Enhanced vaccine control of epidemics in adaptive networks

Analytical calculation of fragmentation transitions in adaptive networks

In adaptive networks, fragmentation transitions have been observed in which the network breaks into disconnected components. We present an analytical approach for calculating the transition point in general adaptive network models. Using the example of an adaptive voter model, we demonstrate that the proposed approach yields good agreement with numerical results.

Maximal sensitive dependence and the optimal path to epidemic extinction

Extinction of an epidemic or a species is a rare event that occurs due to a large, rare stochastic fluctuation. Although the extinction process is dynamically unstable, it follows an optimal path that maximizes the probability of extinction. We show that the optimal path is also directly related to the finite-time Lyapunov exponents of the underlying dynamical system in that the optimal path displays maximum sensitivity to initial conditions. We consider several stochastic epidemic models, and examine the extinction process in a dynamical systems framework. Using the dynamics of the finite-time Lyapunov exponents as a constructive tool, we demonstrate that the dynamical systems viewpoint of extinction evolves naturally toward the optimal path.

Opinion formation on adaptive networks with intensive average degree

We study the evolution of binary opinions on a simple adaptive network of N nodes. At each time step, a randomly selected node updates its state ("opinion") according to the majority opinion of the nodes that it is linked to; subsequently, all links are reassigned with probability p̃ (q̃) if they connect nodes with equal (opposite) opinions. In contrast to earlier work, we ensure that the average connectivity ("degree") of each node is independent of the system size ("intensive"), by choosing p̃ and q̃ to be of O(1/N). Using simulations and analytic arguments, we determine the final steady states and the relaxation into these states for different system sizes. We find two absorbing states, characterized by perfect consensus, and one metastable state, characterized by a population split evenly between the two opinions. The relaxation time of this state grows exponentially with the number of nodes, N. A second metastable state, found in the earlier studies, is no longer observed.