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Consider stochastic models for the spread of an infection in a structured community, where this structured community is itself described by a random network model. Some common network models and transmission models are defined and large…

The science of networks has revolutionised research into the dynamics of interacting elements. It could be argued that epidemiology in particular has embraced the potential of network theory more than any other discipline. Here we review…

Weight distribution largely impacts the epidemic spreading taking place on top of networks. This paper studies a susceptible-infected-susceptible model on regular random networks with different kinds of weight distributions. Simulation…

Many real networks exhibit a layered structure in which links in each layer reflect the function of nodes on different environments. These multiple types of links are usually represented by a multiplex network in which each layer has a…

When an epidemic spreads in a population, individuals may adaptively change the structure of their social contact network to reduce risk of infection. Here we study the spread of an epidemic on an adaptive network with community structure.…

The study of social networks, and in particular the spread of disease on networks, has attracted considerable recent attention in the physics community. In this paper, we show that a large class of standard epidemiological models, the…

In the past few decades, the frequency of pandemics has been increased due to the growth of urbanization and mobility among countries. Since a disease spreading in one country could become a pandemic with a potential worldwide humanitarian…

The duration, type and structure of connections between individuals in real-world populations play a crucial role in how diseases invade and spread. Here, we incorporate the aforementioned heterogeneities into a model by considering a…

The spread of one disease, in some cases, can stimulate the spreading of another infectious disease. Here, we treat analytically a symmetric coinfection model for spreading of two diseases on a two-layer multiplex network. We allow layer…

A statistical model assuming a preferential attachment network, which is generated by adding nodes sequentially according to a few simple rules, usually describes real-life networks better than a model assuming, for example, a Bernoulli…

Most real-world networks are not isolated. In order to function fully, they are interconnected with other networks, and this interconnection influences their dynamic processes. For example, when the spread of a disease involves two species,…

We show we can control an epidemic reaction-diffusion on a directed, and heterogeneous, network by redirecting the flows, thanks to the optimisation of well-designed loss functions, in particular the basic reproduction number of the model.…

The primary tool for predicting infectious disease spread and intervention effectiveness is the mass action Susceptible-Infected-Recovered model of Kermack and McKendrick. Its usefulness derives largely from its conceptual and mathematical…

Background: Recently developed techniques to study the spread of infectious diseases through networks make assumptions that the initial proportion infected is infinitesimal and the population behavior is static throughout the epidemic. The…

We study by analytical methods and large scale simulations a dynamical model for the spreading of epidemics in complex networks. In networks with exponentially bounded connectivity we recover the usual epidemic behavior with a threshold…

The spread of an epidemic disease and the population's collective behavioural response are deeply intertwined, influencing each other's evolution. Such a co-evolution typically has been overlooked in mathematical models, limiting their…

We study the diffusion of epidemics on networks that are partitioned into local communities. The gross structure of hierarchical networks of this kind can be described by a quotient graph. The rationale of this approach is that individuals…

This work presents a model combining the simplest communicable and non-communicable disease models. The latter is, by far, the leading cause of sickness and death in the World, and introduces basal heterogeneity in populations where…

Infection dynamics have been studied extensively on complex networks, yielding insight into the effects of heterogeneity in contact patterns on disease spread. Somewhat separately, metapopulations have provided a paradigm for modeling…

Infectious disease remains, despite centuries of work to control and mitigate its effects, a major problem facing humanity. This paper reviews the mathematical modelling of infectious disease epidemics on networks, starting from the…