37 research outputs found
Invited review: Epidemics on social networks
Since its first formulations almost a century ago, mathematical models for
disease spreading contributed to understand, evaluate and control the epidemic
processes.They promoted a dramatic change in how epidemiologists thought of the
propagation of infectious diseases.In the last decade, when the traditional
epidemiological models seemed to be exhausted, new types of models were
developed.These new models incorporated concepts from graph theory to describe
and model the underlying social structure.Many of these works merely produced a
more detailed extension of the previous results, but some others triggered a
completely new paradigm in the mathematical study of epidemic processes. In
this review, we will introduce the basic concepts of epidemiology, epidemic
modeling and networks, to finally provide a brief description of the most
relevant results in the field.Comment: 17 pages, 13 figure
Associative memory on a small-world neural network
We study a model of associative memory based on a neural network with
small-world structure. The efficacy of the network to retrieve one of the
stored patterns exhibits a phase transition at a finite value of the disorder.
The more ordered networks are unable to recover the patterns, and are always
attracted to mixture states. Besides, for a range of the number of stored
patterns, the efficacy has a maximum at an intermediate value of the disorder.
We also give a statistical characterization of the attractors for all values of
the disorder of the network.Comment: 5 pages, 4 figures (eps
A random walk model to study the cycles emerging from the exploration-exploitation trade-off
We present a model for a random walk with memory, phenomenologically inspired
in a biological system. The walker has the capacity to remember the time of the
last visit to each site and the step taken from there. This memory affects the
behavior of the walker each time it reaches an already visited site modulating
the probability of repeating previous moves. This probability increases with
the time elapsed from the last visit. A biological analog of the walker is a
frugivore, with the lattice sites representing plants. The memory effect can be
associated with the time needed by plants to recover its fruit load. We propose
two different strategies, conservative and explorative, as well as intermediate
cases, leading to non intuitive interesting results, such as the emergence of
cycles.Comment: To appear in Phys. Rev.
Non-local interaction effects in models of interacting populations
We consider a couple of models for the dynamics of the populations of two
interacting species, inspired by Lotka-Volterra's classical equations. The
novelty of this work is that the interaction terms are non local and the
interaction occurs within a bounded range. These terms include the competitive
intraspecific interaction among individuals and the interspecific terms for
which we consider two cases: Competition and predation. The results show that
not only the non-locality induces spatial structures but also allows for the
survival of the species when due to predation or the competitive exclusion
extinction was expected, and even promotes spatio-temporal patterns not linked
to eventual temporal oscillations in the local case. In this work we also
explore some interesting details about the behavior of the population dynamics
that shows spatial patterns that interfere in a way that leads to non-trivial
results
Space use by foragers consuming renewable resources
We study a simple model of a forager as a walk that modifies a relaxing
substrate. Within it simplicity, this provides an insight on a number of
relevant and non-intuitive facts. Even without memory of the good places to
feed and no explicit cost of moving, we observe the emergence of a finite home
range. We characterize the walks and the use of resources in several
statistical ways, involving the behavior of the average used fraction of the
system, the length of the cycles followed by the walkers, and the frequency of
visits to plants. Preliminary results on population effects are explored by
means of a system of two non directly interacting animals. Properties of the
overlap of home ranges show the existence of a set of parameters that provides
the best utilization of the shared resource
Small world effect in an epidemiological model
A model for the spread of an infection is analyzed for different population
structures. The interactions within the population are described by small world
networks, ranging from ordered lattices to random graphs. For the more ordered
systems, there is a fluctuating endemic state of low infection. At a finite
value of the disorder of the network, we find a transition to self-sustained
oscillations in the size of the infected subpopulation