Monday, January 25, 2010

Transmission of ideas, fads and diseases

As we learn from the previous posts, real networks are scale-free networks, and there is much similarities between different scale free networks, however, by studying some of them, we could model the others.

Before adopting any innovation, we normally ask ourselves several questions: Should I spend time evaluating the new product? Should I spend money on it? How would I know it would work for me as promised? As there were little guarantee that the extra benefits would be worth it, the first adopters still took the risks, and this group are called the innovators.

All of us know some innovators. They are the first ones who buy the Android Phones, and drive the new hybrid cars. 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. If the hubs resist a product, they form such an impedance that even the best innovations fail, however if the hubs accept it, they influence a large number of people. These hubs or -- opinion leaders are nearly changing everything we know regarding the spread of ideas, innovations, and virtues.

Threshold model

To explain the disappearance of some fads and virtues, and the spread of others, the threshold model is developed. The speed at which the likelihood that it will be adopted by a person introduced to it is not the only factor that determine whether or not people will adopt it. There is a threshold -- a critical number of people that is required to adopt it before the innovation spreads, and the number of people adopting it will increase exponentially until everybody who could use it does.

Understanding this phenomena is an important conceptual advance in understanding spreading and diffusions. Epidemiologists work with it when they model the probability that a new infection will run into an epidemic, as the AIDS virus did. Marketing textbooks talk about it when estimating the likelihood a product will make it in the marketplace or understand why some never do. Sociologists use it to explain the spread of birth control practices among women.

This simple paradigm dominated our treatment of diffusion problem. 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, but we have learnt that some viruses and innovations are oblivious to it.

Of the hundred of social links each of us have, 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. With the relatively low contagiousness, you should find the epidemic should have died out by now. Despite the odds, however, AIDS has already infected 50 million people, and the numbers continue to rise. To understand the spread of the disease better, one would need a map of the sex web, but this is simply impossible. Hardly anyone would give out the names of everybody with whom they had sex with in the past.

Despite the fact that there are several effective treatments for AIDS, there are still lots of people infected worldwide. The crisis faced by Africa is most severe. The problem is not only that most African countries cannot pay for the drug. Even if they drug prices were to drop, these nations lack the infrastructure to distribute and administer the treatment.

The early spread of AIDS were attributed by mainly homosexual sex, today heterosexual sex is the leading means of transmission. As we've learnt that hubs play a key role in spreading AIDS, as long as resource is finite, we should treat the hubs, before the others, but the problem is often not as simple as many other factors play a role. Doubtless, many hubs will go undiscovered and a few nonhubs will make the list. Furthermore, any selective process will raise an ethical question: "Are we rewarding the promiscuous?" Are we ready to offer drugs to the more connected poor prostitute than to the wealthier but sexually less connected middle class?

Currently, the world spends US$350 million on AIDS vaccine research and more than US$3 billion on AIDS drugs in America and Europe.

Though networks can be modeled after well documented spread of diseases, there are still many unpredictable differences and factors which are hard to model in the real world. The concept is similar and it can help us understand the diffusions through hubs, and know is half the battle won.

-- Robin Low

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