Simply Complexity (28 page)

The work of Mike Spagat and Jorge Restrepo tells us an enormous amount about the character of wars. However, as anyone on the ground knows, it would be even more useful to know something about the pattern of attacks in time – in particular on a daily scale. Judging from the news from Iraq that we hear, it certainly doesn’t seem like there is any pattern. Monday there might be two attacks in Baghdad, with five casualties in one attack and thirty in the other. Tuesday, there might be one attack in Basra with ten casualties. And so it goes on. So is there any method at all underlying this madness?

It turns out that there is. Sean Gourley and Juan Camilo Bohorquez, working with Mike Spagat and Jorge Restrepo, took the output time-series from this Complex System – in particular, they took the list of the number of attacks per day in Iraq – and started looking for patterns. Unfortunately most statistical tests require lots of data – and the Iraq war is a one-off event, so it only has one set of data. The researchers were therefore faced with a problem which is analogous to the following situation. Imagine someone has told you that they have shuffled a deck of cards. You don’t believe them, and so you want to check. If they have indeed shuffled them, then the sequence in which the cards appear should look random. But what does this mean? It means that the actual sequence of cards should look similar to a deck which has been thoroughly shuffled. Now let’s suppose that the sequence of cards in the deck represents the sequence of attacks-per-day in the Iraq war. In particular, each card represents a day, and the number of points on each card represents the number of attacks
on that day. For example, the three of clubs, hearts, diamonds or spades would correspond to a day with three attacks. Hence the total number of attacks that the insurgent force can produce over the length of the war, is equal to the total number of points in the deck. What Sean and Juan Camilo wanted to find out is if there is any specific order in which the insurgent force is performing these daily attacks – in other words, if there is any specific order in which the cards are arranged?

The card analogy gave Sean and Juan Camilo the clue as to how to proceed with the real Iraq data. They took the deck of cards – or equivalently the set of attacks-per-day – and shuffled them thoroughly. In doing so, they produced a “random Iraq war” in which the numbers of attacks on consecutive days are unrelated. They then repeated this process in order to obtain a large set of such random Iraq wars. Since this analysis of the number of events doesn’t involve the size of each event, each of these random wars has exactly the same distribution of casualties as the actual Iraq war, i.e. it would produce exactly the same power-law as in
figure 9.3
and with the same slope. However, the order in which the attacks-per-day occurred would be different in each version. By repeating this procedure many times, they were able to get a picture of what the war in Iraq would be like if the sequence of daily attacks was random.

What they have found so far is remarkable. The actual sequence of daily attacks in Iraq shows more order than for a random war. In other words, there does indeed seem to be some systematic timing in the attacks and hence some forward planning by the insurgent groups – just as we would expect from a Complex System containing a collection of competitive, decision-making agents. Going further, they have been able to deduce the particular sequences of daily attacks which occur more often than expected, and those which occur less often than expected. What is even more surprising is that they find similar results for the case of Colombia. Needless to say, they are currently hard at work on further tests to uncover the full extent of the temporal patterns underlying such attacks.

Diseases represent a particularly dark side of Complexity. In particular, the most lethal diseases have managed to tap into the heart of what makes a Complex System so difficult to predict, manage and control – thereby outsmarting the body’s sophisticated, but ultimately limited, defense mechanisms. Cancer is a particularly powerful example. There may be many others, either lurking on the horizon or yet to be created.

While we as a Society are focused on fighting off old and new threats to our health, so too the world of the pathogen is also becoming more complex. Indeed, the natural process of evolution is continually working against us by allowing pathogens to mutate – with the possibility that any one of these new forms may have the ability to leapfrog over our body’s defenses, or resist our man-made medications.

Collections of potentially lethal pathogens, including viruses and bacteria, are continually interacting with us and our immune systems. In short, we are surrounded by natural-born killers. At the time of writing this book, avian or “bird” flu is on the increase. Indeed, most scientists believe that a global epidemic of deadly flu will strike the human population soon, and bird flu is the most likely trigger. In particular, there is one virus, H5N1, that causes avian flu and which is particularly worrying. Most experts believe
that the virus will soon adapt itself in such a way that it can spread easily among humans – probably in very much the same way that human flu and the common cold are spread.

Human flu shouldn’t be taken lightly either. In the U.S. the human flu season typically occurs between October and April and leads to about 10 percent of the population contracting the disease each year – in other words, millions of people. In addition some 30,000 people die from its complications each year. What makes influenza so difficult to prevent is that the viruses are always changing. Our immune systems can adapt gradually by producing new antibodies after exposure to a virus; however, if the virus mutates very quickly or dramatically most people’s bodies are effectively defenseless.

Even the common cold can prove more than a match for us. According to the major U.S. websites which deal with common-cold issues, the average American adult gets about three colds every year and the annual total for the U.S. is about 500 million colds. The common cold is the most frequently acquired illness in the U.S. and causes the loss of more than 100 million workdays and 20 million school days each year. It therefore costs the U.S. about $50 billion each year. This makes the common cold far more expensive than diseases such as asthma or even heart failure. Furthermore, the common cold can result from more than 100 different types of virus, each of which may have several strains. And the only reward for having been infected with one of these viruses is that we are briefly immune to re-infection by that same strain – but just that strain. As a result we can actually catch “a cold” over and over again, as any long-suffering parent of school-age children knows.

It has been estimated by U.S. government researchers that a superflu such as a human transmitted bird-flu would spread fastest among children of school age. It is thought that it would infect about 40 percent of them, and that this number would then decline with age. The overall health costs – neglecting the cost of
disruption of the economy – are estimated to be at least $180 billion for even a moderately bad outbreak. All such estimates, and hence contingency plans, are based on our current understanding of how the virus will spread around the community.

But how
do
such influenza-like viruses pass around a particular community? Most theories of how transmissible diseases pass among a population focus on treating the population as a large homogenous group in which everyone is treated equally. In particular, everyone has the same chance of receiving or passing on the virus. But clearly this cannot be right. If someone lives on a desert island with no outside contact they will be far less likely to either get or transmit a particular virus which happened to be at epidemic levels elsewhere on the planet. By contrast, a teacher in a school would have a far greater chance of picking up the virus.

The world’s population consists of a collection of objects – people – who are connected together in different ways. Many people have very strong connections with a certain subset of other people – for example, a teacher in a class of children. In other words, we tend to be organized into communities of one form or another and this will tend to dictate our chances of picking up and transmitting a virus. If our own particular community is isolated from any infected communities then the chances of someone in our community picking up the virus are relatively low. So the community structure – or network as discussed in
chapter 5
– is very important in determining how a virus passes. Given the fact that we are naturally organized into towns and countries of varying sizes and with varying levels of inter-connectedness, the way in which a potential killer virus such as bird-flu will pass across the planet is not at all obvious.

So policy makers face a fundamental problem regarding what to do in order to reduce the spread of a given disease. In particular, imagine that an unknown virus, or viruses, appears. What should be done at the level of each community in order to reduce the chances of it spreading? More specifically, given that public resources are always finite, how much effort should we spend on controlling the transmission
within
communities as opposed to the transmission
between
communities?

This is the question that Roberto Zarama and Juan Pablo Calderon at the Universidad de Los Andes in Bogota, Colombia, asked themselves. In particular, they wanted to carry out an experiment in which they could study the transmission of viruses within a population which was arranged into communities, and yet where there was contact between these communities. Without having to know the particular virus or its strains, they wondered if they could then deduce something about the effective connectivities between people within a given community, and then between communities, and therefore be able to say something about possible strategies to reduce or contain the virus. In addition, given the possible virulence of flu-like viruses among children, they wanted a large part of the study to focus upon children. For this reason they hit upon the idea of studying the common cold in a large school containing many classes.

There have been many studies of the common cold, although most of these have been in a single community such as a prison or a submarine. By contrast, what seems to be important in real-world situations involving flu-like viruses and superbugs is the competition between transmission within a community and transmission between communities.

Most social systems involve clusters or “communities” within which people have many interactions. Interactions between communities tend to be less strong, or less frequent, but nonetheless do still exist. Unfortunately, most theoretical models of disease transmission tend to ignore such community structure since it makes the analysis too complicated. Roberto and his colleagues came up with the idea of carrying out the experiment in a school since a school contains natural communities in the form of classes. In other words, children interact with other children in their own class – what we could call intra-class interactions – and then at recess will interact with children in different classes – what we could call inter-class interactions. These interactions will also involve teachers, and the teachers themselves interact at recess.

So they went ahead and contacted the school, Colegio Nueva Granada, a U.S.-run school high up in the Andes in Bogota, Colombia. The principals, administration and teachers – in particular Dr. Barry McCombs, Dr. Barry Gilman, Ms. Natalia Hernandez, and science teacher Anne Gregory – were all extremely supportive and helped organize the infrastructure for this school-wide project. There are several important factors that make the resulting study that they did unique in scientific terms:

(1) The Colegio Nueva Granada is one of the largest overseas U.S.-run schools in the world, with a population of close to two thousand and with kids from the ages of four to eighteen. Hence it covers a wide age-range. It is also a relatively tight-knit community, which means that siblings tend to attend the same school, and kids and parents tend to mix with each other out of school hours. This means that it is also a relatively isolated system in that anyone who catches a cold during the school year will probably have caught it from someone else in the school. This is not always the case, of course, but it should happen fairly frequently.

(2) Since the school sits close to the equator, it effectively experiences no seasons. Hence the researchers could, to a good first approximation, ignore the possible effects of seasonality which tend to plague such epidemiology studies elsewhere.

(3) The younger kids are organized into classes, and hence would be expected to interact more frequently with classmates than with children in other classes. By contrast, the older kids are more strongly mixed because of the lack of such a rigid classroom structure higher up in the school. There is therefore a natural community structure – yet just like the real world, it is non-trivial in that the communities are not all of the same type or size, nor do they have the same degree of connectedness (i.e. connectivity).

(4) Since a cold typically lasts for about one week, the process of measuring who has a cold only needs to be carried out once a week. In other words, the kids can be asked once a week whether they have a cold or not, and this should then be often enough to track the spread of the cold. Now it might seem that this is a minor detail – but it isn’t. Teachers are busy people and typically have a million and one other things that they have to deal with in any
given week. Given the fact that the researchers could not afford to have any missing weeks in the data collected, this feature was crucial for ensuring that the study could be implemented successfully over a long period of time.