Related papers: Randomized migration processes between two epidemi…
The epidemic threshold of a social system is the ratio of infection and recovery rate above which a disease spreading in it becomes an epidemic. In the absence of pharmaceutical interventions (i.e. vaccines), the only way to control a given…
Modeling and simulating movement of vehicles in established transportation infrastructures, especially in large urban road networks is an important task. It helps with understanding and handling traffic problems, optimizing traffic…
In this brief note, we find formulas for the distribution and the transition probability matrices of a stochastic process described as a time-reversion in a finite time window of a Markov chain, with cluster observation of the Markov state…
Many epidemic processes in networks spread by stochastic contacts among their connected vertices. There are two limiting cases widely analyzed in the physics literature, the so-called contact process (CP) where the contagion is expanded at…
Many analyses of resource-allocation problems employ simplistic models of the population. Using the example of a resource-allocation problem of Marecek et al. [arXiv:1406.7639], we introduce rather a general behavioural model, where the…
The paper is devoted to studies of perturbed Markov chains commonly used for description of information networks. In such models, the matrix of transition probabilities for the corresponding Markov chain is usually regularised by adding a…
Random walks on networks is the standard tool for modelling spreading processes in social and biological systems. This first-order Markov approach is used in conventional community detection, ranking, and spreading analysis although it…
Network--based epidemic models that account for heterogeneous contact patterns are extensively used to predict and control the diffusion of infectious diseases. We use census and survey data to reconstruct a geo--referenced and…
The initial transient phase of an emerging epidemic is of critical importance for data-driven model building, model-based prediction of the epidemic trend, and articulation of control/prevention strategies. In principle, quantitative models…
A birth-death-move process with mutations is a Markov model for a system of marked particles in interaction, that move over time, with births and deaths. In addition the mark of each particle may also change, which constitutes a mutation.…
In real world, there is a significant relation between human behaviors and epidemic spread. Especially, the reactions among individuals in different communities to epidemics may be different, which lead to cluster synchronization of human…
Recent years have seen a large amount of interest in epidemics on networks as a way of representing the complex structure of contacts capable of spreading infections through the modern human population. The configuration model is a popular…
We propose a generalization of the random matrix theory following the basic prescription of the recently suggested concept of superstatistics. Spectral characteristics of systems with mixed regular-chaotic dynamics are expressed as weighted…
The spread of viruses in biological networks, computer networks, and human contact networks can have devastating effects; developing and analyzing mathematical models of these systems can be insightful and lead to societal benefits. Prior…
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…
Connectivity patterns in intermittently-connected mobile networks (ICMN) can be modeled as edge-Markovian dynamic graphs. We propose a new model for epidemic propagation on such graphs and calculate a closed-form expression that links the…
We present a class of SEIR Markov chain models for infectious diseases observed over discrete time in a random human population living in a closed environment. The population changes over time through random births, deaths, and transitions…
We study the motion of substance in a finite channel that belongs to a network. The channel splits to two arms in a node of the network. There is an additional split of the secondary arm. We obtain analytical relationships for the…
Life is on the razor's edge as resulting from competitive birth and death random forces. We illustrate this aphorism in the context of three Markov chain population models where systematic random immigration events promoting growth are…
We present a contact-based model to study the spreading of epidemics by means of extending the dynamic message passing approach to temporal networks. The shift in perspective from node- to edge-centric quantities enables accurate modelling…