Recent CDC estimates put the amount of possible Ebola cases at around 1.4 million as of January 2015. This is just four months from now; however, they do not say what will happen one year from now based on their own, projective, logic.
If the current rate of transmission persists, with an exponential doubling time around 1 month, the human population will be infected to 2016. This will happen. There will be a thousand more cases in just 10 months… It just grows exponentially from there: five million cases as of Sept 2015; 5 billion cases by Sept 2016, i.e. the total human population. At a 70 % mortality rate, only 2 billion people will survive, but the situation could be even worse if we take into account mutations of the virus and the consequences of a pandemic catastrophe…
http://brighterbrains.org/articles/entry/does-the-ebola-virus-constitute-an-existential-risk
Projecting ebola cases though 6 orders of magnitude as if the exponential will definitely continue unmodified through all limits is so wrong it’s not even funny. (I have the same objection to projections of Moore’s law or economic growth.) SO many curves have pieces of them that look exponential… though it is true that the exponentials usually come from the early parts of such curves.
Viruses mutate but a membrane-bound filamentous virus that doesn’t live in epithelia as its main host cells is never something that becomes stable airborne, and other evolving viruses change virulence or symptoms not mode of transmission. You don’t just change fundamental physical attributes.
Still a scary disease that must be contained, most especially from entering other poor urban areas where it is capable of exponentiating and could be utterly horrifying. But cut the bad math and baseless fearmongering in favor of its actual issues.
EDIT: This is not to say pandemics are not a big deal. Pandemics are actually probably the worst actual risks humans will face this century, seeing as the world situation is kind of perfectly primed for zoonotic disease by population growth habitat destruction urbanism and mobility. This is the sort of thing we will have to deal with for a long time. We’d better get used to it and get good at it or we will regret it.
Viruses mutate but a membrane-bound filamentous virus that doesn’t live in epithelia as its main host cells is never something that becomes stable airborne
Can you explain like to a non-cellbioguy, what does the above sentence mean in relation to this?
Yes! Thanks for pointing me at that paper, I hadn’t seen it before.
Enveloped viruses are in general much more fragile than non-enveloped viruses. They contain the genetic material of the virus and viral proteins surrounded by a lipid membrane derived from the membrane of a host cell, which they then fuse with the membrane of another host cell to get the genome in. Easier entry to the host cell at the expense of fragility. If the membrane is broken the virus is dead, and a bubble of membrane is a lot more fragile than a protein/RNA crystal (which is basically the entire structure of non-enveloped viruses which need to somehow pass through the cell membrane without killing the cell which is more difficult). In particular, dessication tends to kill enveloped viruses fairly quickly meaning they need to be wet from host to host. Ebola viruses are filamentous viruses, meaning their genome is stretched out in a long ribonucleoprotein fiber which is surrounded by a big tube of membrane (those long funny shapes we have all been seeing), so they have a lot more membrane per particle than most viruses and are particularly vulnerable.
One might note that the flu virus is also membrane-bound but goes through the air. Sort of. It empirically requires droplets of several microns in size to move through the air in natural conditions, which only make it so far (a few feet) before drying out or settling to the ground. In real-world conditions smaller droplets or dry particles don’t seem to be important for its spread, though you can set up experiments where a few manage to make it through that way. Also, any flu virus that gets breathed in or on a mucous membrane is already in its perfect environment—epithelial cells—so a very small viral dose is required to make it in, whereas in living organisms ebolaviruses seem to have a much lower affinity for epithelial cells than blood vessel or connective tissue cells from research I’ve been able to look up, so you need more viruses to get into and infect a surface.
In the above-linked experiment, monkeys had their heads put in a sealed 8-liter box inches away from a nebulizer that produced aerosols from a liquid containing ebolaviruses, kicking up single-micron-sized droplets. They found that in this circumstance as few as 400 functional virus particles delivered this way to the respiratory tract/face was enough to cause a lethal infection (as compared to <10 functional virions via injection, though they did not try lower viral levels for inhalation), showing that a smallish number of freshly-aerosolized viruses landing on a respiratory surface can cause disease.
However, that you can set up an experiment in which you give enough viruses through the air to cause infection does not mean that under normal conditions that circumstance is likely to happen—the latter being the usual definition of ‘airborne’. There’s also a difference between ‘airborne’ and ‘screwed if someone sneezes on your face’ which is more akin to what’s happening here.
They note this. Quotes from the paper:
“Epidemiology studies of human disease outbreaks in sub-Saharan Africa did not suggest that aerosol transmission of filoviruses was likely in that setting [emphasis mine]. Virus did not spread easily from person to person during the Ebola virus epidemics in Africa, and attack rates were highest in individuals who were in direct physical contact with a primary case… no cases occurred in children whose only known exposure to the virus was sleeping in the huts occupied by their fatally ill parents.”
“It is possible that the quantity and distribution of virus within most patients’ respiratory tracts may have been below the level needed to establish effective aerosol transmission.”
The structural factors that make Ebola more fragile in the air are not ones that are likely to change much via mutation—that’s things like cell affinity, how obvious it is to the immune system, replication speed, or toxicity to infected cells. There’s reasons that viruses generally don’t change their modes of spread during evolution.
On the other hand, there’s this:
“Both elevated temperature and relative humidity (RH) have been shown to reduce the aerosol stability of viruses… Our experiments were conducted at 24C and < 40% RH, conditions which are known to favour the aerosol stability of at least two other African haemorrhagic fever viruses… If the same holds true for filoviruses, aerosol transmission is a greater threat in modern hospital or laboratory settings than it is in the natural climatic ranges of viruses… As previously stated, aerosol spread was implicated in the spread of disease among the monkeys at Reston [an accidental 1990s outbreak of ebolavirus among monkeys in a laboratory of a strain that could not infect/cause disease in humans, after work I may look up more about it to see what they mean about ‘implicated’]”
And this:
“While both parenteral [injected] and aerosol exposure to Ebola virus cause a systemic disease involving all organs, monkeys exposed to viral aerosols during our study developed strong immunoreactivity for Ebola virus antigen in airway epithelium, in oral and nasal secretions, and in bronchial and tracheobronchial lymphoid tissue. By electron microscopy, viral replication after aerosol exposure occurred in the lungs and tracheobronchial lymph nodes, and extracellular virus accumulated in alveoli of the lung.” The monkeys exposed via fresh aerosol developed much more shedding virus in the lungs than their needle-exposed counterparts which you could imagine affecting infectivity.
You may find another paper making the rounds about aerosol transmission between monkeys and pigs; these were in a cage separated by bars and space and scientists make note that in that circumstance they can’t necessarily tell the difference between respiratory aerosols, splashed liquid, and liquid kicked up during periodic cage cleaning.
In cold air droplets could live much longer. This is why we have flu outbreaks in winter. Ebola was never “tested” in winter conditions but it could become more contagious in winter in Europe and Norther US.
Anyway, the question will it become airborne or not is not important as it already has doubling period 1 month and it is enough to infect almost all human population to 2016. To be airborne is only an option.
The main question is how and when exponential growth will be stopped? What is your opinion?
This joke maybe good in any other site but not on Lesswrong which is based on idea of unlimited AI self-improving. Of cause Ebola will end it exponential growth—I just interested to know how and when. Will it burn out in Africa, or we get herd immunity after 100 million victims, or effective vaccine will be created, or we will nuke all places with Ebola?
This joke maybe good in any other site but not on Lesswrong which is based on idea of unlimited AI self-improving.
Some people here, including the founder, believe that recursive AI self-improvement is a realistic possibility, but I’m pretty sure that even the most hardcore believers acknowledge that there are physical limits, and that you can’t just expect an exponential function to be a good fit for a trend when you get close to the limit.
The basic function you should be looking for modelling this kind of phenomena is the logistic function. It’s the basic model for phenomena that include both positive feedback mechanisms (e.g. self-replication) and negative feedback mechanisms (e.g. resource constraints).
If you look at the graph of the logistic function, you may notice that initially, when positive feedback is dominant, it very closely resembles an exponential, then it becomes about linear around the middle point and then, negative feedback is dominant, it becomes close to a negative exponential.
If a disease had a constant basic reproduction number$R_0>1$, and it could infect anyone, and infected people never died because of the infection and remained infectious for life, then the prevalence of the disease over time would be well approximated by a logistic function, with the world population size as the supremum value (the “capacity”).
In an actual epidemic, of course, people can die or heal, and the R factor varies over time as the disease spreads to different places, people and institution change their behavior, better treatment becomes available, and so on, thus you don’t really get an exact logistic trend, but that’s the first-order model for forecasting the long-term prevalence disease, not an exponential model that neglects feedback loops. An exponential model is only useful when the disease prevalence is still quite far from the capacity, that is, when a typical infected person is mostly surrounded by uninfected (and infectable) people.
If the current rate of transmission persists, with an exponential doubling time around 1 month, the human population will be infected to 2016. This will happen.
Recent CDC estimates put the amount of possible Ebola cases at around 1.4 million as of January 2015. This is just four months from now; however, they do not say what will happen one year from now based on their own, projective, logic.
If the current rate of transmission persists, with an exponential doubling time around 1 month, the human population will be infected to 2016. This will happen. There will be a thousand more cases in just 10 months… It just grows exponentially from there: five million cases as of Sept 2015; 5 billion cases by Sept 2016, i.e. the total human population. At a 70 % mortality rate, only 2 billion people will survive, but the situation could be even worse if we take into account mutations of the virus and the consequences of a pandemic catastrophe… http://brighterbrains.org/articles/entry/does-the-ebola-virus-constitute-an-existential-risk
Projecting ebola cases though 6 orders of magnitude as if the exponential will definitely continue unmodified through all limits is so wrong it’s not even funny. (I have the same objection to projections of Moore’s law or economic growth.) SO many curves have pieces of them that look exponential… though it is true that the exponentials usually come from the early parts of such curves.
Viruses mutate but a membrane-bound filamentous virus that doesn’t live in epithelia as its main host cells is never something that becomes stable airborne, and other evolving viruses change virulence or symptoms not mode of transmission. You don’t just change fundamental physical attributes.
Still a scary disease that must be contained, most especially from entering other poor urban areas where it is capable of exponentiating and could be utterly horrifying. But cut the bad math and baseless fearmongering in favor of its actual issues.
EDIT: This is not to say pandemics are not a big deal. Pandemics are actually probably the worst actual risks humans will face this century, seeing as the world situation is kind of perfectly primed for zoonotic disease by population growth habitat destruction urbanism and mobility. This is the sort of thing we will have to deal with for a long time. We’d better get used to it and get good at it or we will regret it.
Can you explain like to a non-cellbioguy, what does the above sentence mean in relation to this?
Yes! Thanks for pointing me at that paper, I hadn’t seen it before.
Enveloped viruses are in general much more fragile than non-enveloped viruses. They contain the genetic material of the virus and viral proteins surrounded by a lipid membrane derived from the membrane of a host cell, which they then fuse with the membrane of another host cell to get the genome in. Easier entry to the host cell at the expense of fragility. If the membrane is broken the virus is dead, and a bubble of membrane is a lot more fragile than a protein/RNA crystal (which is basically the entire structure of non-enveloped viruses which need to somehow pass through the cell membrane without killing the cell which is more difficult). In particular, dessication tends to kill enveloped viruses fairly quickly meaning they need to be wet from host to host. Ebola viruses are filamentous viruses, meaning their genome is stretched out in a long ribonucleoprotein fiber which is surrounded by a big tube of membrane (those long funny shapes we have all been seeing), so they have a lot more membrane per particle than most viruses and are particularly vulnerable.
One might note that the flu virus is also membrane-bound but goes through the air. Sort of. It empirically requires droplets of several microns in size to move through the air in natural conditions, which only make it so far (a few feet) before drying out or settling to the ground. In real-world conditions smaller droplets or dry particles don’t seem to be important for its spread, though you can set up experiments where a few manage to make it through that way. Also, any flu virus that gets breathed in or on a mucous membrane is already in its perfect environment—epithelial cells—so a very small viral dose is required to make it in, whereas in living organisms ebolaviruses seem to have a much lower affinity for epithelial cells than blood vessel or connective tissue cells from research I’ve been able to look up, so you need more viruses to get into and infect a surface.
In the above-linked experiment, monkeys had their heads put in a sealed 8-liter box inches away from a nebulizer that produced aerosols from a liquid containing ebolaviruses, kicking up single-micron-sized droplets. They found that in this circumstance as few as 400 functional virus particles delivered this way to the respiratory tract/face was enough to cause a lethal infection (as compared to <10 functional virions via injection, though they did not try lower viral levels for inhalation), showing that a smallish number of freshly-aerosolized viruses landing on a respiratory surface can cause disease.
However, that you can set up an experiment in which you give enough viruses through the air to cause infection does not mean that under normal conditions that circumstance is likely to happen—the latter being the usual definition of ‘airborne’. There’s also a difference between ‘airborne’ and ‘screwed if someone sneezes on your face’ which is more akin to what’s happening here.
They note this. Quotes from the paper:
“Epidemiology studies of human disease outbreaks in sub-Saharan Africa did not suggest that aerosol transmission of filoviruses was likely in that setting [emphasis mine]. Virus did not spread easily from person to person during the Ebola virus epidemics in Africa, and attack rates were highest in individuals who were in direct physical contact with a primary case… no cases occurred in children whose only known exposure to the virus was sleeping in the huts occupied by their fatally ill parents.”
“It is possible that the quantity and distribution of virus within most patients’ respiratory tracts may have been below the level needed to establish effective aerosol transmission.”
The structural factors that make Ebola more fragile in the air are not ones that are likely to change much via mutation—that’s things like cell affinity, how obvious it is to the immune system, replication speed, or toxicity to infected cells. There’s reasons that viruses generally don’t change their modes of spread during evolution.
On the other hand, there’s this:
“Both elevated temperature and relative humidity (RH) have been shown to reduce the aerosol stability of viruses… Our experiments were conducted at 24C and < 40% RH, conditions which are known to favour the aerosol stability of at least two other African haemorrhagic fever viruses… If the same holds true for filoviruses, aerosol transmission is a greater threat in modern hospital or laboratory settings than it is in the natural climatic ranges of viruses… As previously stated, aerosol spread was implicated in the spread of disease among the monkeys at Reston [an accidental 1990s outbreak of ebolavirus among monkeys in a laboratory of a strain that could not infect/cause disease in humans, after work I may look up more about it to see what they mean about ‘implicated’]”
And this:
“While both parenteral [injected] and aerosol exposure to Ebola virus cause a systemic disease involving all organs, monkeys exposed to viral aerosols during our study developed strong immunoreactivity for Ebola virus antigen in airway epithelium, in oral and nasal secretions, and in bronchial and tracheobronchial lymphoid tissue. By electron microscopy, viral replication after aerosol exposure occurred in the lungs and tracheobronchial lymph nodes, and extracellular virus accumulated in alveoli of the lung.” The monkeys exposed via fresh aerosol developed much more shedding virus in the lungs than their needle-exposed counterparts which you could imagine affecting infectivity.
You may find another paper making the rounds about aerosol transmission between monkeys and pigs; these were in a cage separated by bars and space and scientists make note that in that circumstance they can’t necessarily tell the difference between respiratory aerosols, splashed liquid, and liquid kicked up during periodic cage cleaning.
Thanks a thousand times. That was awesome!
If you’re interested here’s an article that refers to several more aerosol related Ebola papers.
Thank you for writing this clear and well-researched post, really useful stuff.
In cold air droplets could live much longer. This is why we have flu outbreaks in winter. Ebola was never “tested” in winter conditions but it could become more contagious in winter in Europe and Norther US. Anyway, the question will it become airborne or not is not important as it already has doubling period 1 month and it is enough to infect almost all human population to 2016. To be airborne is only an option. The main question is how and when exponential growth will be stopped? What is your opinion?
...and 40 billion cases by December 2016. Beware exponential extrapolation.
This joke maybe good in any other site but not on Lesswrong which is based on idea of unlimited AI self-improving. Of cause Ebola will end it exponential growth—I just interested to know how and when. Will it burn out in Africa, or we get herd immunity after 100 million victims, or effective vaccine will be created, or we will nuke all places with Ebola?
Some people here, including the founder, believe that recursive AI self-improvement is a realistic possibility, but I’m pretty sure that even the most hardcore believers acknowledge that there are physical limits, and that you can’t just expect an exponential function to be a good fit for a trend when you get close to the limit.
The basic function you should be looking for modelling this kind of phenomena is the logistic function. It’s the basic model for phenomena that include both positive feedback mechanisms (e.g. self-replication) and negative feedback mechanisms (e.g. resource constraints).
If you look at the graph of the logistic function, you may notice that initially, when positive feedback is dominant, it very closely resembles an exponential, then it becomes about linear around the middle point and then, negative feedback is dominant, it becomes close to a negative exponential.
If a disease had a constant basic reproduction number $R_0>1$, and it could infect anyone, and infected people never died because of the infection and remained infectious for life, then the prevalence of the disease over time would be well approximated by a logistic function, with the world population size as the supremum value (the “capacity”).
In an actual epidemic, of course, people can die or heal, and the R factor varies over time as the disease spreads to different places, people and institution change their behavior, better treatment becomes available, and so on, thus you don’t really get an exact logistic trend, but that’s the first-order model for forecasting the long-term prevalence disease, not an exponential model that neglects feedback loops.
An exponential model is only useful when the disease prevalence is still quite far from the capacity, that is, when a typical infected person is mostly surrounded by uninfected (and infectable) people.
So, do you think that half of the population will be infected?
No.
http://xkcd.com/605/
http://xkcd.com/1007/
SCNR.