The Exponential Nature of Ebola

Otto E. Rossler

Institute for Physical and Theoretical Chemistry, University of Tubingen, Auf der Morgenstelle 8, 72076 Tubingen, Germany

Inscribed on the UN Building:
Human beings are members of a whole,
In creation of one essence and soul;
If one member is afflicted with pain,
Other members uneasy will remain;
If you have no sympathy for human pain,
The name of human you cannot retain.
(Saadi, 1210–1292)

Abstract

A survey of the epidemiology of Ebola and the logically necessary responses is offered.

(October 23, 2014)

Ebola is of interest to mathematicians, of all things. Medical epidemiology is basically a mathematical discipline. The exponential growth curve of the number of victims – published on en.wikipedia
(http://en.wikipedia.org/wiki/Ebola_virus_epidemic_in_West_Africa#mediaviewer/File:Evolution_of_the_2014_Ebola_outbreak_in_semiLog_plot..png ) – exhibits a visible doubling every three weeks over six months time by now, with an incredible inexorability of the mathematical trend displayed. It represents an unprecedented medical record. It shows that the amazingly constant 3 weeks long incubation period, with subsequent likely death (50 percent) and with on average two newly infected persons, is something like a law of nature. It is a “phenomenon” in the sense of the
exact sciences.

The perfection in which this behavior is observable in an ordinary if poor population is unprecedented. The contagiousness of the disease is extraordinary. And because of the 3 weeks long latency in the mom-infectious incubation period, the upcoming fate is hidden from the infected persons. They are healthy and nothing prevents them from leading a normal life. On the last two days before becoming bed-ridden on the 21st day, say, they carry the disease further.
When they are not at home – in town, say, or at their work place – they propagate the disease, and they do so at home thereafter as long as being cared for. Such a disease – once it has surpassed
an initial threshold of a minimum number of cases – is pre-programmed to spread and conquer.

Preventive immunization is hoped to be available, on an at first small and then grander scale, after a time gap of several months. It would be great if the race could be won earlier. This would stop the spreading if most everyone gets the protective shot. A curative – or at least preventive-acting – serum is also in preparation. And plasma can be collected from survivors who must be paid for this. (See the splendid review talk hiven most recently by the discoverer and name-giver of Ebola,Peter Piot: http://www.oxfordmartin.ox.ac.uk/videos/view/415 ). But these measures can help stop the spreading only after long further months have passed. After a 4-months delay, for
example (or roughly 18 weeks), the disease will – if no other measures are taken – have passed through six doubling periods of three weeks and hence have killed 64 times the current number of
about 5.000, which means about 300.000. And if the grand-scale vaccination or therapy takes twice as long in coming (8 months), it is 64 times more casualties again or 20 million deaths. If the
delay is 12 months (one year), it is again 64 times that number or one billion.

Therefore, relying on therapy or vaccination is like relying on a straw right now. What is it that can be done in the meantime? Flying-in nurses and doctors? No: Locomotion control is the only other causal measure that can be taken. It will not reduce the ongoing course of the infection in the sealed-off areas but it will, after reducing the population there to about one half in the worst case, stop the disease. This is a very sad prospect.

However, this prospect is too optimistic still. For it presupposes that the closed-off areas are provided with water and food as “catastrophe zones.” At the time being, this is perhaps still
feasible. But it will soon exhaust planet-wide capacities. This is a war going on. A war that is waged for once not by reluctant human beings but by a soulless parasite.

Obviously, it is not volunteering doctors and nurses that are needed as a causal measure, but water and food supply chains in motorized units, sure to reach even the remotest areas of the declared “closed zones.”

The “epidemiological approach” just sketched looks rather soulless: Is really the provision of basic needs more important than treatment? It indeed is much more causal – sadly. It is tragic to
see that neglecting this support strategy is much more deadly than the withdrawal of all therapeutic volunteers could be since they are “a drop on a hot stone” by comparison.

But is this not terrible? It is tragic. It is even more tragic since the disease itself is so uniquely cruel. It demands that healthy persons keep away from victims unless provided with an expensive protective gear (or unless being survivors). Therefore, the latter gear needs to be provided in very large numbers soon to be distributed in the closed-off zones immediately to prevent the death rate inside from becoming maximal.

A caretaker with a feeling heart coined the word “dying twice” for Ebola. The first time because you get abandoned – no one can come close to you, touch you, serve you. You are made a leper. Your mother must not hug you or come close any more (remember, even the dying Jesus had his mother at his side). Then you die once more in agony.

We come to a conclusion. Should the rational medical information given above be made public? The answer is: of course. But is this not another catastrophic news about Ebola? It surely is. This is the
first time in history that a war against nature needs to be waged. The greatest heroes are the vaccination developers. The next guild is the drug developers. The third league is the first league in terms of importance: The administrators who close down whole areas to be no longer left by anyone living there. On the same level are the providers of water and food for the closed-down areas. Their
mission is preventing death on a mega-scale. Until the eventually millions of sera and immunization kits needed are available, the twice weekly water and food squadrons are the life-saving troup.
They have the most important job as the green angels.

Volunteers are needed for this large-scale operation. And nations are needed to send-in the needed subsistence supplies soon, subito, immediately. For every three weeks’ delay causes a doubling in the
size of the effort needed, or perhaps even a quadrupling since the area to be served quadruples. For the infected areas cannot be closed before the support system is in place! These volunteers are
the life-saving angels – not the doctors, not the nurses. The latter are needed, too, but their humanitarian activities are in vain without the causal hygiene measure of closed areas supported
from the outside.

A new type of volunteer – the water-and-food squad – needs to be founded immediately. Any objections from my readers? Does anyone see a glimmer of hope beyond the above proposed desperate measures?

Acknowledgments

I thank Klaus Dietz for a discussion. For J.O.R.