Albert-László Barabási | Viruses and Fads
Tratto da Albert-László Barabási, Linked. The new science of networks, Perseus Books Group, 2002
Gaetan Dugas had everything he could wish for, and he knew it. With a wardrobe culled from the trendiest shops in London and Paris, and a well-built but not muscle-bound body, he was a standout in any club. He had only to proposition in his charming French Canadian accent and he could seduce anybody he wanted. “I am the prettiest,” he used to say, and his friends agreed. Lately, however, he had been avoiding the popular discos and the hottest nightclubs. His preference had shifted to the steamy mirrors and heavy air of the Bay Area bathhouses. Despite his narcissistic perfection, Dugas began developing a taste for the darker houses that revealed little of his mesmerizing physical characteristics. The long hallways of shady cubicles now made him most comfortable. One night in 1982, as he prepared to exit one of those cubicles, he switched on the lights, slowly turned towards the man he had first met a few minutes before and immediately had sex with, and pointed to the purplish spots and bumps on his face. “I’ve got gay cancer,” he said. “I’m going to die and so are you.”
Dugas, once a French Canadian flight attendant, is often called Patient Zero of the AIDS epidemic. This is not because he was the first to be diagnosed with the disease but rather because at least 40 of the 248 people diagnosed with AIDS by April 1982 had either had sex with him or with someone who had. He was at the center of an emerging complex sexual network among gay men, a web anchored between the East and West Coasts of North America, spanning San Francisco, New York, Florida, and Los Angeles.
His central role is far from coincidental. Dugas was one of the first gay men in North America to be diagnosed with Kaposi’s sarcoma. By 1983 it was increasingly clear that the illness Dugas and several hundred other gay men came down with had some infectious source, and Dugas was again one of the first patients to be told that. But he continued to insist that he had skin cancer only. As cancer is not contagious, for many years he never admitted to himself that he would pose any risk to his sexual partners. Proud of his attractiveness and sexual conquests, he later confided to health care workers the intimate details of his sexual habits. He figured that he had about 250 sexual partners a year. While some estimates put the total number of his partners as high as 20,000, his decade of promiscuity in gay clubs and bathhouses clearly put him in sexual contact with at least 2,500 people.
It is not clear whether Dugas brought AIDS to North America. He traveled frequently to France, where some of the earliest cases have been discovered, but we will never know for sure if he was infected there or in the United States. What we do know, however, is that many of the earliest cases in North America were linked to him, placing him at the root of an epidemic that by now has killed almost 20 million people.
Dugas played an important role in turning the AIDS epidemic in a few short years from an obscure and rare “gay cancer” to a North American health care crisis. He is a terrifying example of the failure of classical epidemic models and evidence of the power of hubs in our highly mobile and connected society. Indeed, when it comes to viruses and epidemics, hubs make a deadly difference.
Like millions of other Americans, Mike Collins saw a picture of the controversial Florida butterfly ballot on TV the night of November 8, 2000. “Jeez, how could they not follow the arrows to the dots?” was his first reaction. “Maybe I’ll draw something up that will make it more confusing.” Collins, a twenty-six-year-old municipal water board engineer and amateur cartoonist from Elmira, New York, drew a cartoon of four lines and e-mailed it to thirty friends. The next day was his birthday and the day his sister gave birth to a daughter, so he was out all day. When he returned home that evening, a huge present awaited: 17,000 new hits on his Webpage and several hundred e-mails. While he was away his cartoon perfectly expressing everybody’s frustration with the 2000 presidential election had circled the globe. Anybody who spotted it wanted a copy. Newspapers and Websites from the United States to Japan were bombarding him with requests for permission to publish. In a few hours he went from “Mike” to an instant celebrity, with girls hitting on him and parents wanting to fix him up with their daughters. While the election debate eventually died down, Collins’s signature drawing became perhaps the most recognized cartoon of the decade, popping up on everything from T-shirts, which he sells through his Website, to greeting cards. It is probably the single most enduring image of the ill-fated 2000 Florida ballot.
Mike Collins’s instant path to celebrity is a replay of the classic American dream. But what is unusual is the speed with which it took place. A few decades ago it was impossible to gain worldwide fame literally overnight, even in America. Something has changed. We normally credit the Internet with these changes, and certainly the medium nurtures and spreads fame. But an explanation based entirely on technology is not sufficient. We are witnessing something qualitatively new, something that is allowing ideas and fads to reach everybody with the speed of light.
Gaetan Dugas and Mike Collins ostensibly have little in common. One spread a cruel disease; the other was a small-town amateur who hit it big with a clever idea. AIDS took a decade to escape its African source and permeate the world, passing from partner to partner primarily through sexual intercourse. Collins’s cartoon exploded overnight, circling the world via clicks and e-mails. Nevertheless, they have something important in common. They are both examples of diffusion in a complex network. AIDS spread following the links of the intricate sexual network of the 1980s, aided by the emergence of a highly sexually active gay culture. The ballot cartoon spread instantly through the entangled network of computers, aided by our ability to reach our friends through e-mail. Both, however, followed the same fundamental laws governing the spread of fads, ideas, and epidemics in complex networks. These laws have been intensively researched by marketing executives trying to figure out how to get their product in your pocket; by sociologists seeking to understand fads, fashions, and riots; by political scientists tracking voting patterns and political fortunes; by doctors and epidemiologist hoping to curb everything from the Ebola virus to the recurring early winter flu; by teenagers writing computer viruses aiming to destroy all of Microsoft’s products overnight; and by system managers determined to prevent viruses from doing just that. These laws were believed to be universal, as indeed they are. But our emerging knowledge about complex networks prompts us to see them from a new perspective.
Whereas in 1933 hybrid corn was cultivated on only 40,000 acres across North America, by 1939 it had reached 24 million acres, one fourth of the nation’s corn acreage. It revolutionized and reshaped American farming, eventually sweeping the whole of Midwestern agriculture in less than ten years. Iowa was particularly quick to adopt it. Though the new seed was not available before 1929, by 1939 as much as 75 percent of Iowa’s corn acreage was devoted to hybrid. This rapid expansion, combined with the farmers’ good bookkeeping, offered the first opportunity for researching how innovations spread. Bryce Ryan and Neal C. Cross from Iowa State College embarked on this study in 1943.
Before adopting any innovation, we normally ask ourselves several simple questions: Should I spend time evaluating the new product? Should I spend money on it? How do I know that it will work for me as promised? The questions were no different for the hybrid. To adopt it, farmers had to invest in the new seeds to replace those they already had. Though the switch promised a larger, heartier yield, there was little guarantee that the extra benefits would offset the initial investment. The risk was particularly relevant for the first adopters. Nevertheless, the hybrid took root in Iowa thanks to a small group of people willing to take risks. Today we call such people innovators.
All of us know some innovators. They are our acquaintances who jumped to buy the Apple Newton handheld computer, only to discover that the technology did not live up to its promises. A few years later they were the first to scribble characters onto the gray screen of the first Palm Pilots, this time jump-starting the handheld revolution. They are the teens who pick up on new trends before they become mainstream, the artists and intellectuals who nurture ideas well before they reach the rest of us through books, movies, and magazines. In Iowa they were the farmers for whom talking to the sales reps and reading the documentation was enough to persuade them to try the new seed.
Ryan and Cross found that plotting the number of farmers adopting the seed each year yields a curve that increases rapidly until it reaches a maximum, then drops equally fast afterwards. It is a bell curve. If a new product passes the crucial test of the innovators, based on their recommendation, the early adopters will pick it up. They are followed by the numerous early majority, until half of the people who will eventually adopt are already in the game. Beyond this point the number of new adopters starts decreasing, the innovation attracting those who are slow to make a decision but are persuaded by the overwhelming evidence in its favor. This late majority is made up of farmers who have seen half of the fields surrounding them turn over to the hybrid and are finally convinced. The curve inevitably ends with the few laggards, who join only after they have become a clear minority.
The bell curve observed by Ryan and Cross is not unique to Iowa farmers. It characterizes the spread of most innovations, offering an excellent tool by which marketing and planning experts foresee demand for a new product. However, it fails to answer something that everybody from epidemiologists to CEOs wants to know these days: What, if any, role is played by the social network in the spread of a virus or an innovation?
In 1954 Elihu Katz, a researcher in the Bureau of Applied Social Research at Columbia University, circulated a proposal to study the effect of social ties on behavior. It so happened that the director of market research for the pharmaceutical giant Pfizer was a Columbia alumnus. Keen to understand how physicians adopt a new drug, he offered Katz and his two colleagues, James Coleman and Herbert Menzel, $40,000 to track the spread of tetracycline, a powerful antibiotic introduced in the mid-1950s.
Coleman, Katz, and Menzel interviewed 125 doctors from a small Illinois town, asking them to list separately the three doctors with whom they most often discussed medical practices, three from whom they sought advice regarding a medicine, and three whom they considered friends. These lists allowed them to reconstruct the complex network of social ties and influence within the medical community.
The results indicated significant differences among doctors. A few were named by a large fraction of their colleagues as playing an important role in their day-to-day decisions. They were the hubs of the medical community. The majority, however, played a much smaller role. When it came to the spread of tetracycline, the doctors named by three or more other doctors as friends were three times more likely to adopt the new drug than those who had not been named by anybody.
Using prescription records from pharmacies, the researchers could follow the spread of the drug’s use along the social links. It turned out that the early adopters and early majority were predominantly doctors with numerous social links. These highly connected doctors were more likely to be in touch with innovators, thus learning about the new drug more quickly. Once adopted by these doctors, the drug spread from these hubs to their less connected colleagues, who formed the late majority. Finally came the laggards, doctors who resisted adopting the new drug until the very end.
The Pfizer study demonstrated that innovations spread from innovators to hubs. The hubs in turn send the information out along their numerous links, reaching most people within a given social or professional network. Hubs, the integral components of scale-free networks, are the statistically rare, highly connected individuals who keep social networks together. In the AIDS epidemic, the gay flight attendant Gaetan Dugas clearly qualified as a major hub. And the well-traveled Paul, with his extended circle of friends and followers, was one of the most influential hubs of early Christianity.
Hubs, often referred to in marketing as “opinion leaders,” “power users,” or “influencers,” are individuals who communicate with more people about a certain product than does the average person. With their numerous social contacts, they are among the first to notice and use the experience of the innovators. Though not necessarily innovators themselves, their conversion is the key to launching an idea or an innovation. If the hubs resist a product, they form such an impenetrable and influential wall that the innovation can only fail. If they accept it, they influence a very large number of people.
Sociologists and marketing experts are fully aware of these opinion leaders. But until recently they treated hubs as unique phenomena, with little understanding of why and how many of them are out there. Social network models did not support the existence of hubs. The framework offered by scale-free networks has for the first time provided the legitimacy hubs deserve. As we will see, hubs are changing nearly everything we know regarding the spread of ideas, innovations, and viruses.
Unveiled in 1993 as the brainchild of John Sculley, Apple’s Pepsi-bred CEO, the much promoted handheld computer Newton never made it. Nevertheless, it started a revolution.
Today there are millions of pocket-sized devices in circulation. Despite this enormous number, many believe that we are still at the beginning of the bell curve for market penetration. The problem for Apple is that none of these handy devices is a Newton. Palm, Handspring, various Pocket PCs, and their countless cousins have chewed up the Apple vision, offering powerful proof that the first mover does not always have the advantage. Newton pulled together many new technologies in a “first-ever” device, promising a dream come true. It wasn’t that easy, however. The nightmare started with a series of bad reviews ridiculing Newton’s handwriting recognition capabilities. Critics pointed out that it voraciously consumed batteries after a mere twenty minutes of use. Disappointment followed disappointment, and sales of the MessagePad, the redesigned version of Newton, peaked at a dismal 85,000 in 1995. The product was discontinued three years later in an attempt to curtail losses after Steve Jobs was reinstalled as Apple’s interim CEO.
The failure of the Newton handheld and many other products begs for an explanation. Why do some inventions, rumors, and viruses take over the globe, while others diffuse only partially or simply disappear? Why and how are losers different from winners? Clearly advertisement is not a sufficient explanation. After all, Newton failed despite Apple’s enormous marketing machine. The billion-dollar question is, how does one spot the rotten apples?
Aiming to explain the disappearance of some fads and viruses and the spread of others, social scientists and epidemiologists developed a very useful tool called the threshold model. We all differ in our willingness to accept innovation. In general, with sufficient positive evidence, each of us can be convinced to adopt a new idea. However, the level of acceptable testimony differs from one person to another. Acknowledging our differences, diffusion models assign a threshold to each individual, quantifying the likelihood that he or she will adopt a given innovation. For example, those who bought the Newton right after its release had close to a zero threshold for handheld devices. Before swiping our credit cards, however, most of us want to see a new product working; thus most of us display a higher threshold.
Despite significant differences in purpose and detail, all diffusion models predict the same phenomenon: Each innovation has a well-defined spreading rate, representing the likelihood that it will be adopted by a person introduced to it. For example, the spreading rate incorporates the likelihood that after being shown a new handheld, you will be prompted to buy it. Yet knowing the spreading rate alone is not sufficient to decide the fate of an innovation. For that we must calculate the critical threshold, a quantity determined by the properties of the network in which the innovation spreads. If the spreading rate of the innovation is less than the critical threshold, it will die out shortly. If it is over the threshold, however, then the number of people adopting it will increase exponentially until everybody who could use it does.
Recognizing that passing a critical threshold is the prerequisite for the spread of fads and viruses was probably the most important conceptual advance in understanding spreading and diffusion. Currently the critical threshold is part of every diffusion theory. Epidemiologists work with it when they model the probability that a new infection will turn into an epidemic, as the AIDS virus did. Marketing textbooks talk about it when estimating the likelihood that a product will make it in the marketplace or to understand why some never do. Sociologists use it to explain the spread of birth control practices among women. Political science exploits it to explain the life cycle of parties and movements or to model the likelihood that peaceful demonstrations will turn into riots.
For decades, a simple but powerful paradigm dominated our treatment of diffusion problems. If we wanted to estimate the probability that an innovation would spread, we needed only to know its spreading rate and the critical threshold it faced. Nobody questioned this paradigm. Recently, however, we have learned that some viruses and innovations are oblivious to it.
Launched from the Philippines, Love Bug, the most damaging computer virus ever, reached every computer-literate corner of the world in hours. On May 8, 2000, the sun rose on continent after continent to the fall of computers, thousands at a time—a global domino effect sweeping from east to west. Computer security experts had hardly begun assisting the first victims in Hong Kong when system administrators of a major German newspaper watched in horror as the virus consumed 2,000 digital photographs. Spreading to Belgium, it handicapped ATM machines, denying customers vital currency. London, waking an hour later, witnessed Parliament’s shutdown. Before moving on from Europe, as many as 70 percent of Swedish, German, and Dutch computers were in ruins. The carnage spread to the United States, where it sneaked into the Capitol building’s computers in Washington D.C., infected 80 percent of all federal agencies, including the defense and state departments, and shut down the Bush presidential campaign’s e-mail communications.
Love Bug, causing over $10 billion in damage from 45 million destroyed computers worldwide, was a well-engineered psychological booby trap that nobody could resist. How could you not immediately open a message entitled LOVE-LETTER-FOR-YOU? If you did yield to the temptation, the activated virus then erased a series of documents from your hard drive, with a particular appetite for jpeg and mp3 files that encode digital pictures and music. Next it looked for a Microsoft Outlook Express e-mail program. If it did find one, it sent new copies of the love letter to all your friends and acquaintances whose e-mail addresses you stored there.
The carnage slowed when Richard Cheng and Maricel Soriano, from the Philippines, created an antidote, a program that could immunize a computer against the bug. What is amazing about Love Bug, however, is that despite the widely and freely available antidote, the virus still exists. According to Virus Bulletin, an online resource that collects virus occurrences, Love Bug was still the seventh most active virus in April 2001, a year after the release of the program that detects and deactivates it. I received a copy as late as July 2001.
It is tempting to speculate that perhaps Love Bug is so virulent that it is virtually impossible to eradicate. But its continued presence cannot be explained by virulence alone. This was the conclusion of two physicists, Romualdo Pastor-Satorras and Alessandro Vespignani, who showed that in contrast to the solid predictions of threshold models, in real networks high virulence does not guarantee a virus’s spread.
The unique northern Italian town of Trieste, with its mixed and tumultuous historical heritage, is home to the prestigious International Center for Theoretical Physics. Founded and directed for decades by the Nobel prizewinning Pakistani physicist Abdus Salam, it offers a safe and intellectually challenging haven for Third World physicists, bringing them in contact with their colleagues from around the world. Romualdo Pastor-Satorras, a Spanish physicist, finished a two-year postdoctoral position at the center in 1999 before returning to Barcelona to assume a professorship. In the summer of 2000 he went back to Trieste for a two-month visit, planning to finish up several overdue projects that he and his former mentor Alessandro Vespignani had initiated during his earlier stay. While compiling the bibliography of a new manuscript, they stumbled across a computer science paper titled Open Problems in Computer Virus Research by Steve R. White, a computer virus expert from IBM. The paper argued that biologically inspired epidemic models do not properly describe the spread of Love Bug and other computer viruses.
Intrigued by this observation, the researchers decided to dissect the problem more carefully. Using the records of the Virus Bulletin, an online resource for computer virus prevention, they determined the likelihood that a virus would still exist several months after its first occurrence. The results were astonishing: The characteristic life of most viruses ranges between six and fourteen months. That is, viruses are infecting computers more than a year after their first occurrence and supposed eradication. As Pastor-Satorras and Vespignani put it, “these characteristic times are impressively large if compared with the interval in which antivirus software is available on the market (usually within days or weeks after the first incident report).” Like the Mummy, viruses are awakened over and over again from their sarcophagi, unable to rest.
Researchers normally use various versions of the standard threshold models to describe how computer viruses spread. In these models each computer can be either healthy or infected. During each time interval, a healthy computer can be infected by the virus if it is in contact with an already infected computer. As soon as an infected computer is cured, it becomes susceptible to infection again. Assuming that computers are connected randomly to each other, this model confirms the classical scenario of virus spread: A virulent virus, with contagiousness larger than a critical threshold, reaches most computers. In contrast, if the virus’s virulence is less than the threshold, the number of newly infected computers decreases quickly, until the virus dies out.
By August 2000 Pastor-Satorras and Vespignani had concluded that White was right: Computer viruses defy the predictions of the classical epidemic models. The source of this discrepancy, however, remained unclear to them. As luck would have it, my research group’s paper on the Internet’s Achilles’ heel was featured on the cover of Nature that very week. Reading it, they suddenly found the missing piece. On the Internet, computers are not connected to each other randomly. Rather, the underlying network has a scale-free topology. Thus, computer viruses should be modeled on a scale-free network instead of the random one used in all previous studies. Pastor-Satorras and Vespignani rushed to do just that, investigating for the first time diffusion in a realistic scale-free network. The results were highly surprising: In scale-free networks the epidemic threshold miraculously vanished! That is, even if a virus is not very contagious, it spreads and persists. Defying all wisdom accumulated during five decades of diffusion studies, viruses traveling in scale-free networks do not appear to notice any threshold. They are practically unstoppable.
The source of this highly unexpected behavior lies in the uneven topology of the Internet. Scale-free networks are dominated by hubs. Because each hub is linked to a very large number of other computers, it has a high chance of being infected by one of them. Once infected, a hub can pass the virus to all the other computers it is linked to. Thus, highly linked hubs offer a unique means by which viruses persist and spread. Whereas virulent species quickly reach all nodes in any network, in a scale-free environment their mildly contagious counterparts also have a good chance for survival.
These results are not limited to computer viruses. The models used by Pastor-Satorras and Vespignani, with some modifications, offer a simple description of the spread of ideas, innovations, and new products and the diffusion of infectious diseases. In a rough approximation, they capture the process that aids the spread of religions as well: Paul, a highly connected and mobile hub, helped the beliefs of early Christianity reach as many people as possible. Ideas and innovations diffuse from person to person along the links of the social web. Since the social network appears to have a scale-free topology, the anomalies observed in computer viruses should be present in these systems as well.
Of the hundreds of social links each of us has, only a few are intimate enough to transmit a sexual disease. Therefore, AIDS advances on a very sparse subnet of our highly interlinked social web. Add to this the disease’s relatively low contagiousness, and you find that the epidemic should have slowed and died out by now. Despite the odds, however, AIDS has already infected approximately 50 million people, and the numbers continue to rise. It is tempting to take the Trieste study at face value and attribute the rapid spread of the AIDS epidemic to the scale-free topology of the social network. But because not all social ties represent sexually active links, we need to ask, what is the topology of the sexual network that carries this deadly disease?
During a late November day in 2000, Carina Mood Roman, a Ph.D. student in sociology at the University of Stockholm, Sweden, was trying to make sense of an extremely skewed error plot she received while working on a class assignment. She had set out to predict the number of sexual partners of a group of Swedish subjects. Sexual mores in Sweden, one of the first countries to give legal rights to unmarried couples living together, are comparatively liberal. Sweden also prides itself on its remarkable and expansive health coverage and social services. As AIDS started to take its toll in northern Europe, Swedish researchers embarked on an extensive survey of sexual contacts, hoping to find the means to slow the epidemic.
Obtaining a map of the sex web, which links people via sexual relationships, is simply impossible. Would you be willing to give me the name of everybody with whom you have been intimately involved, knowing that I would then have to contact them all to sketch out their sexual links as well? Fortunately, we do not need a complete map of the sex web to decide whether it is scale-free or random. We need only measure the degree distribution by asking a representative subset of society how many sexual partners each has had. Not requiring our subjects to reveal the identity of their partners, we suddenly face a less challenging job. In 1996 Swedish scientists conducted thousands of interviews with a random sample of 4,781 individuals aged eighteen to seventy-four, collecting information regarding their sexual habits. With a response rate of 59 percent, they obtained the number of links for 2,810 nodes in the Swedish sex web.
Today students often are given the collected data to test various statistical methods. Roman had a copy of the data when she turned to her roommate, Fredrik Liljeros, for help in interpreting her error plot. Early in his sociology studies Liljeros was so favorably impressed during a series of lectures on mathematical sociology that he had devoted himself to the field, focusing on the evolution of social organizations. This research exposed him to a wide range of mathematical tools and concepts, including self-organization and power laws. Though typically Nordic in mien, when it comes to his passion, research, the twenty-something Liljeros does not share the stereotypical calm and reserved tone of his compatriots. “This looks like a power law!” he screamed to his roommate after spotting the plot on Roman’s screen. Instead of helping her with her assignment, he asked for the data, and proceeded to verify his hunch. Next he e-mailed a copy to Luis Amaral at Boston University, with whom he had previously collaborated. Amaral had recently turned his attention to complex networks, authoring several seminal papers on modeling scale-free topology. He immediately saw that the data Liljeros e-mailed him contained the information key to answering our earlier question: What is the topology of the sex web?
Each study on our sexual habits faces severe memory biases: Men seem to remember more sexual partners than women do. Therefore, the subjects of the Swedish study first were asked to reveal how many sexual partners they’d had in the previous year only, in hopes the answer would be somewhat accurate. It was clear that their answers as to the number of partners they remembered having in their lifetime would be strongly affected by failing memories and expectations. Despite these potential biases, the results were consistent. They indicated that the majority of respondents had between one and ten sexual partners during their lifetime. Some, however, had dozens or more. A few had several hundred. The distribution followed a power law, regardless of whether one examined the one-year interval, considered all sexual partners, or focused only on either males or females. Taken together, the data offered striking evidence that the network of our sexual relationships has a scale-free topology, a conclusion reinforced by a subsequent study focusing on the American population.
Gaetan Dugas would seemingly hold the record with 250 sexual partners a year. But Wilt Chamberlain’s claim that he’d had sex with a staggering 20,000 women clearly surpassed that measure. “Yes, that’s correct, twenty thousand different ladies,” he wrote. “At my age, that equals to having sex with 1.2 woman a day, every day, since I was fifteen years old.” The NBA Hall of Famer’s macho accounting made him a lighting rod for criticism by those offended by his promiscuity. The Stockholm-Boston collaboration, however, found that he is not that unique. The scale-free topology implies that, though most people have only a few sexual links, the web of sexual contacts is held together by a hierarchy of highly connected hubs. They are the Wilt Chamberlains and the Gaetan Dugas, collecting an astounding number of sexual partners.
In light of these results, the Trieste predictions offer a new perspective on the AIDS epidemic. The deadly virus must have followed the route already spotted in the spread of innovation and computer viruses: Hubs are among the first infected thanks to their numerous sexual contacts. Once infected, they quickly infect hundreds of others. If our sex web formed a homogeneous, random network, AIDS might have died out long ago. The scale-free topology at AIDS’s disposal allowed the virus to spread and persist.
When in 1997 we saw the first decline of AIDS deaths in the United States, we thought that the worst was over. We were wrong. Currently, every day 15,000 people are infected worldwide. The majority of them will die of the disease within a decade. If you are a fifteen-year-old in Botswana today, your risk of contracting and dying of AIDS during your lifetime is almost 90 percent. In fact we would be hard-pressed to pick a teenager from this or several other sub-Saharan countries who sooner or later will not be killed by the pandemic. This is despite the fact that several relatively effective treatments for AIDS are already on the market. To be sure, none of these treatments is a cure for the disease. But each does render it a chronic illness with which most patients can live almost indefinitely. The biggest problem is that these $15,000-a-year treatments are out of financial reach for most countries outside Europe and North America.
The crisis faced by Africa is the most severe. The problem is not only that most African countries cannot pay for the drugs. Even if drug prices were to drop, these nations lack the infrastructure to distribute and administer the treatment. At twenty, the AIDS epidemic has become a macabre celebrity. Through demonstrations and the aid of high-profile backers ranging from Bill Gates to any number of pop starts, AIDS activism has captured the spotlight, forcing the big pharmaceutical companies to deliver drugs at cost to poor nations. This is only the first step, however. It is clear that, despite the several-billion-dollars-strong international fund, there will not be enough money to buy treatments for everyone, even at cost. So who gets them?
Whereas the early spread of AIDS was attributed primarily to homosexual sex, today heterosexual sex is the leading means of transmission. As we’ve established, hubs play a key role in these processes. Their unique role suggests a bold but cruel solution: As long as resources are finite we should treat only the hubs. That is, when a treatment exists but there is not enough money to offer it to everybody who needs it, we should primarily give it to the hubs. This was the conclusion reached in two recent studies, one by Pastor-Satorras and Vespignani, the other by Zoltán Dezs?, a graduate student in my research group. The results indicate that if we offer treatment for all nodes with a degree larger than a preselected value, no matter where we set the limit the epidemic threshold becomes finite. The more hubs we treat the larger the epidemic threshold and, thus, the higher the chance that the virus will die out.
The problem is that we do not know for sure who the hubs are. Therefore, Zoltán Dezs? and I set out to address a more difficult question. While we do not know how to identify the hubs with a high degree of confidence, decades of research have produced numerous sociological methods for identifying high-risk groups, as well as individuals most likely to be the source of the epidemic, in a given community. Social status, age, occupation, and many other factors each play a role. Therefore, with a certain probability, one can identify the hubs. Doubtless, many hubs will go undiscovered, while a few nonhubs will make the list. But we must ask whether such an imperfect method is useful. Since doing our best to identify the hubs is not enough, can we still restore the epidemic threshold? To answer this question we must assume that nodes are not treated randomly, but health organizations follow a biased policy that makes an individual with numerous sexual links more likely to be treated than those with only a few links. This stochastic approach allows us to compare those policies that are very effective in identifying and treating the highly connected nodes with those that distribute the treatment randomly. Zoltán Dezs? undertook this comparison and we were surprised by the results. To be sure, each policy that continued to distribute the treatments randomly continued to have zero threshold and failed to stop the virus. But any policy that displayed bias toward the more connected nodes, even a small bias, restored the finite epidemic threshold. That is, even if we are not successful in finding all hubs, by trying to do so we can lower the rate at which the disease spreads.
Any selective policy raises important ethical questions. Indeed, our results indicate that, faced with limited resources, we would end up rewarding promiscuity: The more sexual partners an individual has had, the greater her or his likelihood of being picked for treatment. The better we are at selecting and treating the promiscuous individuals, the fewer people will be affected by the disease. Are we prepared to abandon the less connected patients for the benefit of the population at large? Are we ready to offer drugs to the more connected poor prostitutes than to the wealthier but sexually less connected middle class?
There is a solution that makes such moral debates academic: a vaccine. Currently, the world spends a mere $350 million annually on AIDS vaccine research. That number pales in comparison to the $3 billion plus annually spent on AIDS drugs in America and Europe or to the billion-plus dollar price tag for a single fighter plane. As we continue wrestling with our priorities, my feeling is that in the meantime we should do everything it takes to stop the spread of the disease, even if it requires rewarding promiscuity.
Our understanding of hits and flops, epidemics and fads, has progressed considerably since the pioneering Iowa study. The last few decades have seen an incredible diversification of the subject. We have learned that studying the adoption of new crops can help us understand the spread of AIDS and the emergence of blockbusters. We have learned that, though randomness is involved in every diffusion process, the process follows laws that can be formulated in precise mathematical terms. And we have begun to understand the important role the social network plays in these processes.
Much has changed over the past five decades, however. The worldwide social network has imploded with the spread of high-speed communication devices, ranging from fax machines to e-mail, that bring and keep us together to a degree unprecedented in history. We feel a sense of urgency about understanding how this implosion affects the laws of diffusion. With the increasing threat of bioterrorism and with the steady spread of AIDS, there is a vital need to be able to predict and track deadly viruses in this increasingly mobile world, where infected individuals can hop on a plane and turn a local epidemic into a pandemic. In an increasingly computer-dependent world we have created a new breed of viruses that see no national boundaries. These cousins of Love Bug are more than mere nuisances. They represent a palpable threat to our security and way of life, easily capable of causing life-threatening emergencies. With their proliferation a new breed of epidemiologist has emerged, the computer security expert, who vigilantly monitors the health of our online universe.
Innovations and biological or computer viruses spread across inhomogeneous networks where hubs run the show. The implications of the Trieste study are that we are in for more surprises when it comes to how much we know about spreading and diffusion. I believe that the results obtained so far represent only the tip of the iceberg. Whereas spreading and diffusion have universal properties, individual systems have unique features that are often as important as some of the generic laws. We would be kidding ourselves if we believed that modeling computer viruses would give us a good picture of the AIDS epidemic. To be able to make detailed predictions on the disease’s spread, the models should include many details that are specific to the pandemic. That is still a distant dream. But understanding the fundamental laws that govern spreading and diffusion is the key prerequisite for success. The recent breakthroughs in these directions offer a strong impetus to revisit problems ranging from marketing to the spread of influenza and to critically inspect the inherent assumptions. As we follow this path, I am convinced that many more surprises and potential breakthroughs will surface.
The recent paradigm changes in diffusion and epidemics studies were possible thanks to the wealth of data offered by the Internet, one of the most charted networks. The Internet helped us discover scale-free networks in the first place. The viruses navigating it provided the insights and the necessary data that made the Trieste study possible, uncovering the threshold-free nature of some epidemics. The understanding they offered has prompted us to revisit everything from fads to the AIDS pandemic. Let us step back now and take a look at the entangled medium that made all these discoveries possible and chart the network behind it.