Related papers: Chaos in a spatial epidemic model
The spectral properties of interacting strongly chaotic systems are investigated for growing interaction strength. A very sensitive transition from Poisson statistics to that of random matrix theory is found. We introduce a new random…
By analysing an n-dimensional generalisation of Thomas's cyclically symmetric attractor we find that this chaotic dynamical system behaves like a random walk constrained onto the surface of a hypersphere. The growth of error is limited,…
In this survey we report some recent results in the mathematical modeling of epidemic phenomena through the use of kinetic equations. We initially consider models of interaction between agents in which social characteristics play a key role…
I study the spreading of infectious diseases on heterogeneous populations. I represent the population structure by a contact-graph where vertices represent agents and edges represent disease transmission channels among them. The population…
Chaos is widely understood as being a consequence of sensitive dependence upon initial conditions. This is the result of an instability in phase space, which separates trajectories exponentially. Here, we demonstrate that this criterion…
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…
When an epidemic spreads into a population, it is often unpractical or impossible to have a continuous monitoring of all subjects involved. As an alternative, algorithmic solutions can be used to infer the state of the whole population from…
We characterize the macroscopic attractor of infinite populations of noisy maps subjected to global and strong coupling by using an expansion in order parameters. We show that for any noise amplitude there exists a large region of strong…
We demonstrate the presence of chaos in stochastic simulations that are widely used to study biodiversity in nature. The investigation deals with a set of three distinct species that evolve according to the standard rules of mobility,…
We consider a spatial model related to bond percolation for the spread of a disease that includes variation in the susceptibility to infection. We work on a lattice with random bond strengths and show that with strong disorder, i.e. a wide…
We analyze energy spreading for a system that features mixed chaotic phase-space, whose control parameters (or slow degrees of freedom) vary quasi-statically. For demonstration purpose we consider the restricted 3~body problem, where the…
The spreading of evolutionary novelties across populations is the central element of adaptation. Unless population are well-mixed (like bacteria in a shaken test tube), the spreading dynamics not only depends on fitness differences but also…
The relevance of chaos to evolution is discussed in the context of the origin and maintenance of diversity and complexity. Evolution to the edge of chaos is demonstrated in an imitation game. As an origin of diversity, dynamic clustering of…
We establish sharp rates for propagation of chaos in R\'enyi divergences for interacting diffusion systems at stationarity. Building upon the entropic hierarchy established in Lacker (2023), we show that under strong isoperimetry and weak…
Propagation of initially localized perturbations is investigated in chaotic coupled map lattices with long-range couplings decaying as a power of the distance. The initial perturbation propagates exponentially fast along the lattice, with a…
In this paper, we study the interplay between individual behaviors and epidemic spreading in a dynamical network. We distribute agents on a square-shaped region with periodic boundary conditions. Every agent is regarded as a node of the…
In this paper we study long-term evolution of a finite system of locally interacting birth-and-death processes labelled by vertices of a finite connected graph. A detailed description of the asymptotic behaviour is obtained in the case of…
Arrhythmias are potentially fatal disruptions to the normal heart rhythm, but their underlying dynamics is still poorly understood. Theoretical modeling is an important tool to fill this gap. Typical studies often employ detailed…
Many real world networks are characterized by adaptive changes in their topology depending on the dynamic state of their nodes. Here we study epidemic dynamics in an adaptive network, where susceptibles are able to avoid contact with…
We continue the investigations of an ecosystem where a epidemic-affected population can move between two connected patches, by considering what happens to the system when the migration paths are interrupted in one direction, or when the…