Related papers: The acceleration of evolutionary spread by long-ra…
It is a fundamental question in epidemiology to estimate, model and predict the growth rate of a pandemic. Analogously, analysing the diffusion of innovation, (fake) news, memes, and rumours is of key importance in the social sciences. The…
Random walk is one of the basic mechanisms found in many network applications. We study the epidemic spreading dynamics driven by biased random walks on complex networks. In our epidemic model, each time infected nodes constantly spread…
Epidemic spreading often occurs in spatially heterogeneous environments, yet how quenched heterogeneity reshapes its onset and critical dynamics remains poorly understood. The diffusive epidemic process, a minimal reaction-diffusion model…
Most spreading processes require spatial proximity between agents. The stationary state of spreading dynamics in a population of mobile agents thus depends on the interplay between the time and length scales involved in the epidemic process…
Consider a graph where the sites are distributed in space according to a Poisson point process on $\mathbb R^n$. We study a population evolving on this network, with individuals jumping between sites with a rate which decreases…
The evolution of dispersal is a classical question in evolutionary biology, and it has been studied in a wide range of mathematical models. A selection-mutation model, in which the population is structured by space and a phenotypic trait,…
Infectious pathogens often propagate by superspreading, which focusses onward transmission on disproportionately few infected individuals. At the same time, infector-infectee pairs tend to have more similar transmission potentials than…
A simple, but ``classical``, stochastic model for epidemic spread in a finite, but large, population is studied. The progress of the epidemic can be divided into three different phases that requires different tools to analyse. Initially the…
Theory predicts rapid genetic drift during invasions, yet many expanding populations maintain high genetic diversity. We find that genetic drift is dramatically suppressed when dispersal rates increase with the population density because…
Discrete time, spatially extended models play an important role in ecology, modelling population dynamics of species ranging from micro-organisms to birds. An important question is how 'bottom up', individual-based models can be…
Most infectious diseases spread on a dynamic network of human interactions. Recent studies of social dynamics have provided evidence that spreading patterns may depend strongly on detailed micro-dynamics of the social system. We have…
An epidemic model, where the dispersal is approximated by nonlocal diffusion operator and spatial domain has one ?xed boundary and one free boundary, is considered in this paper. Firstly, using some elementary analysis instead of…
A key problem in modelling the evolution dynamics of infectious diseases is the mathematical representation of the mechanism of transmission of the contagion. Models with a finite number of subpopulations can be described via systems of…
A theory of the spread of epidemics is formulated on the basis of pairwise interactions in a dilute system of random walkers (infected and susceptible animals) moving in n dimensions. The motion of an animal pair is taken to obey a…
Understanding and predicting outbreaks of contagious diseases are crucial to the development of society and public health, especially for underdeveloped countries. However, challenging problems are encountered because of complex epidemic…
Understanding the time evolution of fragmented animal populations and their habitats, connected by migration, is a problem of both theoretical and practical interest. This paper presents a method for calculating the time evolution of the…
Global transport and communication networks enable information, ideas and infectious diseases now to spread at speeds far beyond what has historically been possible. To effectively monitor, design, or intervene in such epidemic-like…
Social distancing as one of the main non-pharmaceutical interventions can help slow down the spread of diseases, like in the COVID-19 pandemic. Effective social distancing, unless enforced as drastic lockdowns and mandatory cordon…
In this paper we study some mathematical models describing evolution of population density and spread of epidemics in population systems in which spatial movement of individuals depends only on the departure and arrival locations and does…
Synchronous oscillations of spatially disjunct populations are widely observed in ecology. Even in the absence of spatially synchronized exogenous forces, metapopulations may synchronize via dispersal. For many species, most dispersal is…