The importance of an airport can be measured in two ways. First, an airport can be measured by its size, and by the number and the size of the airplanes that take off or land, or even by the number of people that travel to and from the airport. A less tangible way of measuring this, however, is by the number of connections a given airport has with other airports. A group of Brazilian, Swiss and Israeli physicists have proposed that this approach be adjusted to de-concentrate the activities of airports and to reduce damages in the case of malicious attacks by hackers on computer networks that guide the movements of millions of people every day.
The equations of the physicists from the Federal University of Ceará (UFC), the Polytechnic School in Zurich, Switzerland, and Israel’s Bar-Ilan University re-design connections to decrease the importance of airport hubs. Thus, a direct flight from the city of Curitiba to the city of Fortaleza, without a stopover in the city of São Paulo, would suffer no changes in the case of a malicious attack on the computer networks at the airport in São Paulo.
Fewer connections, and therefore fewer airplanes and fewer people in transit make an airport less attractive for hackers who want to attack it and to cause as much damage as possible. “We imagine the terrorists’ thought processes before we start developing more efficient ways of protecting computer networks,” says José Soares de Andrade Jr., a researcher from UFC and one of the creators of this new approach.
This computer network protection strategy imitates the structure of an onion, a comparison that the physicists themselves adopted when using the expression onion-like networks to describe what they had done. More specifically, they proposed low-cost modifications in computer networks without modifying the previous number of connections. The insight was to change the geometry of the connections. This approach entails the re-designing of the connections, by creating a main core that represents a set of inter-connected nodes. These nodes are linked to other, less important nodes that represent the first inner layer of the structure. Like an onion, each of these layers of nodes is linked to a deeper layer, with higher average connectivity and to another outer layer with less connectivity.
In this approach, the equal elements are linked to each other: the node with the same degree of importance is connected to another equally important node without going through another node or point that is lower or higher on the hierarchy. “Minor adjustments in the connections can provide more protection for the entire network,” Andrade says. “If one of the more important nodes is attacked, there will always be a residual structure capable of maintaining the integrity and keeping the network in functioning mode, instead of the network disintegrating entirely.”
Normally, in the so-called complex networks, such as those used for commercial flights, or for the distribution of electric power, for the internet or social networks, each important connection, referred to as a node, is randomly connected to other important points and to many other less important points. “The simple network, in which each point connects with all the others, is efficient, but very expensive,” says Andrade. He says that the star-shaped network, where some points are highly connected and most of the other points are not, is a low-cost, albeit fragile, network. “We are proposing an intermediary approach that will maintain the number of connections and increase the robustness of the network through small changes, therefore, at a low cost.”
Christian Schneider, from Zurich, Andrade and other physicists applied this approach to the European electric power grid, comprising 1,811 electric power distribution points and 370 million users, and to an internet network with 1,098 providers and 6,089 connections. They suggest that the substitution of 5% of the connections could increase the protection of the electric power grid by 45% and of the internet network by 55%. Andrade said that he talked to engineers from the Companhia de Eletricidade do Ceará (Coelce), power company, to see how this strategy might also be useful in Brazil.
The physicists applied this mathematical focus to hinder the progress of epidemics. Two initial simulations – one involving an air transportation network with 3,666 airports and another one involving a network of friends with 1,461 students – indicated that it is possible to reduce people’s vulnerability to epidemics by means of slight adjustments to vaccination strategies.
Instead of following the standard procedure (vaccinating as many people as possible in all the places where the epidemic might be rampant), the physicists observed that they could increase the efficacy of immunization by as much as 55% in the airport network and by as much as 15% in the social network by giving priority to the places – or nodes – intensely used by people in transit. Some of them – such as airports – are obvious, but others are less so. This is the case of Vitória da Conquista, a city in the southwest of the State of Bahia with approximately 300 thousand inhabitants. The city is at the crossroads of a highway used by buses that travel to the Northeast and the Southeast of Brazil. Therefore, strategic action is needed to prevent epidemics from spreading throughout Brazil.
At USP’s School of Medicine, the teams led by Eduardo Massad, Marcelo Burattini and Francisco Antonio Bezerra Coutinho resorted to similar mathematical models to predict how dengue fever spreads and to propose strategies to deal with the dengue fever epidemic. One of the conclusions that they reached, based on a study conducted in Singapore, is that there is no need for a continuous effort to control the transmission of the disease; it would suffice to concentrate control actions one day every five weeks. The equations that listed the number of infected, recovered, or immune people, the number of mosquitoes susceptible to the virus, and the infected insects and eggs indicated that, once the epidemic occurs, the best thing to do is to kill the adult mosquitoes. However, eliminating the larvae and the breeding sites is essential to avoid dengue fever epidemics from recurring.
Schneider, C. M. et al. Mitigation of malicious attacks on networks. PNAS. v. 108, n. 10. Feb. 22, 2011.