Will the Ebola Outbreak Become an Epidemic: A Look Into Epidemiological Models

File:Ebola virus em.png

The Ebola Virus.  Found at: http://commons.wikimedia.org/wiki/File:Ebola_virus_em.png

When diseases start to spread unusually or appear more threatening than usual, we have to figure out what the probability is that the disease will spread and become an epidemic, and this is most often done using mathematical models.  If we can model the spread of the disease, using certain parameters specific to the pathogen, we can get a sense of how many people could be infected and how we should respond to the threat.

This is becoming most pertinent now because currently there is an outbreak of Ebola in Africa, spreading from Liberia to Nigeria, and there has been some concern on the news about an epidemic spreading to the United States.  This would be especially problematic because there is no known vaccine or treatment for Ebola.  But, will it actually spread to affect many other countries in the world?

The most common model for diseases is known as the SIR model (which stands for Susceptible Infected Resistant).  In this model, people in the population are either susceptible to the disease (as in they have not contracted it yet), infected with the disease, or they have been infected and recovered and they are now resistant to the disease.  We can plot the spread of the disease as a function of the number of people in the population, the transition rate, and the number of people with the disease at a certain time t, and we get a curve that looks like this:


Found at: http://commons.wikimedia.org/wiki/File:Logistic.png.

Ignoring what the axes mean in this graph, this curve is known as a logistic growth curve.  The disease starts out slow, infecting only a few people, then as more people get it, they pass on the disease to more people, and the disease spreads faster.  Then, it hits a time where so many people are infected and now resistant that the spread slows down and eventually stops.

But, as far as we know, Ebola is not one of the diseases where people who get it once are necessarily resistant.  So then, how does the model change?

Then we can use the SIS model (susceptible infected susceptible), where people can recover from the disease but once they have recovered, they are then susceptible to the disease again.

So, say that people are recovering at some rate a, and the transmission rate is t.  If a > t (or if people are recovering faster than the disease transmits) then the disease won’t spread.  Say the contact rate (the rate of infected people contacting not infected people) is c, then with some math we can figure out that the disease will spread if ct-a is positive, and if ct-a is negative, the disease won’t spread.  We call that number ct-a R, or the basic reproduction number, which tells us the number of susceptible people infected from a single infected person.  If R<1 the disease does not spread, and if R>1, the disease spreads, which makes logical sense because if a single person can infect more than one person, the disease will spread.  If a single person cannot infect one person, than the disease will slowly decline.

We have calculated the R’s (basic reproduction numbers) of certain common diseases; for example, the R of measles is 15 and the R of the flu is 3 (meaning both diseases spread easily, measles way more than the flu).  On a side note, this is why the recent resurgence of measles cases, potentially due to a fear of vaccinations, is so worrisome.

The R for Ebola is hard to say for sure, because R is calculated using data from past cases.  Unfortunately, as of 2004, there have only been a few big Ebola outbreaks, including one in Congo in 1995 and one in Uganda in 2000.  From these two cases, a group of researchers determined that the R is about 1.83 for the Congo outbreak and 1.34 for the Uganda outbreak.  Another group of researchers found the R value to be around 2.7 instead.  This does not necessarily mean that this will be the R value for the current outbreak because there isn’t enough data to say for sure, but it does suggest that the Ebola virus does spread, but not as well as diseases we interact with a lot like the flu.

Why might Ebola have a (comparatively) low R value?  The transmission rate could be low; ebola requires direct contact with bodily fluids with an animal or another human, which occurs far less than contact with viruses that spread in the air or just by touch.  Ebola patients are also contagious for a relatively short amount of time before showing symptoms, so if Ebola is correctly identified quickly (and that is a big if because Ebola is notorious for being misdiagnosed), patients may not be able to spread the disease to many people.  Finally, Ebola tends to kill its host (or show bad enough symptoms that an infected person is hospitalized and under quarantine) fairly quickly, making it harder for an infected person to transit the disease to many people.

Now, this is not to say that the possibility of an Ebola epidemic is zero, because this is currently the biggest Ebola outbreak and it is spreading farther than is usual for Ebola.

However, there is some good news to come of mathematical models – some researchers (their paper can be found here http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2870608/) looked into modeling an Ebola outbreak after medical interventions have occurred (including medical treatments, hospitalizations, and quarantines) and found that the R value dropped significantly (to 0.4 and 0.3, meaning the disease would not spread).  They also found that the time it took for these interventions to happen was one of the determining factors in how big the epidemic would be (as well as decreasing the rate of transmission after death; there have been cases where people have contracted the virus while burying victims of the disease).

Models are never perfect; for example, this particular one did not take into account animal to human transmissions.  However, even simplifications can tell us a lot.

If anyone is interested in modeling, there’s a really cool (and free!) online class on Coursera (coursera.org) called Model Thinking and it’s all about going through different types of models and it actually goes through epidemiological models too.  You should check it out if you’re interested!  https://www.coursera.org/course/modelthinking.

Works Cited









Coursera Course, Model Thinking


How Does Nuclear Power Work?

Many people consider nuclear power to be the future of alternative energy, the solution to climate change and creating a sustainable future.  Others think of nuclear power as far too dangerous and risky to be worth any potential benefits.  So how can we determine how safe nuclear power is?  Well, the first step is to examine how it works…

How do power plants in general create electricity?

Most power plants use some sort of fuel to create heat which then boils water.  This water vaporizes into steam, which is then used to turn a big turbine (as shown below).

File:Altbach Power Plant Turbine on display.JPG

Found at: http://commons.wikimedia.org/wiki/File:Altbach_Power_Plant_Turbine_on_display.JPG.

This turbine spins, creating mechanical energy, and is attached to a generator which turns this energy into electricity.  Both coal-based power plants and nuclear power plants work this way, but the type of fuel they use is different.  Coal-fired plants burn coal to release heat that generates steam.  Nuclear power plants, on the other hand, use nuclear fission.

Nuclear Fission

Everything is made up of atoms, which in turn are made up of a nucleus, the “center” of the atom that contains protons (positively charged) and neutrons (not charged), and electrons (negatively charged), which exist in the space surrounding the nucleus.  Nuclear fission involves splitting an atom, releasing a lot of energy, that is then used to heat the water in the power plant.

During fission reactions, atoms (typically radioactive atoms like uranium, which are very big and therefore easier to break apart) are hit with lone neutrons, causing the atom to split and release more neutrons.  The atom splits because, when the atom comes in contact with the free neutron, it incorporates the neutron into the atom, causing the atom to destabilize and break apart.  Those neutrons that are released then conduct other fission reactions with other atoms, creating a chain reaction.  To prevent the reaction from spinning out of control, the power plant also has control rods that can absorb free neutrons and stop the reaction if needed.


A picture of a nuclear fission reaction, found at: http://commons.wikimedia.org/wiki/File:Kernzerfall.svg

How is a nuclear power plant set up?

The uranium must be enriched, and then it is set up into rods and bundles of rods that are put inside water to prevent them from melting during the reaction.  Then, it heats up that water and turns it into steam, which then goes through a tube to heat up other water that then interacts with the turbine and turns it (so the radioactive materials never go near the turbine itself).

It it Dangerous? 

These reactions can release radiation, which comes in multiple different forms.  Some radiation is high energy electrons being released from the reaction, some is high-energy protons.  There are multiple levels of safety measures taken at any nuclear power plant, including making the containment vessel coated in steel and two levels of concrete protecting the vessel.

The radioactive waste definitely does have to be taken care of safely, and there is still a debate going on about exactly how to best ensure the safety of everyone when disposing of the waste.

In the next few posts, we will look at the problems at Chernobyl and Fukushima, and exactly how safe nuclear power really is in comparison to current types of energy production.

Works Cited






Global Warming Potential: How We Measure Harm to the Environment

There are lots of different greenhouse gases – including water vapor, methane, nitrous oxide, and, of course, carbon dioxide.  So why is everyone so concerned about just carbon dioxide – why aren’t we focusing on the other gases?  Part of it has to do with global warming potential, which is a measure of how much heat energy is absorbed by each gas and how long those gases stay in the atmosphere.

File:Annual greenhouse gas index, 1979-2008 (EPA, 2010). Indicator of radiative forcing.png

The above is a graph of the different greenhouse gases and how concentrated they are in the atmosphere over time – found at http://commons.wikimedia.org/wiki/File:Annual_greenhouse_gas_index,_1979-2008_%28EPA,_2010%29._Indicator_of_radiative_forcing.png.

Greenhouse gases become a problem when they absorb a lot of energy and stay in the atmosphere for a very long time, allowing a single molecule of the gas to absorb far more heat as time goes on.

For example, water vapor is one of the most potent greenhouse gases because it absorbs a lot of heat (far more so than carbon dioxide), but its concentration in the atmosphere changes almost daily as atmospheric temperatures change and precipitation happens.  Therefore, it does not have time to sit in the atmosphere and collect heat, making the atmosphere warmer.  (However, there is some evidence that if temperatures keep increasing due to other gases, like carbon dioxide, more water vapor will collect in the atmosphere, further exacerbating global warming – this is known as a positive feedback).

On the other hand, nitrous oxide stays in the atmosphere for a long time (about 114 years) and can absorb a lot of heat in that time, making it even more potent a greenhouse gas than carbon dioxide.  To see a full list of global warming potentials from the UN, go here: http://unfccc.int/ghg_data/items/3825.php.

So, if there are much more potent greenhouse gases, why focus on carbon dioxide?  Because carbon dioxide is a potent greenhouse gas and it is increasing in concentration far faster than the other gases, making it a big problem.  There have been other efforts to reduce some of the other gases (the Montreal Protocol banned in some countries CFC’s and other gases with high global warming potential), but at the moment it seems that carbon dioxide is the biggest concern.

Works Cited





What’s So Cool About Hydrothermal Vents?

File:Explorer Ridge sulfide chimney.jpg

Picture of a hydrothermal vent, found at: http://commons.wikimedia.org/wiki/File:Explorer_Ridge_sulfide_chimney.jpg

Hydrothermal vents: giant vents at the bottom of the ocean that spew out incredibly hot, mineral rich water from beneath the crust of the Earth.  I think they’re incredibly cool, and here’s why:

1. The geology of hydrothermal vents.  The Earth is made up of plates of crust called tectonic plates, and these plates sit on top of a viscous layer of magma (molten rock), called the asthenosphere.  Because the plates are separate and sit on this viscous layer, they can move, either drifting away from each other (divergent boundary), colliding into each other (convergent boundary), or sliding next to each other (transform boundary).  So, when oceanic crust separates, it allows the magma, along with lots of other minerals that cycle through the Earth, to come up out of the Earth’s surface and cool into new crust.

Well, sometimes water seeps down near the magma through cracks in the Earth’s crust.  This water mixes with lots of minerals underneath the Earth’s surface and then shoots back up in these hydrothermal vents.

File:Mid-ocean ridge topography.gif

Found at: http://commons.wikimedia.org/wiki/File:Mid-ocean_ridge_topography.gif

2. The temperature changes.  Because the hydrothermal vents are located at the bottom of the ocean, no sunlight reaches that far down, and therefore it is incredibly cold (around 2 degrees Celsius, almost freezing).  However, where the hydrothermal vents spew water heated by magma, the waters get up to be around 400 degrees Celsius (to put this in perspective, 100 degrees Celsius is boiling).  So, there’s water that’s 400 degrees Celsius, but go out a few feet and suddenly the water becomes 2 degrees Celsius.

3. The massive pressure.  Hydrothermal vents are located at the deepest parts of our oceans, around two miles below the surface of the water.  This creates massive pressure at the bottom of the ocean, accumulated from the tons of water sitting on top.

4. The fact that organisms actually live down there.  It’s really incredible that organisms can live in an environment with such huge temperatures differences and intense pressure.  But they do, and in fact thriving ecosystems have formed around these hydrothermal vents.


A picture of tubeworms near hydrothermal vents, found at: http://commons.wikimedia.org/wiki/File:Nur04507.jpg.

5. The Tubeworms.  I put a picture of tubeworms above; these creatures are sessile and they are most commonly found near hydrothermal vents.  They have no way of feeding and no digestive system, but instead in their tissues they have bacteria that live on the (to most creatures) toxic minerals that the hydrothermal vents spew out.  The bacteria digest the toxic minerals and produce sugars and food for the worms inside of the worms.  They get nutrition without ever having to eat, hunt down prey, or find food.  Food is just inside of them.

6. The chemosynthesis.  This is one of the only (if not the only) ecosystem on Earth that survives completely independently (for the most part) of the Sun.*  On land, all energy comes from the Sun; the Sun produces light which plants turn into food by photosynthesis, then herbivores eat the plants, then carnivores eat the herbivores.  However, in this specific ecosystem, the organisms get their energy from chemicals through chemosynthesis; the bacteria (like the ones inside tubeworms) turn chemicals into food for other organisms, who then are eaten by other organisms, and thus you have a similar food chain.  So, if something happened to block all light from the Sun (but still kept all other physical properties of the Sun intact), that ecosystem would be the one to survive.

*I say for the most part, because some creatures do feed off of food particles that drift down from the surface, which is dependent on the Sun for energy.

7. The fact that hydrothermal vents cycle a lot of nutrients into the oceans.  Hydrothermal vents are essential for cycling minerals and nutrients from beneath the Earth’s surface, regulating the oceans.

If you’re still interested in the deep seas, check out the episode of the documentary Blue Planet called “The Deep.”  It’s pretty amazing.

Works Cited






MSG: Is It Really Bad For You?

File:MSG crystals.JPG

Picture of MSG crystals; found at: http://commons.wikimedia.org/wiki/File:MSG_crystals.JPG

Monosodium glutamate, or MSG, has been mass produced and put into lots of dishes to produce a meaty, hearty flavor (umami).  But, recently there has been a lot of pushback against eating MSG.  Some people say it causes dizziness and headaches, and even others claim more drastic symptoms, like chest pains and nausea.  Some say these claims are not true in general.  Is MSG really bad for you?

What is MSG?

MSG is a salt, made of sodium and glutamate.  What is funny is that one of the amino acids that make up many of our proteins in our body is glutamic acid, which is an incredibly similar compound to MSG.  When ingested, monosodium glutamate separates into sodium and glutamate ions, which can then react with acid to make glutamic acid.  In fact, the FDA says, “The glutamate in MSG is chemically indistinguishable from glutamate present in food proteins.”

So, glutamate is definitely not bad for humans, as it is naturally produced in a lot of metabolic processes.  So what is bad about MSG?  It has sodium, which could be considered bad at high levels, but it does not have any more sodium than common salt does.

Is MSG Bad?

Actually, there is no clinical research that has shown any causation between MSG and any negative symptoms (here is a link to a scientific article that examined the prominent literature researching MSG symptoms: http://www.ncbi.nlm.nih.gov/pubmed/19389112).  There could be some people who have an allergy to MSG, which would cause negative effects, but MSG in general has not been shown to be bad for humans.    In fact, a bunch of naturally occurring foods have glutamate in it, including tomatoes…but they are definitely still good for you!  So, next time you see MSG in a food product, don’t let that be the sole reason to avoid that food!

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Evolution of Viruses: A Few Hypotheses

We looked in the last post about the structure and life cycle of viruses and we saw that viruses are very different from all other cellular life.  So where did they come from?

So, if we go back a very long time ago, we have the Ancestral Virus, the original virus or type of virus to evolve.  We also have LUCA, the Last Universal Common Ancestor of cellular life (the domains Archaea, Bacteria, and Eukarya, of which humans are a part).  There are a few different hypotheses:

Pre-Cellular Theory

This theory suggests that viruses originated from the parasites of LUCA.

Evidence: This theory is popular because there are such vast morphological differences between viruses and cellular life that it makes sense that they would have evolved separately.

Some scientists have looked for evidence in analyzing the viral genome or the sequences of their proteins.  However, this can be very difficult.  Viruses evolve very quickly, and therefore any similarities or patterns in the genome could disappear pretty quickly.

Endogenous Theory

This theory says that Ancestral Virus evolved from the escaped genetic material of LUCA.

Evidence: This theory came about after the realization that there are similarities in genetic material (they all use either DNA or RNA or both) between the three domains and viruses, which suggests that they did at some point have a common ancestor.  Viruses may have evolved to gain the same genetic information, but then they split off before the evolution of the plasma membrane or ribosomes (part of the cellular component that creates proteins).  Another piece of evidence for this theory is the fact that viruses give a cell their genetic information for the cell to then replicate and translate into proteins.  This means that the genetic material of the virus and the replication machinery of the cell have to be somewhat compatible, suggesting they did have a common ancestor at one point.

Reductive Theory

This theory says that Ancestral Virus originated from cellular organisms that were parasites of other cellular life, and then they lost most cellular components, including enzymes and other machinery needed to do replication.

Evidence: Since the host cell provides much of the needed components to survive, the virus can get away with having a much smaller genome, which could cause it to, over time, lose genes.

Secondly, mimiviruses have been studied as evidence for the Reductive Theory.  Mimiviruses have some morphology that resembles cellular morphology.  They have a cell-like structure during development, a larger genome than most other viruses, some machinery that can translate genetic material, and they have both DNA and RNA.  This suggests that maybe viruses used to have all these parts just like cells do, but then they lost it.

There still is not enough evidence for each individual theory to make a conclusive statement about the evolution of viruses (and there are definitely more theories out there), but each new piece of evidence helps us come a bit closer.

Works Cited

Holmes, Edward C. The evolution and emergence of RNA viruses. http://books.google.com/books?id=PN8oFf2Id4kC&printsec=frontcover&dq=The+Evolution+and+Emergence+of+RNA+Viruses&hl=en&src=bmrr&ei=XQPMTe23EMji0QGglMXZBg&sa=X&oi=book_result&ct=book-thumbnail&resnum=1&ved=0CDwQ6wEwAA#v=onepage&q&f=false

Bandea, Claudiu. The Origin and Evolution of Viruses as Molecular Organisms. Available from Nature Precedings (http://hdl.handle.net/10101/npre.2009.3886.1), 2009.



What is a Virus?

Many human diseases, including the cold and the flu, are caused by viruses, made up mostly of a coat made of protein that surrounds either DNA or RNA.

How do they multiply?

Cells multiply using either mitosis or meiosis, processes which require much more complex machinery than viruses contain.  So, how do they make more viruses?  A virus reaches a cell and injects its own DNA or RNA into the cell, where it can then use the components of that host cell to make more viral genetic material.  In the lytic cycle of the virus, the viral genetic material is then translated and used to create lots of new viruses, which all eventually break out of the host cell, killing it.  Some viruses avoid killing the host cell by extending a part of the cell’s membrane and pinching off.  Then, those viruses can go off and infect more host cells, creating even more viruses.

Some viruses choose not to immediately break out of the host cell.  Instead, they insert their genetic material into the material of the host cell, which then gets passed onto all the offspring (or daughters) of that cell.  This makes more and more viral genetic material, which can then all at once make lots of viruses and break out of cells in large numbers.  This is called the lysogenic cycle.

Viruses are so different from all other “life” (and I put life in quotes because it is  up for debate whether viruses are actually living) that many scientists have found the following question very interesting: how did viruses evolve?  Did they evolve from bacteria and animals, or did they evolve completely separately?  We’ll look at the hypotheses to this question in the next post!

Works Cited