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In this paper we study the diffusion of an SIS-type epidemics on a network under the presence of a random environment, that enters in the definition of the infection rates of the nodes. Accordingly, we model the infection rates in the form…
In this paper we study the household-structure SIS epidemic spreading on general complex networks. The household structure gives us the way to distinguish inner and the outer infection rate. Unlike household-structure models on homogenous…
The study proposes a modeling framework for investigating the disease dynamics with adaptive human behavior during a disease outbreak, considering the impacts of both local observations and global information. One important application…
The contact process is a simple model for the spread of an infection in a structured population. We investigate the case when the underlying structure evolves dynamically as a degree-dependent dynamical percolation model. Starting with a…
We propose a new model that describes the dynamics of epidemic spreading on connected graphs. Our model consists in a PDE-ODE system where at each vertex of the graph we have a standard SIR model and connexions between vertices are given by…
In this paper we present a model describing Susceptible-Infected-Susceptible (SIS) type epidemics spreading on a dynamic contact network with random link activation and deletion where link ac- tivation can be locally constrained. We use and…
We consider the qualitative behavior of a mathematical model for transmission dynamics with two nonlinear stages of contagion. The proposed model is inspired by phenomena occurring in epidemiology (spread of infectious diseases) or social…
We study SIS epidemic spreading models under population dispersal on multi-layer networks. We consider a patchy environment in which each patch comprises individuals belonging to different classes. Individuals disperse to other patches on a…
Mathematical modeling of epidemic propagation on networks is extended to hypergraphs in order to account for both the community structure and the nonlinear dependence of the infection pressure on the number of infected neighbours. The exact…
Up to now, the effects of having heterogeneous networks of contacts have been studied mostly for diseases which are not persistent in time, i.e., for diseases where the infectious period can be considered very small compared to the lifetime…
We study the stability properties of a susceptible-infected-susceptible (SIS) diffusion model, so-called the $n$-intertwined Markov model, over arbitrary directed network topologies. As in the majority of the work on infection spread…
Understanding the spread of diseases through complex networks is of great interest where realistic, heterogeneous contact patterns play a crucial role in the spread. Most works have focused on mean-field behavior -- quantifying how contact…
The disease spreading on complex networks is studied in SIR model. Simulations on empirical complex networks reveal two specific regimes of disease spreading: local containment and epidemic outbreak. The variables measuring the extent of…
Time-discrete dynamical systems on a finite state space have been used with great success to model natural and engineered systems such as biological networks, social networks, and engineered control systems. They have the advantage of being…
We study the spreading of an infection within an SIS epidemiological model on a network. Susceptible agents are given the opportunity of breaking their links with infected agents, and reconnecting those links with the rest of the…
Nowadays, information spreading on social networks has triggered an explosive attention in various disciplines. Most of previous works in this area mainly focus on discussing the effects of spreading probability or immunization strategy on…
We formulate models for the spread of infection on networks that are amenable to analysis in the large population limit. We distinguish three different levels: (1) binding sites, (2) individuals, and (3) the population. In the tradition of…
In this paper we study the susceptible-infectious (SI) epidemiological model using dynamical graphs. Dynamical structures have been recently applied in many areas including complex systems. Dynamical structures include the mutual…
Social systems are in a constant state of flux with dynamics spanning from minute-by-minute changes to patterns present on the timescale of years. Accurate models of social dynamics are important for understanding spreading of influence or…
Disease, opinions, ideas, gossip, etc. all spread on social networks. How these networks are connected (the network structure) influences the dynamics of the spreading processes. By investigating these relationships one gains understanding…