Emergence of Hopf bifurcation in an extended SIR dynamic.

In this paper, the original SIR model is improved by considering a new compartment, representing the hospitalization of critical cases. A system of differential equations with four blocks is developed to analyze the treatment of severe cases in an Intensive Care Unit (ICU). The outgoing rate of the infected individuals who survive is divided into nI and [Formula: see text] where the second term represents the transition rate of critical cases that are hospitalized in ICU.

Emergence of synergistic and competitive pathogens in a coevolutionary spreading model.

Cooperation and competition between pathogens can alter the amount of individuals affected by a coinfection. Nonetheless, the evolution of the pathogens' behavior has been overlooked. Here, we consider a coevolutionary model where the simultaneous spreading is described by a two-pathogen susceptible-infected-recovered model in an either synergistic or competitive manner.

Effects of measures on phase transitions in two cooperative susceptible-infectious-recovered dynamics.

In recent studies, it has been shown that a cooperative interaction in a co-infection spread can lead to a discontinuous transition at a decreased threshold. Here, we investigate the effects of immunization with a rate proportional to the extent of the infection on phase transitions of a cooperative co-infection. We use the mean-field approximation to illustrate how measures that remove a portion of the susceptible compartment, like vaccination, with high enough rates can change discontinuous transitions in two coupled susceptible-infectious-recovered dynamics into continuous ones while increasing the threshold of transitions.

Social distancing in pedestrian dynamics and its effect on disease spreading.

Nonpharmaceutical measures such as social distancing can play an important role in controlling the spread of an epidemic. In this paper, we use a mathematical model combining human mobility and disease spreading. For the mobility dynamics, we design an agent-based model consisting of pedestrian dynamics with a novel type of force to resemble social distancing in crowded sites.

Impact of temporal correlations on high risk outbreaks of independent and cooperative SIR dynamics.

We first propose a quantitative approach to detect high risk outbreaks of independent and coinfective SIR dynamics on three empirical networks: a school, a conference and a hospital contact network. This measurement is based on the k-means clustering method and identifies proper samples for calculating the mean outbreak size and the outbreak probability. Then we systematically study the impact of different temporal correlations on high risk outbreaks over the original and differently shuffled counterparts of each network.

Interplay between competitive and cooperative interactions in a three-player pathogen system.

In ecological systems, heterogeneous interactions between pathogens take place simultaneously. This occurs, for instance, when two pathogens cooperate, while at the same time, multiple strains of these pathogens co-circulate and compete. Notable examples include the cooperation of human immunodeficiency virus with antibiotic-resistant and susceptible strains of tuberculosis or some respiratory infections with strains.

Exact solution of generalized cooperative susceptible-infected-removed (SIR) dynamics.

In this paper, we introduce a general framework for coinfection as cooperative susceptible-infected-removed (SIR) dynamics. We first solve the SIR model analytically for two symmetric cooperative contagions [L. Chen et al.

Particle velocity controls phase transitions in contagion dynamics.

Interactions often require the proximity between particles. The movement of particles, thus, drives the change of the neighbors which are located in their proximity, leading to a sequence of interactions. In pathogenic contagion, infections occur through proximal interactions, but at the same time, the movement facilitates the co-location of different strains.

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.

Extracting information from S-curves of language change.

It is well accepted that adoption of innovations are described by S-curves (slow start, accelerating period and slow end). In this paper, we analyse how much information on the dynamics of innovation spreading can be obtained from a quantitative description of S-curves. We focus on the adoption of linguistic innovations for which detailed databases of written texts from the last 200 years allow for an unprecedented statistical precision.

Stability of Boolean and continuous dynamics.

Regulatory dynamics in biology is often described by continuous rate equations for continuously varying chemical concentrations. Binary discretization of state space and time leads to Boolean dynamics. In the latter, the dynamics has been called unstable if flip perturbations lead to damage spreading.