Related papers: Comparison of mean-field based theoretical analysi…
Reaction-diffusion processes can be adopted to model a large number of dynamics on complex networks, such as transport processes or epidemic outbreaks. In most cases, however, they have been studied from a fermionic perspective, in which…
For preventing the spread of epidemics such as the coronavirus disease COVID-19, social distancing and the isolation of infected persons are crucial. However, existing reaction-diffusion equations for epidemic spreading are incapable of…
The interaction among spreading processes on a complex network is a nontrivial phenomenon of great importance. It has recently been realized that cooperative effects among infective diseases can give rise to qualitative changes in the…
Real epidemic spreading networks often composed of several kinds of networks interconnected with each other, and the interrelated networks have the different topologies and epidemic dynamics. Moreover, most human diseases are derived from…
In this work, we aim to understand the influence of the heterogeneity of infection rates on the Susceptible-Infected-Susceptible (SIS) epidemic spreading. Employing the classic SIS model as the benchmark, we study the influence of the…
We develop an analytical approach to the susceptible-infected-susceptible (SIS) epidemic model that allows us to unravel the true origin of the absence of an epidemic threshold in heterogeneous networks. We find that a delicate balance…
We present and analyze a mathematical model to study the feedback between behavior and epidemic spread in a population that is actively assessing and reacting to risk of infection. In our model, a population dynamically forms an opinion…
In most models of the spread of disease over contact networks it is assumed that the probabilities per unit time of disease transmission and recovery from disease are constant, implying exponential distributions of the time intervals for…
In this paper we derive and analyse mean-field models for the dynamics of groups of individuals undergoing a random walk. The random motion of individuals is only influenced by the perceived densities of the different groups present as well…
The review is devoted to analysis of mathematical models used for describing epidemic processes. A main focus is done on the models that are based on partial differential equations (PDEs), especially those that were developed and used for…
We investigate the effects of risk perception in a simple model of epidemic spreading. We assume that the perception of the risk of being infected depends on the fraction of neighbors that are ill. The effect of this factor is to decrease…
In this paper, we propose a modified susceptible-infected-recovered (SIR) model, in which each node is assigned with an identical capability of active contacts, $A$, at each time step. In contrast to the previous studies, we find that on…
The study of SIS epidemics on networks has stressed the role of the network topology on the spreading process. However, accurate models of SIS epidemics rely on the complete knowledge of the network topology, which is often not available.…
Modeling and control of epidemics such as the novel Corona virus have assumed paramount importance at a global level. A natural and powerful dynamical modeling framework to use in this context is a continuous time Markov decision process…
We present the generalised mean-field and pairwise models for non-Markovian epidemics on networks with arbitrary recovery time distributions. First we consider a hyperbolic system, where the population of infective nodes and links are…
We develop a feedback control method for networked epidemic spreading processes. In contrast to most prior works which consider mean field, open-loop control schemes, the present work develops a novel framework for feedback control of…
Since its first formulations almost a century ago, mathematical models for disease spreading contributed to understand, evaluate and control the epidemic processes.They promoted a dramatic change in how epidemiologists thought of the…
We study convergence properties of competing epidemic models of the Susceptible-Infected-Susceptible (SIS) type. The SIS epidemic model has seen widespread popularity in modelling the spreading dynamics of contagions such as viruses,…
The mean-field limit of a Markovian model describing the interaction of several classes of permanent connections in a network is analyzed. Each of the connections has a self-adaptive behavior in that its transmission rate along its route…
The main difficulty that arises in the analysis of most machine learning algorithms is to handle, analytically and numerically, a large number of interacting random variables. In this Ph.D manuscript, we revisit an approach based on the…