Related papers: Fractional epidemics from quantum loops

Pattern-forming nonequilibrium systems are ubiquitous in nature, from driven quantum matter and biological life forms to atmospheric and interstellar gases. Identifying universal aspects of their far-from-equilibrium dynamics and statistics…

We propose an extension of the classical susceptible infectious recovered (SIR) model that incorporates the effects of spatial propagation of an epidemic through a small number of additional compartments. The model is designed to capture…

We explore whether quantum field theory can be understood as the statistical mechanics of a time-reversal-invariant stochastic generalization of Hamiltonian dynamics. The motivation for this project, started with this paper, is to assign…

Fractional models and their parameters are sensitive to changes in the intrinsic micro-structures of anomalous materials. We investigate how such physics-informed models propagate the evolving anomalous rheology to the nonlinear dynamics of…

We analyze the dynamics of a population of independent random walkers on a graph and develop a simple model of epidemic spreading. We assume that each walker visits independently the nodes of a finite ergodic graph in a discrete-time…

Fractional calculus allows one to generalize the linear, one-dimensional, diffusion equation by replacing either the first time derivative or the second space derivative by a derivative of fractional order. The fundamental solutions of…

We discuss dual time evolution scenarios which, albeit running according to the same real time clock, in each considered case may be mapped among each other by means of an analytic continuation in time. This dynamical duality is a generic…

Epidemic models often reflect characteristic features of infectious spreading processes by coupled non-linear differential equations considering different states of health (such as Susceptible, Infected, or Recovered). This compartmental…

The motion of contaminant particles through complex environments such as fractured rocks or porous sediments is often characterized by anomalous diffusion: the spread of the transported quantity is found to grow sublinearly in time due to…

It is well recognized that population heterogeneity plays an important role in the spread of epidemics. While individual variations in social activity are often assumed to be persistent, i.e. constant in time, here we discuss the…

Seasonal variation in environmental variables, and in rates of contact among individuals, are fundamental drivers of infectious disease dynamics. Unlike most periodically-forced physical systems, for which the precise pattern of forcing is…

Motivated by the modeling of three-dimensional fluid turbulence, we define and study a class of stochastic partial differential equations (SPDEs) that are randomly stirred by a spatially smooth and uncorrelated in time forcing term. To…

We present a modified diffusive epidemic process that has a finite threshold on scale-free graphs. The diffusive epidemic process describes the epidemic spreading in a non-sedentary population, and it is a reaction-diffusion process. In the…

Despite the advanced stage of epidemic modeling, there is a major demand for methods to incorporate behavioral responses to the spread of a disease such as social distancing and adoption of prevention methods. Mobility plays an important…

Infectious diseases are caused by pathogenic microorganisms and can spread through different ways. Mathematical models and computational simulation have been used extensively to investigate the transmission and spread of infectious…

Contemporary epidemiological models often involve spatial variation, providing an avenue to investigate the averaged dynamics of individual movements. In this work, we extend a recent model by Vaziry, Kolokolnikov, and Kevrekidis [Royal…

The generalized diffusion equations with fractional order derivatives have shown be quite efficient to describe the diffusion in complex systems, with the advantage of producing exact expressions for the underlying diffusive properties.…

Wave-like spatial statistics in walking-droplet quantum analogs are typically attributed to spatial or temporal nonlocal wave effects. We show instead that such behavior arises generically from the low-dimensional nonlinear dynamics of an…

We present a generic epidemic model with stochastic parameters, in which the dynamics self-organize to a critical state with suppressed exponential growth. More precisely, the dynamics evolve into a quasi-steady-state, where the effective…

Anomalous transport in a tilted periodic potential is investigated numerically within the framework of the fractional Fokker-Planck dynamics via the underlying CTRW. An efficient numerical algorithm is developed which is applicable for an…