Related papers: Long-range competition on the torus
We introduce the effect of site contamination in a model for spatial epidemic spread and show that the presence of site contamination may have a strict effect on the model in the sense that it can make an otherwise subcritical process…
We consider an SIR epidemic model propagating on a configuration model network, where the degree distribution of the vertices is given and where the edges are randomly matched. The evolution of the epidemic is summed up into three…
A bootstrap percolation process on a graph $G$ is an "infection" process which evolves in rounds. Initially, there is a subset of infected nodes and in each subsequent round each uninfected node which has at least $r$ infected neighbours…
In this paper, we discuss optimal $1$-toroidal graphs (abbreviated as O1TG), which are drawn on the torus so that every edge crosses another edge at most once, and has $n$ vertices and exactly $4n$ edges. We first consider connectivity of…
We extend the spatial $\Lambda$-Fleming-Viot process introduced in [Electron. J. Probab. 15 (2010) 162-216] to incorporate recombination. The process models allele frequencies in a population which is distributed over the two-dimensional…
Resource-based competition between microorganisms species in continuous culture has been studied extensively both experimentally and theoretically, mostly for bacteria through Monod and and Contois "constant yield" models, or for…
The spread of certain diseases can be promoted, in some cases substantially, by prior infection with another disease. One example is that of HIV, whose immunosuppressant effects significantly increase the chances of infection with other…
Using our previously developed model we demonstrate here, that (1) solid tumor growth and cell invasion are linked, not only qualitatively but also quantitatively, that (2) the onset of invasion marks the time point when the tumor cell…
We study the interaction between epidemic spreading and a vaccination process. We assume that, similar to the disease spreading, also the vaccination process occurs through direct contact, i.e., it follows the standard…
We consider two independent branching random walks that start next to each other on the $d$-dimensional hypercubic lattice and that carry two different colors. Vertices of the lattice are colored according to the color of the walker cloud…
We study the competition and the evolution of nodes embedded in Euclidean restricted spaces. The population evolves by a branching process in which new nodes are generated when up to two new nodes are attached to the previous ones at each…
Network properties govern the rate and extent of various spreading processes, from simple contagions to complex cascades. Recently, the analysis of spreading processes has been extended from static networks to temporal networks, where nodes…
Consider an SI process on a graph $G$ where each S--I connection becomes I--I at rate $\lambda$. Here S and I stand for ``susceptible'' and ``infected'' respectively. The evoSI model is a modification of the SI model in which S--I edges are…
Network properties govern the rate and extent of spreading processes on networks, from simple contagions to complex cascades. Recent advances have extended the study of spreading processes from static networks to temporal networks, where…
In random cellular systems, both observation and maximum entropy inference give a specific form to the topological pair correlation: it is bi-affine in the cells number of edges with coefficients depending on the distance between the two…
Understanding spreading dynamics will benefit society as a whole in better preventing and controlling diseases, as well as facilitating the socially responsible information while depressing destructive rumors. In network-based spreading…
Interplay between kinetic roughening and phase ordering is studied in a growth SOS model with two kinds of particles and Ising-like interaction by Monte Carlo simulations. We found that, for a sufficiently large coupling, growth is strongly…
We introduce a generalized version of the frog model to describe the invasion of a parasite population in a spatially structured immobile host population with host immunity on the integer line. Parasites move according to simple symmetric…
We studied interplay between kinetic roughening and phase ordering in 1+1 dimensional single-step solid-on-solid growth model with two kinds of particles and Ising-like interaction. Evolution of both geometrical and compositional properties…
Increasingly, experimentalists and modellers alike have come to recognise the important role of spatial structure in infection dynamics. Almost invariably, spatial computational models of viral infections - as with in vitro experimental…