Fractional diffusion emulates a human mobility network during a simulated disease outbreak

From footpaths to flight routes, human mobility networks facilitate the spread of communicable diseases. Control and elimination efforts depend on characterizing these networks in terms of connections and flux rates of individuals between contact nodes. In some cases, transport can be parameterized with gravity-type models or approximated by a diffusive random walk. As a alternative, we have isolated intranational commercial air traffic as a case study for the utility of non-diffusive, heavy-tailed transport models. We implemented new stochastic simulations of a prototypical influenza-like infection, focusing on the dense, highly-connected United States air travel network. We show that mobility on this network can be described mainly by a power law, in agreement with previous studies. Remarkably, we find that the global evolution of an outbreak on this network is accurately reproduced by a two-parameter space-fractional diffusion equation, such that those parameters are determined by the air travel network.Comment: 26 pages, 4 figure

Hybrid approaches for multiple-species stochastic reaction-diffusion models

Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction-diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. This way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model.Comment: 38 pages, 8 figure

Nonlinear Dynamics

This volume covers a diverse collection of topics dealing with some of the fundamental concepts and applications embodied in the study of nonlinear dynamics. Each of the 15 chapters contained in this compendium generally fit into one of five topical areas: physics applications, nonlinear oscillators, electrical and mechanical systems, biological and behavioral applications or random processes. The authors of these chapters have contributed a stimulating cross section of new results, which provide a fertile spectrum of ideas that will inspire both seasoned researches and students

6th International congress of the Serbian society of mechanics: Review

Ovaj rad prikazuje najvažnije informacije o 6. kongresu Srpskog društva za mehaniku, koji je održan na Tari od 19. do 21. juna 2017. Kongres je organizovan od strane Srpskog društva za mehaniku. Dat je kratak prikaz najznačajnijih radova predstavljenih na ovom kongresu, a koji se bave teorijskom i primenjenom mehanikom.This paper presents the most important information and describes the activities of the 6th Congress of the Serbian Society of Mechanics which was held on mountain Tara, on 19- 21 June, 2017. The Congress was organized by the Serbian Society of Mechanics. Brief summaries of the plenary lectures and some of 99 accepted papers, which admittedly attracted the most interest were shown as well

6th International congress of the Serbian society of mechanics: Review

Ovaj rad prikazuje najvažnije informacije o 6. kongresu Srpskog društva za mehaniku, koji je održan na Tari od 19. do 21. juna 2017. Kongres je organizovan od strane Srpskog društva za mehaniku. Dat je kratak prikaz najznačajnijih radova predstavljenih na ovom kongresu, a koji se bave teorijskom i primenjenom mehanikom.This paper presents the most important information and describes the activities of the 6th Congress of the Serbian Society of Mechanics which was held on mountain Tara, on 19- 21 June, 2017. The Congress was organized by the Serbian Society of Mechanics. Brief summaries of the plenary lectures and some of 99 accepted papers, which admittedly attracted the most interest were shown as well