Related papers: Epidemics on random intersection graphs
We focus on an epidemiological model (the archetypical SIR system) defined on graphs and study the asymptotic behavior of the solutions as the number of vertices in the graph diverges. By relying on the theory of so called graphons we…
The duration, type and structure of connections between individuals in real-world populations play a crucial role in how diseases invade and spread. Here, we incorporate the aforementioned heterogeneities into a model by considering a…
Heterogeneity is an important property of any population experiencing a disease. Here we apply general methods of the theory of heterogeneous populations to the simplest mathematical models in epidemiology. In particular, an SIR…
Individual contributions to the spread of an epidemic vary widely due to an individual's location in a social network and their intrinsic ability to spread or contract diseases. While the effect of heterogeneous population structure and…
We consider the problem of finding the graph on which an epidemic cascade spreads, given only the times when each node gets infected. While this is a problem of importance in several contexts -- offline and online social networks,…
Current modeling of infectious diseases allows for the study of complex and realistic scenarios that go from the population to the individual level of description. However, most epidemic models assume that the spreading process takes place…
We study the SIR epidemic model with infections carried by $k$ particles making independent random walks on a random regular graph. Here we assume $k\leq n^{\epsilon}$, where $n$ is the number of vertices in the random graph, and $\epsilon$…
The SIR model is a three-compartment model of the time development of an epidemic. After normalizing the dependent variables, the model is a system of two non-linear differential equations for the susceptible proportion $S$ and the infected…
We introduce a kinetic framework for modeling the time evolution of the statistical distributions of the population densities in the three compartments of susceptible, infectious, and recovered individuals, under epidemic spreading driven…
A random graph model with prescribed degree distribution and degree dependent edge weights is introduced. Each vertex is independently equipped with a random number of half-edges and each half-edge is assigned an integer valued weight…
We study the susceptible-infected-susceptible (SIS) model on directed complex networks within the quenched mean-field approximation. Combining results from random matrix theory with an analytic approach to the distribution of fixed-point…
We study extensions of the classical SIR model of epidemic spread. First, we consider a single population modified SIR epidemics model in which the contact rate is allowed to be an arbitrary function of the fraction of susceptible and…
We consider a very general stochastic model for an SIR epidemic on a network which allows an individual's infectious period, and the time it takes to contact each of its neighbours after becoming infected, to be correlated. We write down…
Motivated by recent epidemic outbreaks, including those of COVID-19, we solve the canonical problem of calculating the dynamics and likelihood of extensive outbreaks in a population within a large class of stochastic epidemic models with…
In the recent COVID-19 pandemic we assisted at a sequence of epidemic waves intertwined by anomalous fade-outs with periods of low but persistent epidemic prevalence. These long-living epidemic states complicate epidemic control and…
Many complex networks exhibit vulnerability to spreading of epidemics, and such vulnerability relates to the viral strain as well as to the network characteristics. For instance, the structure of the network plays an important role in…
Epidemic spread in single-host systems strongly depends on the population's contact network. However, little is known regarding the spread of epidemics across networks representing populations of multiple hosts. We explored cross-species…
A random network model which allows for tunable, quite general forms of clustering, degree correlation and degree distribution is defined. The model is an extension of the configuration model, in which stubs (half-edges) are paired to form…
Using the continuous-time susceptible-infected-susceptible (SIS) model on networks, we investigate the problem of inferring the class of the underlying network when epidemic data is only available at population-level (i.e. the number of…
The SIRS process is a continuous-time process for how infections spread on a graph. In this model, each vertex is in one of the following three states: susceptible (to the infection; S), infected (I), or recovered (R) and thus immune to the…