: Guinea, Liberia, Sierra Leone and Nigeria, which had previously indicated that its outbreak was under control.
A simple thought experiment starting at 3,000 cases now, and doubling the number of cases each month produces a simple forecast:
August 3,000
September 6,000
October 12,000
November 24,000
December 48,000
January 96,000
February 192,000
Let's stop here under the optimistic that government and health authorities get this under control by then. We haven't seen any evidence of this control yet, but authorities do seem to be waking up to to how serious this is, and will continue to be unless something is done. So let's assume they do what is necessary by then.
As we get coordinate and escalate our response with education, identification, isolation, and behavioral change the number of new cases per infected case should drop. This negative feedback loop can be predicted to slow the transmission rates and hopefully bring this epidemic under control. When we look at the total death rates we will see what we call "S-Shaped" growth.
However, for now we are appear to be in a growth phase dominated by the positive feedback loop as infections rage out of control.
Nigeria reports its first case outside of those in Lagos infected as a consequence of Patrick Sawyer who traveled from Liberia.
The W.H.O. is calling for a "massively scaled and coordinated international response.
The two new cases of Ebola in the Democratic Republic of Congo are a different outbreak and are caused by a different strain of the virus.
Our prayers and best wishes are with all of the afflicted, their loved, ones and all Western Africans who are struggling to overcome this terrible contagion.
8:34 AM PT: Please consider making a donation to Medecins Sand Frontieres, aka Doctors Without Borders. The are an independent, non-profit organization, and they have been doing heroic work on the front lines of this epidemic since we heard of the first case in March. Thank you.
8:58 AM PT: Please consider making a donation to MSF aks Doctors Without Bordes. They have been the primary "boots on the ground" so far heroically trying to help local authorities contain this outbreak.