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Bootstrap percolation is a process that is used to model the spread of an infection on a given graph. In the model considered here each vertex is equipped with an individual threshold. As soon as the number of infected neighbors exceeds…
We present a model for the evolution of networks of occupied sites on undirected regular graphs. At every iteration step in a parallel update I randomly chosen empty sites are occupied and occupied sites having degree outside of a given…
Analytical description of propagation phenomena on random networks has flourished in recent years, yet more complex systems have mainly been studied through numerical means. In this paper, a mean-field description is used to coherently…
The theory of life history evolution provides a powerful framework to understand the evolutionary dynamics of pathogens in both epidemic and endemic situations. This framework, however, relies on the assumption that pathogen populations are…
Within epidemiological modeling, the majority of analyses assume a single epidemic process for generating ground-truth data. However, this assumed data generation process can be unrealistic, since data sources for epidemics are often…
Empirical records of epidemics reveal that fluctuations are important factors for the spread and prevalence of infectious diseases. The exact manner in which fluctuations affect spreading dynamics remains poorly known. Recent analytical and…
We introduce a new percolation model to describe and analyze the spread of an epidemic on a general directed and locally finite graph. We assign a two-dimensional random weight vector to each vertex of the graph in such a way that the…
This article introduces epidemia, an R package for Bayesian, regression-oriented modeling of infectious diseases. The implemented models define a likelihood for all observed data while also explicitly modeling transmission dynamics: an…
We perform an analytical sensitivity analysis for a model of a continuous-time branching process evolving on a fixed network. This allows us to determine the relative importance of the model parameters to the growth of the population on the…
Modeling long-range epidemic spreading in a random environment, we consider a quenched disordered, $d$-dimensional contact process with infection rates decaying with the distance as $1/r^{d+\sigma}$. We study the dynamical behavior of the…
Entropy is a classical measure to quantify the amount of information or complexity of a system. Various entropy-based measures such as functional and spectral entropies have been proposed in brain network analysis. However, they are less…
The gamma distribution is a useful model for small area prediction of a skewed response variable. We study the use of the gamma distribution for small area prediction. We emphasize a model, called the gamma-gamma model, in which the area…
By generating the specifics of a network structure only when needed (on-the-fly), we derive a simple stochastic process that exactly models the time evolution of susceptible-infectious dynamics on finite-size networks. The small number of…
We introduce an interacting particle system that models the spread of an epidemic in terms of heterogeneous diffusive dynamics, rather than exogenous contact and transmission rates at the population level as in classical compartmental…
Multigraphs are graphs in which multiple links between pairs of nodes are allowed, whereas they are forbidden in simple graphs, the latter being widely used in network science. Simple graphs generated by the configuration model have served…
In our paper selected linguistic features of genomes to study the statistics of the gene codes are considered. We present the information theory from which it follows that if the system is described by distributions of hyperbolic type it…
This paper is concerned with the growth rate of SIR (Susceptible-Infectious-Recovered) epidemics with general infectious period distribution on random intersection graphs. This type of graph is characterized by the presence of cliques…
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…
In this work, the aim is to study the spread of a contagious disease and information on a multilayer social system. The main idea is to find a criterion under which the adoption of the spreading information blocks or suppresses the epidemic…
We develop a framework for non-Markovian, well-mixed SIR and SIS models beyond mean field, utilizing the continuous-time random walk formalism. Using a gamma distribution for the infection and recovery inter-event times as a test case, we…