Dynamical Network Design for Controlling Virus Spread
This Demonstration shows the dynamics of the spread of the SARS virus in Hong Kong's 18 districts when the optimal resources allocation is used. In the simulation, the color green represents an infection-free district, that is, one in which the number of infected people is smaller than one. For infected districts, shades of red are used to indicate the level of infection. Darker red means that there are more infected people in the region and lighter red means that fewer people are infected. The viewer can see that the virus is stopped very quickly using the optimal design: the regions quickly turn green regardless of the initial conditions.
The viewer should note that the initial number of infectives in each district can be set using the sliders on the left side of the screen.
This Demonstration illustrates the dynamical network design method developed in Y. Wan, S. Roy, and A. Saberi, "A New Focus in the Science of Networks: Towards Methods for Design," Proceedings of the Royal Society A, 464(2091), 2008 pp. 513–535. In particular, the performance of a design for stopping virus spread is demonstrated.
Recently, problems of network management and design have become more and more important in such diverse areas as air traffic flow management and virus-spread control. Several problems of interest can be abstracted to the problems of allocating resources to a network based on its graph topology, so as to optimize its dynamic performance. The referenced article shows how available local resources can be optimally allocated to different nodes or parts in the network, using matrix analysis methods.
As an example, epidemic control can be viewed as reducing the average number of secondary infections produced during an infected individual's infectious period. The spatially inhomogeneous dynamics for epidemic spread in a population network are often represented using a class of models known as multi-group models. Using the multi-group model, the authors have posed and solved the problem of inhomogeneously allocating local resources to minimize spread (i.e., secondary infection population). Conceptually, the method yields that more control resources should be placed in the highly connected parts of the network, and fewer in isolated parts. In the Demonstration, regions receiving the most resources have the symbol "*" next to their names. In this way, the virus's spread can be stopped quickly and so the virus will quickly die off.