Related papers: Two golden times in two-step contagion models
The dynamics of epidemic spreading is often reduced to the single control parameter $R_0$, whose value, above or below unity, determines the state of the contagion. If, however, the pathogen evolves as it spreads, $R_0$ may change over…
Contacts between individuals serve as pathways where infections may propagate. These contact patterns can be represented by network structures. Static structures have been the common modeling paradigm but recent results suggest that…
Behavioral adoptions are influenced by peers in different ways. While some individuals may change after a single incoming influence, others need multiple cumulated attempts. These two mechanism, known as the simple and the complex…
A great deal of effort has gone into trying to model social influence --- including the spread of behavior, norms, and ideas --- on networks. Most models of social influence tend to assume that individuals react to changes in the states of…
Mathematical models of infectious diseases, which are in principle analytically tractable, use two general approaches. The first approach, generally known as compartmental modeling, addresses the time evolution of disease propagation at the…
Prior social contagion models consider the spread of either one contagion at a time on interdependent networks or multiple contagions on single layer networks or under assumptions of competition. We propose a new threshold model for the…
Time-limited states characterise many dynamical processes on networks: disease infected individuals recover after some time, people forget news spreading on social networks, or passengers may not wait forever for a connection. These…
Time plays an essential role in the diffusion of information, influence and disease over networks. In many cases we only observe when a node copies information, makes a decision or becomes infected -- but the connectivity, transmission…
Recent research has focused on the monitoring of global-scale online data for improved detection of epidemics, mood patterns, movements in the stock market, political revolutions, box-office revenues, consumer behaviour and many other…
Contagion processes, representing the spread of infectious diseases, information, or social behaviors, are often schematized as taking place on networks, which encode for instance the interactions between individuals. The impact of the…
We consider the SIR model and study the first time the number of infected individuals begins to decrease and the first time this population is below a given threshold. We interpret these times as functions of the initial susceptible and…
The spread of infectious diseases near the epidemic threshold is investigated. Scaling laws for the size and the duration of outbreaks originating from a single infected individual in a large susceptible population are obtained. The maximal…
Contagious processes, such as spread of infectious diseases, social behaviors, or computer viruses, affect biological, social, and technological systems. Epidemic models for large populations and finite populations on networks have been…
A key parameter in models for the spread of infectious diseases is the basic reproduction number $R_0$, which is the expected number of secondary cases a typical infected primary case infects during its infectious period in a large mostly…
Motivated by the analysis of social networks, we study a model of random networks that has both a given degree distribution and a tunable clustering coefficient. We consider two types of growth processes on these graphs: diffusion and…
In this paper we conduct a simulation study of the spread of an epidemic like COVID-19 with temporary immunity on finite spatial and non-spatial network models. In particular, we assume that an epidemic spreads stochastically on a…
Binary-state models are those in which the constituent elements can only appear in two possible configurations. These models are fundamental in the mathematical treatment of a number of phenomena such as spin interactions in magnetism,…
We show that a certain model for the spread of an infection has a phase transition in the recuperation rate. The model is as follows: There are particles or individuals of type A and type B, interpreted as healthy and infected,…
A social (sexual) network is modeled by an extension of the configuration model to the situation where edges have weights, e.g. reflecting the number of sex-contacts between the individuals. An epidemic model is defined on the network such…
Epidemiological data on seasonal influenza show that the growth rate of the number of infected individuals can increase passing from one exponential growth rate to another one with a larger exponent. Such behavior is not described by…