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We review and introduce a generalized reaction-diffusion approach to epidemic spreading in a metapopulation modeled as a complex network. The metapopulation consists of susceptible and infected individuals that are grouped in subpopulations…

Although suppressing the spread of a disease is usually achieved by investing in public resources, in the real world only a small percentage of the population have access to government assistance when there is an outbreak, and most must…

We investigate the role of migration patterns on the spread of epidemics in complex networks. We enhance the SIS-diffusion model on metapopulations to a nonlinear diffusion. Specifically, individuals move randomly over the network but at a…

We propose an efficient strategy to suppress epidemic explosion in heterogeneous metapopulation networks, wherein each node represents a subpopulation with any number of individuals and is assigned a curing rate that is proportional to…

Recent studies have demonstrated that the allocation of individual resources has a significant influence on the dynamics of epidemic spreading. In the real scenario, individuals have a different level of awareness for self-protection when…

One of the famous results of network science states that networks with heterogeneous connectivity are more susceptible to epidemic spreading than their more homogeneous counterparts. In particular, in networks of identical nodes it has been…

Several systems can be modeled as sets of interdependent networks where each network contains distinct nodes. Diffusion processes like the spreading of a disease or the propagation of information constitute fundamental phenomena occurring…

We study the dynamics of epidemic and reaction-diffusion processes in metapopulation models with heterogeneous connectivity pattern. In SIR-like processes, along with the standard local epidemic threshold, the system exhibits a global…

The impact that information diffusion has on epidemic spreading has recently attracted much attention. As a disease begins to spread in the population, information about the disease is transmitted to others, which in turn has an effect on…

A model for epidemic spreading on rewiring networks is introduced and analyzed for the case of scale free steady state networks. It is found that contrary to what one would have naively expected, the rewiring process typically tends to…

The study of how diseases spread has greatly benefited from advances in network modeling. Recently, a class of networks known as multilayer graphs has been shown to describe more accurately many real systems, making it possible to address…

The analysis of contagion-diffusion processes in metapopulations is a powerful theoretical tool to study how mobility influences the spread of communicable diseases. Nevertheless, many metapopulation approaches use indistinguishable agents…

In this paper, we study the interplay between the epidemic spreading and the diffusion of awareness in multiplex networks. In the model, an infectious disease can spread in one network representing the paths of epidemic spreading (contact…

The spatial structure of populations is a key element in the understanding of the large scale spreading of epidemics. Motivated by the recent empirical evidence on the heterogeneous properties of transportation and commuting patterns among…

One of the major issues in the theoretical modeling of epidemic spreading is the development of methods to control the transmission of an infectious agent. Human behavior plays a fundamental role in the spreading dynamics and can be used to…

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 study the interplay between individual behaviors and epidemic spreading in a dynamical network. We distribute agents on a square-shaped region with periodic boundary conditions. Every agent is regarded as a node of the…

Epidemic spreading often occurs in spatially heterogeneous environments, yet how quenched heterogeneity reshapes its onset and critical dynamics remains poorly understood. The diffusive epidemic process, a minimal reaction-diffusion model…

The spread of disease on complex networks has attracted widely attention in the physics community. Recent works have demonstrated that heterogeneous degree and weight distributions have a significant influence on the epidemic dynamics. In…

Epidemic models currently play a central role in our attempts to understand and control infectious diseases. Here, we derive a model for the diffusion limit of stochastic susceptible-infectious-removed (SIR) epidemic dynamics on a…