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We introduce an interacting particle system that models the spread of an epidemic in terms of heterogeneous diffusive dynamics, rather than exogenous contact and transmission rates at the population level as in classical compartmental…
Most spreading processes require spatial proximity between agents. The stationary state of spreading dynamics in a population of mobile agents thus depends on the interplay between the time and length scales involved in the epidemic process…
Infectious diseases are practically represented by models with multiple states and complex transition rules corresponding to, for example, birth, death, infection, recovery, disease progression, and quarantine. In addition, networks…
In an increasingly interconnected world, a key scientific challenge is to examine mechanisms that lead to the widespread propagation of contagions, such as misinformation and pathogens, and identify risk factors that can trigger large-scale…
Infectious diseases that incorporate pre-symptomatic transmission are challenging to monitor, model, predict and contain. We address this scenario by studying a variant of a stochastic susceptible-exposed-infected-recovered model on…
We consider the effects of noise on a model of epidemic outbreaks, where the outbreaks appear. randomly. Using a constructive transition approach that predicts large outbreaks, prior to their occurrence, we derive an adaptive control.…
Although ubiquitous, interactions of groups of individuals (e.g., modern messaging applications, group meetings, or even a parliament discussion) are not yet thoroughly studied. Frequently, single-groups are modeled as critical-mass…
This thesis investigates critical phenomena and equilibrium states in various stochastic models through three interconnected studies. In the first chapter, we analyze the Activated Random Walk model on a one-dimensional ring in the…
Panic may spread over a crowd in a similar fashion as contagious diseases do in social groups. People no exposed to a panic source may express fear, alerting others of imminent danger. This social mechanism initiates an evacuation process,…
The spread of infectious diseases, rumors, fashions, innovations are complex contagion processes, embedded both in networked and spatial contexts. Here we investigate the pattern dynamics of a complex contagion, where two agents, say $A$…
By incorporating segregated spatial domain and individual-based linkage into the SIS (susceptible-infected-susceptible) model, we investigate the coupled effects of random walk and intragroup interaction on contagion. Compared with the…
Epidemiological contact network models have emerged as an important tool in understanding and predicting the spread of infectious disease, due to their capacity to engage individual heterogeneity that may underlie essential dynamics of a…
The vast majority of strategies aimed at controlling contagion processes on networks considers the connectivity pattern of the system as either quenched or annealed. However, in the real world many networks are highly dynamical and evolve…
We present a thorough inspection of the dynamical behavior of epidemic phenomena in populations with complex and heterogeneous connectivity patterns. We show that the growth of the epidemic prevalence is virtually instantaneous in all…
The rate of adoption of new information depends on reinforcement from multiple sources in a way that often cannot be described by simple contagion processes. In such cases, contagion is said to be complex. Complex contagion happens in the…
This study is concerned with the dynamical behaviors of epidemic spreading over a two-layered interconnected network. Three models in different levels are proposed to describe cooperative spreading processes over the interconnected network,…
We study a self-consistent approach to introduce higher-order effects in a branching process model of complex contagion on clustered networks. Branching processes operate over an infinite population such that they never circle back and…
Epidemic spreading and cascading failure are two important dynamical processes over complex networks. They have been investigated separately for a long history. But in the real world, these two dynamics sometimes may interact with each…
After the recent COVID-19 outbreaks, it became increasingly evident that individuals' thoughts and beliefs can have a strong impact on disease transmission. It becomes therefore important to understand how information and opinions on…
The dynamics of many epidemic compartmental models for infectious diseases that spread in a single host population present a second-order phase transition. This transition occurs as a function of the infectivity parameter, from the absence…