L. Chen

Outbreaks of coinfections: the critical role of cooperativity

Modeling epidemic dynamics plays an important role in studying how diseases spread, predicting their future course, and designing strategies to control them. In this letter, we introduce a model of SIR (susceptible-infected-removed) type which explicitly incorporates the effect of cooperative coinfection. More precisely, each individual can get infected by two different diseases, and an individual already infected with one disease has an increased probability to get infected by the other. Depending on the amount of this increase, we prove different threshold scenarios. Apart from the standard continuous phase transition for single-disease outbreaks, we observe continuous transitions where both diseases must coexist, but also discontinuous transitions are observed, where a finite fraction of the population is already affected by both diseases at the threshold. All our results are obtained in a mean-field model using rate equations, but we argue that they should hold also in more general frameworks.

Fast synchronization in neuronal networks

We study the fast synchronization in complex networks of coupled Hindmarsh-Rose neurons. The relation between the maximal Lyapunov exponent corresponding to the least stable transverse mode and the speed of synchronization is given, based on which we can obtain an optimal value of global coupling strength, with which the network synchronizes with the minimal synchronization time. The speed limits of several kinds of complex networks (small-world, scale-free, and modular) with different eigenratios are studied. Finally, we extend to the modified Hodgkin-Huxley neuron case.

Phase Transitions in Cooperative Coinfections: Simulation Results for Networks and Lattices

We study the spreading of two mutually cooperative diseases on different network topologies, and with two microscopic realizations, both of which are stochastic versions of a susceptible-infected-removed type model studied by us recently in mean field approximation. There it had been found that cooperativity can lead to first order transitions from spreading to extinction. However, due to the rapid mixing implied by the mean field assumption, first order transitions required nonzero initial densities of sick individuals. For the stochastic model studied here the results depend strongly on the underlying network. First order transitions are found when there are few short but many long loops: (i) No first order transitions exist on trees and on 2-d lattices with local contacts. (ii) They do exist on Erdős-Rényi (ER) networks, on d-dimensional lattices with d≥4, and on 2-d lattices with sufficiently long-ranged contacts. (iii) On 3-d lattices with local contacts the results depend on the microscopic details of the implementation. (iv) While single infected seeds can always lead to infinite epidemics on regular lattices, on ER networks one sometimes needs finite initial densities of infected nodes. (v) In all cases the first order transitions are actually hybrid; i.e., they display also power law scaling usually associated with second order transitions. On regular lattices, our model can also be interpreted as the growth of an interface due to cooperative attachment of two species of particles. Critically pinned interfaces in this model seem to be in different universality classes than standard critically pinned interfaces in models with forbidden overhangs. Finally, the detailed results mentioned above hold only when both diseases propagate along the same network of links. If they use different links, results can be rather different in detail, but are similar overall.

Transition from winnerless competition to synchronization in time-delayed neuronal motifs

The dynamics of brain functional motifs are studied. It is shown that different rhythms can occur in the motifs when time delay is taken into account. These rhythms include synchronization, winnerless competition (WLC) and two plus one (TPO). The main discovery is that the transition from WLC to synchronization can be induced simply by time delay. It is also concluded that some medium time delay is needed to achieve WLC in the realistic case. The motifs composed of heterogeneous neurons are also considered.

Adaptive network models of collective decision making in swarming systems

We consider a class of adaptive network models where links can only be created or deleted between nodes in different states. These models provide an approximate description of a set of systems where nodes represent agents moving in physical or abstract space, the state of each node represents the agents heading direction, and links indicate mutual awareness. We show analytically that the adaptive network description captures a phase transition to collective motion in some swarming systems, such as the Vicsek model, and that the properties of this transition are determined by the number of states (discrete heading directions) that can be accessed by each agent.

Fundamental properties of cooperative contagion processes

We investigate the effects of cooperation between two interacting infectious diseases that spread and stabilize in a host population. We propose a model in which individuals that are infected with one disease are more likely to acquire the second disease, both diseases following the susceptible-infected-susceptible reaction scheme. We analyze cooperative coinfection in stochastic network models as well as the idealized, well-mixed mean field system and show that cooperative mechanisms dramatically change the nature of phase transitions compared to single disease dynamics. We show that, generically, cooperative coinfection exhibits discontinuous transitions from the disease free to high prevalence state when a critical transmission rate is crossed. Furthermore, cooperative coinfection exhibits two distinct critical points, one for outbreaks the second one for eradication that can be substantially lower. This implies that cooperative coinfection exhibits hysteresis in its response to changing effective transmission rates or equivalently the basic reproduction number. We compute these critical parameters as a function of a cooperativity coefficient in the well-mixed mean field system. We finally investigate a spatially extended version of the model and show that cooperative interactions between diseases change the general wave propagation properties of conventional spreading phenomena of single diseases. The presented work may serve as a starting and reference point for a more comprehensive understanding of interacting diseases that spread in populations.

Dynamical symmetry and synchronization in modular networks

The effects of dynamical symmetry on the chaotic pattern synchronization in modular networks have been studied. It is found that the topological and the coupling symmetries between modules (subnetworks) can both enhance and speed up the chaotic pattern synchronization between modules. The calculation of Lyapunov exponent shows that this dynamical symmetry is a necessary condition for complete chaotic pattern synchronization in both modular networks composed by identical oscillators and heterogeneous modular networks if the states of nodes are much different from one another.

Searching good indicators for predicting the synchronizability of heterogeneous networks and beyond

In searching the indicators of synchronizability of complex networks, the maximal betweenness centrality is usually proposed as a good indicator. However, we find that a better indicator for synchronizability in heterogeneous networks is the maximal degree from both the average results and the individual realization of a network, which usually makes more sense in practice. Both the largest eigenvalue and the eigenratio are found, in a wide range of heterogeneity, to hold linear relations with the maximal degree. Our results may provide some clues to mathematically solve the relation between the synchronizability and the network degree, also to the optimal strategies to enhance synchronization.

Time-delay–induced synchronization in complex networks: Exploring the dynamical mechanism

We show that delayed coupling could induce or enhance stable chaotic synchronization in complex networks, where no or weak synchrony would exist for the usual instantaneous coupling. The mechanism behind this phenomenon reveals that the phase structure of the coupled chaotic oscillator plays the main role. Numerical results for Rossler and Lorenz oscillators as network nodes confirm the generality of this phenomenon. Together with our previous findings, we highlight the importance of taking the dynamical structure into account when studying or designing large-scale networks for stable synchronization.

Manipulating synchronous states by dynamical flow in complex networks

We show that if the dynamical flow, i.e., the non-vanishing coupling term, exists between nodes in synchronized networks, a wide variety of stable synchronous states of complex networks may occur, which may differ substantially from the dynamics of an individual isolated node. Stability analysis of the dynamics of Hindmarsh-Rose and foodweb networks shows that controlling this dynamical flow can greatly enhance the synchronization and generate both chaotic and regular synchronous states for whatever state of an isolated node. Our results provide a possibility for the control of synchronization in complex networks by the manipulation of the dynamical flow.