Related papers: A Network Epidemic Model for Online Community Comm…
We introduce a random graph model based on k-trees, which can be generated by applying a probabilistic preferential attachment rule, but which also has a simple combinatorial description. We carry out a precise distributional analysis of…
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…
Preferential attachment in a directed scale-free graph is widely used to model the evolution of social networks. Statistical analyses of social networks often relies on node based data rather than conventional repeated sampling. For our…
Two versions of the susceptible-infected-susceptible epidemic model, which have different transmission rules, are analysed. Both models are considered on a weighted network to simulate a mitigation in the connection between the individuals.…
In real life, networks are dynamic in nature; they grow over time and often exhibit power-law degree sequences. To model the evolving structure of the internet, Barab\'{a}si and Albert introduced a simple dynamic model with a power-law…
We introduce a class of generative network models that insert edges by connecting the starting and terminal vertices of a random walk on the network graph. Within the taxonomy of statistical network models, this class is distinguished by…
Modelling epidemics using contact networks provides a significant improvement over classical compartmental models by explicitly incorporating the network of contacts. However, while network-based models describe disease spread on a given…
The graph of communities is a network emerging above the level of individual nodes in the hierarchical organisation of a complex system. In this graph the nodes correspond to communities (highly interconnected subgraphs, also called modules…
Viruses constantly undergo mutations with genomic changes. The propagation of variants of viruses is an interesting problem. We perform numerical simulations of the microscopic epidemic model based on network theory for the spread of…
Exponential-family random network (ERN) models specify a joint representation of both the dyads of a network and nodal characteristics. This class of models allow the nodal characteristics to be modelled as stochastic processes, expanding…
We propose a compartmental model for epidemiology wherein the population is split into groups with either comply or refuse to comply with protocols designed to slow the spread of a disease. Parallel to the disease spread, we assume that…
Our work introduces an approach for estimating the contribution of attachment mechanisms to the formation of growing networks. We present a generic model in which growth is driven by the continuous attachment of new nodes according to…
Many epidemic models approximate social contact behavior by assuming random mixing within mixing groups (e.g., homes, schools and workplaces). The effect of more realistic social network structure on estimates of epidemic parameters is an…
We study mixing patterns in networks, meaning the propensity for nodes of different kinds to connect to one another. The phenomenon of assortative mixing, whereby nodes prefer to connect to others that are similar to themselves, has been…
To understand the contact patterns of a population -- who is in contact with whom, and when the contacts happen -- is crucial for modeling outbreaks of infectious disease. Traditional theoretical epidemiology assumes that any individual can…
The paper is devoted to the spreading of a message within the random graph evolving by the Norros-Reittu preferential attachment model. The latter model forms random Poissonian numbers of edges between newly added nodes and existing ones.…
The number of common friends (or connections) in a graph is a commonly used measure of proximity between two nodes. Such measures are used in link prediction algorithms and recommendation systems in large online social networks. We obtain…
Communities are a common and widely studied structure in networks, typically under the assumption that the network is fully and correctly observed. In practice, network data are often collected by querying nodes about their connections. In…
Networks provide a skeleton for the spread of contagions, like, information, ideas, behaviors and diseases. Many times networks over which contagions diffuse are unobserved and need to be inferred. Here we apply survival theory to develop…
Many models in mathematical epidemiology are developed with the aim to provide a framework for parameter estimation and then prediction. It is well-known that parameters are not always uniquely identifiable. In this paper we consider…