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We consider a multi-population epidemic model with one or more (almost) isolated communities and one mobile community. Each of the isolated communities has contact within itself and, in addition, contact with the outside world but only…
All interesting and fascinating collective properties of a complex system arise from the intricate way in which its components interact. Various systems in physics, biology, social sciences and engineering have been successfully modelled as…
The susceptible-infected-recovered (SIR) model has been used extensively to model disease spread and other processes. Despite the widespread usage of this ordinary differential equation (ODE) based model which represents the mean-field…
This paper is focused on SIS (Susceptible-Infected-Susceptible) epidemic dynamics (also known as the contact process) on populations modelled by homogeneous Poisson point processes of the Euclidean plane, where the infection rate of a…
In this work, the spread of a contagious disease on a society where the individuals may take precautions is modeled. The primary assumption is that the infected individuals transmit the infection to the susceptible members of the community…
Current epidemics in the biological and social domains are challenging the standard assumptions of mathematical contagion models. Chief among them are the complex patterns of transmission caused by heterogeneous group sizes and infection…
The goal of this work is to study an infectious disease spreading in a medium size population occupying a confined environment. For this purpose, we consider a kinetic theory approach to model crowd dynamics in bounded domains and couple it…
Modeling epidemic dynamics plays an important role in studying how diseases spread, predicting their future course, and designing strategies to control them. In this letter, we introduce a model of SIR (susceptible-infected-removed) type…
Since 1927, until recently, models describing the spread of disease have mostly been of the SIR-compartmental type, based on the assumption that populations are homogeneous and well-mixed. The focus of these models have typically been on…
Binary-state dynamics (such as the susceptible-infected-susceptible (SIS) model of disease spread, or Glauber spin dynamics) on random networks are accurately approximated using master equations. Standard mean-field and pairwise theories…
Mean field approximation is a popular method to study the behaviour of stochastic models composed of a large number of interacting objects. When the objects are asynchronous, the mean field approximation of a population model can be…
The hypergraph offers a platform to study structural properties emerging from more complicated and higher-order than pairwise interactions among constituents and dynamical behavior such as the spread of information or disease. Recently, a…
Discrete- and continuous-time approaches are frequently used to model the role of heterogeneity on dynamical interacting agents on the top of complex networks. While, on the one hand, one does not expect drastic differences between these…
The paper describes and compares three approaches to modeling an epidemic spread. The first approach is a well-known system of SIR ordinary differential equations. The second is a mean-field model, in which an isolation strategy for each…
The metapopulation framework is adopted in a wide array of disciplines to describe systems of well separated yet connected subpopulations. The subgroups or patches are often represented as nodes in a network whose links represent the…
A dynamical model of an ecological community is analyzed within a "mean-field approximation" in which one of the species interacts with the combination of all of the other species in the community. Within this approximation the model may be…
We derive and asymptotically analyze mass-action models for disease spread that include transient pair formation and dissociation. Populations of unpaired susceptibles and infecteds are distinguished from the population of three types of…
Stochastic spreading models defined on complex network topologies are used to mimic the diffusion of diseases, information, and opinions in real-world systems. Existing theoretical approaches to the characterization of the models in terms…
People organize in groups and contagions spread across them. A simple stochastic process, yet complex to model due to dynamical correlations within and between groups. Moreover, groups can evolve if agents join or leave in response to…
The course of an epidemic is not only shaped by infection transmission over face-to-face contacts, but also by preventive behaviour caused by risk perception and social interactions. This study explores the dynamics of coupled awareness and…